%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP039^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:04 AM UTC 2026
% Result : Theorem 1.83s 0.61s
% Output : Refutation 1.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP039^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n013.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:39:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.24/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.46 % (2559929)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.46 % (2559934)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2367230700:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.46 % (2559938)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3290461929:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.46 % (2559936)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2597144573:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.46 % (2559935)lrs+10_16_si=on:nwc=1.5:random_seed=3495567362:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.46 % (2559937)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3327688562:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.30/0.46 % (2559936)Instruction limit reached!
% 0.30/0.46 % (2559936)------------------------------
% 0.30/0.46 % (2559936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (2559936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (2559936)CaDiCaL version: 2.1.3
% 0.30/0.46 % (2559936)Termination reason: Instruction limit
% 0.30/0.46 % (2559936)Termination phase: shuffling
% 0.30/0.46 % (2559936)Time elapsed: 0.003 s
% 0.30/0.46 % (2559936)Peak memory usage: 10 MB
% 0.30/0.46 % (2559936)Instructions burned: 4 (million)
% 0.30/0.46 % (2559940)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.46 % (2559940)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.30/0.46 % (2559939)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2082765618:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.46 % (2559940)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1752054251:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.46 % (2559935)Instruction limit reached!
% 0.30/0.46 % (2559935)------------------------------
% 0.30/0.46 % (2559935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (2559935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (2559935)CaDiCaL version: 2.1.3
% 0.30/0.46 % (2559935)Termination reason: Instruction limit
% 0.30/0.46 % (2559935)Termination phase: shuffling
% 0.30/0.46 % (2559935)Time elapsed: 0.010 s
% 0.30/0.46 % (2559935)Peak memory usage: 10 MB
% 0.30/0.46 % (2559935)Instructions burned: 19 (million)
% 0.30/0.46 % (2559938)Instruction limit reached!
% 0.30/0.46 % (2559938)------------------------------
% 0.30/0.46 % (2559938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (2559938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (2559938)CaDiCaL version: 2.1.3
% 0.30/0.46 % (2559938)Termination reason: Instruction limit
% 0.30/0.46 % (2559938)Termination phase: shuffling
% 0.30/0.46 % (2559938)Time elapsed: 0.012 s
% 0.30/0.46 % (2559938)Peak memory usage: 10 MB
% 0.30/0.46 % (2559938)Instructions burned: 24 (million)
% 0.30/0.46 % (2559934)Instruction limit reached!
% 0.30/0.46 % (2559934)------------------------------
% 0.30/0.46 % (2559934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (2559934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (2559934)CaDiCaL version: 2.1.3
% 0.30/0.46 % (2559934)Termination reason: Instruction limit
% 0.30/0.46 % (2559934)Termination phase: Preprocessing 3
% 0.30/0.46 % (2559934)Time elapsed: 0.025 s
% 0.30/0.46 % (2559934)Peak memory usage: 12 MB
% 0.30/0.46 % (2559934)Instructions burned: 90 (million)
% 0.30/0.46 % (2559946)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3527602801:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.46 % (2559946)Instruction limit reached!
% 0.30/0.46 % (2559946)------------------------------
% 0.30/0.46 % (2559946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.51 % (2559946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.51 % (2559946)CaDiCaL version: 2.1.3
% 1.07/0.51 % (2559946)Termination reason: Instruction limit
% 1.07/0.51 % (2559946)Termination phase: shuffling
% 1.07/0.51 % (2559946)Time elapsed: 0.002 s
% 1.07/0.51 % (2559946)Peak memory usage: 10 MB
% 1.07/0.51 % (2559946)Instructions burned: 2 (million)
% 1.07/0.51 % (2559950)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.07/0.51 % (2559951)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3917485296:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.07/0.51 % (2559949)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3148155368:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.07/0.51 % (2559950)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1582287992:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.07/0.51 % (2559951)Instruction limit reached!
% 1.07/0.51 % (2559951)------------------------------
% 1.07/0.51 % (2559951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.51 % (2559951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.51 % (2559951)CaDiCaL version: 2.1.3
% 1.07/0.51 % (2559951)Termination reason: Instruction limit
% 1.07/0.51 % (2559951)Termination phase: shuffling
% 1.07/0.51 % (2559951)Time elapsed: 0.003 s
% 1.07/0.51 % (2559951)Peak memory usage: 11 MB
% 1.07/0.51 % (2559951)Instructions burned: 12 (million)
% 1.07/0.51 % (2559949)Instruction limit reached!
% 1.07/0.51 % (2559949)------------------------------
% 1.07/0.51 % (2559949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.51 % (2559949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.51 % (2559949)CaDiCaL version: 2.1.3
% 1.07/0.51 % (2559949)Termination reason: Instruction limit
% 1.07/0.51 % (2559949)Termination phase: shuffling
% 1.07/0.51 % (2559949)Time elapsed: 0.003 s
% 1.07/0.51 % (2559949)Peak memory usage: 10 MB
% 1.07/0.51 % (2559949)Instructions burned: 5 (million)
% 1.07/0.51 % (2559950)Instruction limit reached!
% 1.07/0.51 % (2559950)------------------------------
% 1.07/0.51 % (2559950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.51 % (2559950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.51 % (2559950)CaDiCaL version: 2.1.3
% 1.07/0.51 % (2559950)Termination reason: Instruction limit
% 1.07/0.51 % (2559950)Termination phase: shuffling
% 1.07/0.51 % (2559950)Time elapsed: 0.007 s
% 1.07/0.51 % (2559950)Peak memory usage: 10 MB
% 1.07/0.51 % (2559950)Instructions burned: 14 (million)
% 1.07/0.51 % (2559953)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.07/0.51 % (2559953)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.07/0.51 % (2559957)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2261646751:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.07/0.51 % (2559953)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=569696260:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.07/0.51 % (2559939)Instruction limit reached!
% 1.07/0.51 % (2559939)------------------------------
% 1.07/0.51 % (2559939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.51 % (2559939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.51 % (2559939)CaDiCaL version: 2.1.3
% 1.07/0.51 % (2559939)Termination reason: Instruction limit
% 1.07/0.51 % (2559939)Termination phase: Preprocessing 1
% 1.07/0.51 % (2559939)Time elapsed: 0.038 s
% 1.07/0.51 % (2559939)Peak memory usage: 12 MB
% 1.07/0.51 % (2559939)Instructions burned: 75 (million)
% 1.07/0.51 % (2559958)lrs+10_1_si=on:cs=on:random_seed=4241838490:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.07/0.51 % (2559959)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.07/0.54 % (2559959)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3049128262:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.07/0.54 % (2559958)Instruction limit reached!
% 1.07/0.54 % (2559958)------------------------------
% 1.07/0.54 % (2559958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.54 % (2559958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.54 % (2559958)CaDiCaL version: 2.1.3
% 1.07/0.54 % (2559953)Instruction limit reached!
% 1.07/0.54 % (2559953)------------------------------
% 1.07/0.54 % (2559953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.54 % (2559958)Termination reason: Instruction limit
% 1.07/0.54 % (2559958)Termination phase: shuffling
% 1.07/0.54 % (2559953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.54 % (2559958)Time elapsed: 0.006 s
% 1.07/0.54 % (2559953)CaDiCaL version: 2.1.3
% 1.07/0.54 % (2559953)Termination reason: Instruction limit
% 1.07/0.54 % (2559953)Termination phase: shuffling
% 1.07/0.54 % (2559953)Time elapsed: 0.014 s
% 1.07/0.54 % (2559953)Peak memory usage: 11 MB
% 1.07/0.54 % (2559958)Peak memory usage: 10 MB
% 1.07/0.54 % (2559953)Instructions burned: 30 (million)
% 1.07/0.54 % (2559958)Instructions burned: 9 (million)
% 1.07/0.54 % (2559959)Instruction limit reached!
% 1.07/0.54 % (2559959)------------------------------
% 1.07/0.54 % (2559959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.54 % (2559959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.54 % (2559959)CaDiCaL version: 2.1.3
% 1.07/0.54 % (2559959)Termination reason: Instruction limit
% 1.07/0.54 % (2559959)Termination phase: shuffling
% 1.07/0.54 % (2559959)Time elapsed: 0.002 s
% 1.07/0.54 % (2559959)Peak memory usage: 10 MB
% 1.07/0.54 % (2559959)Instructions burned: 3 (million)
% 1.07/0.54 % (2559957)Instruction limit reached!
% 1.07/0.54 % (2559957)------------------------------
% 1.07/0.54 % (2559957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.54 % (2559957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.54 % (2559957)CaDiCaL version: 2.1.3
% 1.07/0.54 % (2559957)Termination reason: Instruction limit
% 1.07/0.54 % (2559957)Termination phase: Property scanning
% 1.07/0.54 % (2559957)Time elapsed: 0.022 s
% 1.07/0.54 % (2559957)Peak memory usage: 12 MB
% 1.07/0.54 % (2559957)Instructions burned: 86 (million)
% 1.07/0.54 % (2559962)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=542272234:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.07/0.54 % (2559968)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1946460348:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.07/0.54 % (2559966)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2700995289:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.07/0.54 % (2559967)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1678242016:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.07/0.54 % (2559965)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2785730246:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.07/0.54 % (2559967)Instruction limit reached!
% 1.07/0.54 % (2559967)------------------------------
% 1.07/0.54 % (2559967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.54 % (2559967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.54 % (2559967)CaDiCaL version: 2.1.3
% 1.07/0.54 % (2559967)Termination reason: Instruction limit
% 1.07/0.54 % (2559967)Termination phase: shuffling
% 1.07/0.54 % (2559967)Time elapsed: 0.008 s
% 1.07/0.54 % (2559967)Peak memory usage: 11 MB
% 1.07/0.54 % (2559967)Instructions burned: 15 (million)
% 1.07/0.54 % (2559962)Instruction limit reached!
% 1.07/0.54 % (2559962)------------------------------
% 1.07/0.54 % (2559962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.54 % (2559962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (2559962)CaDiCaL version: 2.1.3
% 1.07/0.58 % (2559962)Termination reason: Instruction limit
% 1.07/0.58 % (2559962)Termination phase: shuffling
% 1.07/0.58 % (2559962)Time elapsed: 0.019 s
% 1.07/0.58 % (2559962)Peak memory usage: 11 MB
% 1.07/0.58 % (2559962)Instructions burned: 38 (million)
% 1.07/0.58 % (2559966)Instruction limit reached!
% 1.07/0.58 % (2559966)------------------------------
% 1.07/0.58 % (2559966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (2559966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (2559966)CaDiCaL version: 2.1.3
% 1.07/0.58 % (2559966)Termination reason: Instruction limit
% 1.07/0.58 % (2559966)Termination phase: shuffling
% 1.07/0.58 % (2559966)Time elapsed: 0.013 s
% 1.07/0.58 % (2559966)Peak memory usage: 11 MB
% 1.07/0.58 % (2559966)Instructions burned: 25 (million)
% 1.07/0.58 % (2559940)Instruction limit reached!
% 1.07/0.58 % (2559940)------------------------------
% 1.07/0.58 % (2559940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (2559940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (2559940)CaDiCaL version: 2.1.3
% 1.07/0.58 % (2559940)Termination reason: Instruction limit
% 1.07/0.58 % (2559940)Termination phase: Saturation
% 1.07/0.58 % (2559940)Time elapsed: 0.096 s
% 1.07/0.58 % (2559940)Peak memory usage: 14 MB
% 1.07/0.58 % (2559940)Instructions burned: 158 (million)
% 1.07/0.58 % (2559976)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2164187743:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.07/0.58 % (2559974)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=393105808:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.07/0.58 % (2559975)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=600270903:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.07/0.58 % (2559975)Instruction limit reached!
% 1.07/0.58 % (2559975)------------------------------
% 1.07/0.58 % (2559975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (2559975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (2559975)CaDiCaL version: 2.1.3
% 1.07/0.58 % (2559975)Termination reason: Instruction limit
% 1.07/0.58 % (2559975)Termination phase: shuffling
% 1.07/0.58 % (2559975)Time elapsed: 0.002 s
% 1.07/0.58 % (2559975)Peak memory usage: 10 MB
% 1.07/0.58 % (2559975)Instructions burned: 3 (million)
% 1.07/0.58 % (2559974)Instruction limit reached!
% 1.07/0.58 % (2559974)------------------------------
% 1.07/0.58 % (2559974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (2559974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (2559974)CaDiCaL version: 2.1.3
% 1.07/0.58 % (2559974)Termination reason: Instruction limit
% 1.07/0.58 % (2559974)Termination phase: shuffling
% 1.07/0.58 % (2559974)Time elapsed: 0.007 s
% 1.07/0.58 % (2559974)Peak memory usage: 11 MB
% 1.07/0.58 % (2559974)Instructions burned: 14 (million)
% 1.07/0.58 % (2559979)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=589886053:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.07/0.58 % (2559976)Instruction limit reached!
% 1.07/0.58 % (2559976)------------------------------
% 1.07/0.58 % (2559976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (2559976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (2559976)CaDiCaL version: 2.1.3
% 1.07/0.58 % (2559976)Termination reason: Instruction limit
% 1.07/0.58 % (2559976)Termination phase: shuffling
% 1.07/0.58 % (2559976)Time elapsed: 0.014 s
% 1.07/0.58 % (2559976)Peak memory usage: 11 MB
% 1.07/0.58 % (2559976)Instructions burned: 26 (million)
% 1.07/0.58 % (2559987)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3886694669:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.07/0.58 % (2559990)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.07/0.58 % (2559990)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.83/0.61 % (2559979)Instruction limit reached!
% 1.83/0.61 % (2559979)------------------------------
% 1.83/0.61 % (2559979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2559979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2559979)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2559979)Termination reason: Instruction limit
% 1.83/0.61 % (2559979)Termination phase: shuffling
% 1.83/0.61 % (2559979)Time elapsed: 0.012 s
% 1.83/0.61 % (2559979)Peak memory usage: 10 MB
% 1.83/0.61 % (2559979)Instructions burned: 24 (million)
% 1.83/0.61 % (2559990)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2565437703:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.83/0.61 % (2559993)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.83/0.61 % (2559993)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3984765990:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.83/0.61 % (2559990)Instruction limit reached!
% 1.83/0.61 % (2559990)------------------------------
% 1.83/0.61 % (2559990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2559990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2559990)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2559990)Termination reason: Instruction limit
% 1.83/0.61 % (2559990)Termination phase: shuffling
% 1.83/0.61 % (2559990)Time elapsed: 0.007 s
% 1.83/0.61 % (2559990)Peak memory usage: 10 MB
% 1.83/0.61 % (2559990)Instructions burned: 14 (million)
% 1.83/0.61 % (2559993)Instruction limit reached!
% 1.83/0.61 % (2559993)------------------------------
% 1.83/0.61 % (2559993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2559993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2559993)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2559993)Termination reason: Instruction limit
% 1.83/0.61 % (2559993)Termination phase: shuffling
% 1.83/0.61 % (2559993)Time elapsed: 0.005 s
% 1.83/0.61 % (2559993)Peak memory usage: 10 MB
% 1.83/0.61 % (2559993)Instructions burned: 9 (million)
% 1.83/0.61 % (2560000)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2055620834:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.83/0.61 % (2559987)Instruction limit reached!
% 1.83/0.61 % (2559987)------------------------------
% 1.83/0.61 % (2559987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2559987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2559987)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2559987)Termination reason: Instruction limit
% 1.83/0.61 % (2559987)Termination phase: Property scanning
% 1.83/0.61 % (2559987)Time elapsed: 0.028 s
% 1.83/0.61 % (2559987)Peak memory usage: 11 MB
% 1.83/0.61 % (2559987)Instructions burned: 60 (million)
% 1.83/0.61 % (2559968)Instruction limit reached!
% 1.83/0.61 % (2559968)------------------------------
% 1.83/0.61 % (2559968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2559968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2559968)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2559968)Termination reason: Instruction limit
% 1.83/0.61 % (2559968)Termination phase: Saturation
% 1.83/0.61 % (2559968)Time elapsed: 0.088 s
% 1.83/0.61 % (2559968)Peak memory usage: 16 MB
% 1.83/0.61 % (2559968)Instructions burned: 329 (million)
% 1.83/0.61 % (2560004)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1576187710:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.83/0.61 % (2560006)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1820147946:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.83/0.61 % (2560004)Instruction limit reached!
% 1.83/0.61 % (2560004)------------------------------
% 1.83/0.61 % (2560004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2560004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2560004)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2560004)Termination reason: Instruction limit
% 1.83/0.61 % (2560004)Termination phase: shuffling
% 1.83/0.61 % (2560004)Time elapsed: 0.004 s
% 1.83/0.61 % (2560004)Peak memory usage: 10 MB
% 1.83/0.61 % (2560004)Instructions burned: 7 (million)
% 1.83/0.61 % (2560000)Instruction limit reached!
% 1.83/0.61 % (2560000)------------------------------
% 1.83/0.61 % (2560000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2560000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2560000)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2560000)Termination reason: Instruction limit
% 1.83/0.61 % (2560000)Termination phase: shuffling
% 1.83/0.61 % (2560000)Time elapsed: 0.016 s
% 1.83/0.61 % (2560000)Peak memory usage: 11 MB
% 1.83/0.61 % (2560000)Instructions burned: 33 (million)
% 1.83/0.61 % (2560012)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=288546880:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.83/0.61 % (2560012)Instruction limit reached!
% 1.83/0.61 % (2560012)------------------------------
% 1.83/0.61 % (2560012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2560012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2560012)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2560012)Termination reason: Instruction limit
% 1.83/0.61 % (2560012)Termination phase: shuffling
% 1.83/0.61 % (2560012)Time elapsed: 0.005 s
% 1.83/0.61 % (2560012)Peak memory usage: 10 MB
% 1.83/0.61 % (2560012)Instructions burned: 21 (million)
% 1.83/0.61 % (2560006)Instruction limit reached!
% 1.83/0.61 % (2560006)------------------------------
% 1.83/0.61 % (2560006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2560006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2560006)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2560006)Termination reason: Instruction limit
% 1.83/0.61 % (2560006)Termination phase: shuffling
% 1.83/0.61 % (2560006)Time elapsed: 0.011 s
% 1.83/0.61 % (2560006)Peak memory usage: 11 MB
% 1.83/0.61 % (2560006)Instructions burned: 23 (million)
% 1.83/0.61 % (2560013)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1103655025:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.83/0.61 % (2560024)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1856001401:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.83/0.61 % (2560017)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=776152365:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.83/0.61 % (2560018)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2634285938:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.83/0.61 % (2560025)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.83/0.61 % (2560025)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=143333111:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.83/0.61 % (2560024)Instruction limit reached!
% 1.83/0.61 % (2560024)------------------------------
% 1.83/0.61 % (2560024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2560024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2560024)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2560024)Termination reason: Instruction limit
% 1.83/0.61 % (2560024)Termination phase: shuffling
% 1.83/0.61 % (2560024)Time elapsed: 0.011 s
% 1.83/0.61 % (2560024)Peak memory usage: 11 MB
% 1.83/0.61 % (2560024)Instructions burned: 42 (million)
% 1.83/0.61 % (2559965)Instruction limit reached!
% 1.83/0.61 % (2559965)------------------------------
% 1.83/0.61 % (2559965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2559965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2559965)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2559965)Termination reason: Instruction limit
% 1.83/0.61 % (2559965)Termination phase: Saturation
% 1.83/0.61 % (2559965)Time elapsed: 0.124 s
% 1.83/0.61 % (2559965)Peak memory usage: 16 MB
% 1.83/0.61 % (2559965)Instructions burned: 250 (million)
% 1.83/0.61 % (2560025)Instruction limit reached!
% 1.83/0.61 % (2560025)------------------------------
% 1.83/0.61 % (2560025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2560025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2560025)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2560025)Termination reason: Instruction limit
% 1.83/0.61 % (2560025)Termination phase: shuffling
% 1.83/0.61 % (2560025)Time elapsed: 0.005 s
% 1.83/0.61 % (2560025)Peak memory usage: 10 MB
% 1.83/0.61 % (2560025)Instructions burned: 9 (million)
% 1.83/0.61 % (2560040)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3225319216:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.83/0.61 % (2560044)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.83/0.61 % (2559937) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2559929-2559937"...
% 1.83/0.61 % (2560043)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=4077173909:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.83/0.61 % (2560044)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1734128924:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.83/0.61 % (2560044)Instruction limit reached!
% 1.83/0.61 % (2560044)------------------------------
% 1.83/0.61 % (2560044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2560044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2560044)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2560044)Termination reason: Instruction limit
% 1.83/0.61 % (2560044)Termination phase: shuffling
% 1.83/0.61 % (2560044)Time elapsed: 0.004 s
% 1.83/0.61 % (2560044)Peak memory usage: 10 MB
% 1.83/0.61 % (2560044)Instructions burned: 7 (million)
% 1.83/0.61 % (2559937)...printing done.
% 1.83/0.61 % (2559937)Refutation found. Thanks to Tanya!
% 1.83/0.61 % SZS status Theorem for theBenchmark
% 1.83/0.61 % SZS output start Proof for theBenchmark
% 1.83/0.61 thf(type_def_5, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 1.83/0.61 thf(type_def_6, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 1.83/0.61 thf(type_def_7, type, frechet_strm: ($tType * $tType) > $tType).
% 1.83/0.61 thf(type_def_8, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 1.83/0.61 thf(type_def_9, type, product_unit: $tType).
% 1.83/0.61 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 1.83/0.61 thf(type_def_11, type, formula: ($tType * $tType * $tType) > $tType).
% 1.83/0.61 thf(type_def_12, type, sum_sum: ($tType * $tType) > $tType).
% 1.83/0.61 thf(type_def_13, type, trm: ($tType * $tType) > $tType).
% 1.83/0.61 thf(type_def_14, type, real: $tType).
% 1.83/0.61 thf(type_def_15, type, list: $tType > $tType).
% 1.83/0.61 thf(type_def_16, type, set: $tType > $tType).
% 1.83/0.61 thf(type_def_17, type, sz: $tType).
% 1.83/0.61 thf(type_def_18, type, sf: $tType).
% 1.83/0.61 thf(type_def_19, type, sc: $tType).
% 1.83/0.61 thf(type_def_20, type, c: $tType).
% 1.83/0.61 thf(type_def_21, type, b: $tType).
% 1.83/0.61 thf(type_def_22, type, a: $tType).
% 1.83/0.61 thf(type_def_23, type, sTfun: ($tType * $tType) > $tType).
% 1.83/0.61 thf(func_def_0, type, cARD_1: !>[X0: $tType]:($o)).
% 1.83/0.61 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 1.83/0.61 thf(func_def_2, type, top: !>[X0: $tType]:($o)).
% 1.83/0.61 thf(func_def_3, type, finite_finite: !>[X0: $tType]:($o)).
% 1.83/0.61 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 1.83/0.61 thf(func_def_5, type, euclid1678468529ng_gcd: !>[X0: $tType]:($o)).
% 1.83/0.61 thf(func_def_6, type, euclid1155270486miring: !>[X0: $tType]:($o)).
% 1.83/0.61 thf(func_def_7, type, bNF_rel_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1 > $o) > (X2 > X3 > $o) > (X0 > X2) > (X1 > X3) > $o))).
% 1.83/0.61 thf(func_def_8, type, coinci1993344360de_fml: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > $o))).
% 1.83/0.61 thf(func_def_9, type, denotational_Iagree: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2 > $o))).
% 1.83/0.61 thf(func_def_10, type, denotational_Vagree: !>[X0: $tType]:((product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > set @ sum_sum @ X0 @ X0 > $o))).
% 1.83/0.61 thf(func_def_11, type, denotational_fml_sem: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > formula @ X0 @ X1 @ X2 > set @ product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 1.83/0.61 thf(func_def_12, type, denotational_valid: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > $o))).
% 1.83/0.61 thf(func_def_13, type, denota2077489681interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 1.83/0.61 thf(func_def_14, type, freche457001096interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > frechet_good_interp @ X0 @ X1 @ X2 > $o))).
% 1.83/0.61 thf(func_def_15, type, frechet_cr_strm: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > frechet_strm @ X0 @ X1 > $o))).
% 1.83/0.61 thf(func_def_16, type, freche227871258interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > frechet_good_interp @ X0 @ X1 @ X2))).
% 1.83/0.61 thf(func_def_17, type, freche229654227interp: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit))).
% 1.83/0.61 thf(func_def_18, type, frechet_raw_term: !>[X0: $tType, X1: $tType]:((frechet_strm @ X0 @ X1 > trm @ X0 @ X1))).
% 1.83/0.61 thf(func_def_19, type, frechet_simple_term: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > frechet_strm @ X0 @ X1))).
% 1.83/0.61 thf(func_def_20, type, fun_rp_inv_image: !>[X0: $tType, X1: $tType]:((product_prod @ set @ product_prod @ X0 @ X0 @ set @ product_prod @ X0 @ X0 > (X1 > X0) > product_prod @ set @ product_prod @ X1 @ X1 @ set @ product_prod @ X1 @ X1))).
% 1.83/0.61 thf(func_def_21, type, ids: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > X0 > X1 > X1 > X1 > X2 > X2 > X2 > X2 > $o))).
% 1.83/0.61 thf(func_def_22, type, top_top: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_23, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 1.83/0.61 thf(func_def_24, type, product_Sigma: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ product_prod @ X0 @ X1))).
% 1.83/0.61 thf(func_def_25, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1))).
% 1.83/0.61 thf(func_def_26, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 1.83/0.61 thf(func_def_27, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.83/0.61 thf(func_def_28, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 1.83/0.61 thf(func_def_29, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 1.83/0.61 thf(func_def_30, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.83/0.61 thf(func_def_31, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.83/0.61 thf(func_def_32, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.83/0.61 thf(func_def_33, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 1.83/0.61 thf(func_def_34, type, product_product: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ product_prod @ X0 @ X1))).
% 1.83/0.61 thf(func_def_35, type, domainp: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0 > $o))).
% 1.83/0.61 thf(func_def_36, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 1.83/0.61 thf(func_def_37, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.83/0.61 thf(func_def_38, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 1.83/0.61 thf(func_def_39, type, static_FVF: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > set @ sum_sum @ X2 @ X2))).
% 1.83/0.61 thf(func_def_40, type, static_SIGF: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2))).
% 1.83/0.61 thf(func_def_41, type, equiv: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2))).
% 1.83/0.61 thf(func_def_42, type, implies: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2))).
% 1.83/0.61 thf(func_def_43, type, predicational: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > formula @ X1 @ X0 @ X2))).
% 1.83/0.61 thf(func_def_44, type, dfree: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > $o))).
% 1.83/0.61 thf(func_def_45, type, p: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > formula @ X1 @ X0 @ X2))).
% 1.83/0.61 thf(func_def_46, type, singleton: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0 > X0 > trm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_47, type, left_unique: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > $o))).
% 1.83/0.61 thf(func_def_48, type, right_unique: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > $o))).
% 1.83/0.61 thf(func_def_49, type, type_definition: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > set @ X1 > $o))).
% 1.83/0.61 thf(func_def_50, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.83/0.61 thf(func_def_51, type, phi: formula @ a @ b @ c).
% 1.83/0.61 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.83/0.61 thf(func_def_56, type, vIMP: ($o > $o > $o)).
% 1.83/0.61 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_59, type, db4: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_60, type, db3: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_61, type, db2: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_62, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.83/0.61 thf(func_def_63, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.83/0.61 thf(func_def_64, type, vAND: ($o > $o > $o)).
% 1.83/0.61 thf(func_def_65, type, vNOT: ($o > $o)).
% 1.83/0.61 thf(func_def_66, type, db6: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_67, type, db5: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_68, type, db9: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_69, type, db8: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_70, type, db7: !>[X0: $tType]:(X0)).
% 1.83/0.61 thf(func_def_71, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit > product_prod @ list @ formula @ X1 @ X0 @ X2 @ list @ formula @ X1 @ X0 @ X2 > $o) > product_prod @ list @ formula @ X1 @ X0 @ X2 @ list @ formula @ X1 @ X0 @ X2))).
% 1.83/0.61 thf(func_def_72, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit > product_prod @ list @ formula @ X1 @ X0 @ X2 @ list @ formula @ X1 @ X0 @ X2 > $o) > denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit))).
% 1.83/0.61 thf(func_def_73, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X1))).
% 1.83/0.61 thf(func_def_74, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X2))).
% 1.83/0.61 thf(func_def_75, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X3))).
% 1.83/0.61 thf(func_def_76, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X0))).
% 1.83/0.61 thf(func_def_77, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2))).
% 1.83/0.61 thf(func_def_78, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1))).
% 1.83/0.61 thf(func_def_79, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > X2 > $o) > X2 > X1))).
% 1.83/0.61 thf(func_def_80, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > X2 > $o) > X2 > X0))).
% 1.83/0.61 thf(func_def_81, type, sK10: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_82, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X0 > (X2 > X0 > X1) > (X2 > X0 > X1) > X2))).
% 1.83/0.61 thf(func_def_83, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X0 > (X2 > X0 > X1) > (X2 > X0 > X1) > X0))).
% 1.83/0.61 thf(func_def_84, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X2 @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0))).
% 1.83/0.61 thf(func_def_85, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X2 @ X0 > denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit))).
% 1.83/0.61 thf(func_def_86, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X2 @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0))).
% 1.83/0.61 thf(func_def_87, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X2 @ X0 > denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit))).
% 1.83/0.61 thf(func_def_88, type, sK17: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.83/0.61 thf(func_def_89, type, sK18: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.83/0.61 thf(func_def_90, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:(((frechet_good_interp @ X1 @ X2 @ X0 > $o) > denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit))).
% 1.83/0.61 thf(func_def_91, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit > $o) > frechet_good_interp @ X1 @ X0 @ X2))).
% 1.83/0.61 thf(func_def_92, type, sK21: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X1 @ X0 @ X0 > trm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_93, type, sK22: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X1 @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_94, type, sK23: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X0 > $o) > X0))).
% 1.83/0.61 thf(func_def_95, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X1 > X2))).
% 1.83/0.61 thf(func_def_96, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X1 > X4))).
% 1.83/0.61 thf(func_def_97, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X1 > X0))).
% 1.83/0.61 thf(func_def_98, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X1 > X1))).
% 1.83/0.61 thf(func_def_99, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X1 > X3))).
% 1.83/0.61 thf(func_def_100, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.83/0.61 thf(func_def_101, type, sK30: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.83/0.61 thf(func_def_102, type, sK31: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.83/0.61 thf(func_def_103, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit @ product_prod @ list @ formula @ X0 @ X2 @ X1 @ list @ formula @ X0 @ X2 @ X1 > product_prod @ list @ formula @ X0 @ X2 @ X1 @ list @ formula @ X0 @ X2 @ X1))).
% 1.83/0.61 thf(func_def_104, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit @ product_prod @ list @ formula @ X0 @ X2 @ X1 @ list @ formula @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit))).
% 1.83/0.61 thf(func_def_105, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > set @ X1 > (X1 > set @ X0) > X1))).
% 1.83/0.61 thf(func_def_106, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X2))).
% 1.83/0.61 thf(func_def_107, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X1))).
% 1.83/0.61 thf(func_def_108, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X3))).
% 1.83/0.61 thf(func_def_109, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X0))).
% 1.83/0.61 thf(func_def_110, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X2))).
% 1.83/0.61 thf(func_def_111, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X4))).
% 1.83/0.61 thf(func_def_112, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X0))).
% 1.83/0.61 thf(func_def_113, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X3))).
% 1.83/0.61 thf(func_def_114, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X1))).
% 1.83/0.61 thf(func_def_115, type, sK44: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 1.83/0.61 thf(func_def_116, type, sK45: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 1.83/0.61 thf(func_def_117, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit > $o) > frechet_good_interp @ X1 @ X2 @ X0))).
% 1.83/0.61 thf(func_def_118, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 1.83/0.61 thf(func_def_119, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X5 > X3))).
% 1.83/0.61 thf(func_def_120, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X5 > X4))).
% 1.83/0.61 thf(func_def_121, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X5 > X1))).
% 1.83/0.61 thf(func_def_122, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X5 > X2))).
% 1.83/0.61 thf(func_def_123, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X5 > X5))).
% 1.83/0.61 thf(func_def_124, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ X5 > X0))).
% 1.83/0.61 thf(func_def_125, type, sK54: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_126, type, sK55: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X1))).
% 1.83/0.61 thf(func_def_127, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X2))).
% 1.83/0.61 thf(func_def_128, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X1))).
% 1.83/0.61 thf(func_def_129, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X0))).
% 1.83/0.61 thf(func_def_130, type, sK59: (product_prod @ denota1663640101rp_ext @ sf @ sc @ sz @ product_unit @ product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz > product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz)).
% 1.83/0.61 thf(func_def_131, type, sK60: (product_prod @ denota1663640101rp_ext @ sf @ sc @ sz @ product_unit @ product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz > denota1663640101rp_ext @ sf @ sc @ sz @ product_unit)).
% 1.83/0.61 thf(func_def_132, type, sK61: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > set @ X1 > X1))).
% 1.83/0.61 thf(func_def_133, type, sK62: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 1.83/0.61 thf(func_def_134, type, sK63: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 1.83/0.61 thf(func_def_135, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > frechet_good_interp @ X2 @ X1 @ X0))).
% 1.83/0.61 thf(func_def_136, type, sK65: !>[X0: $tType, X1: $tType]:(((frechet_strm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_137, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > $o) > (X2 > X0 > X1) > product_prod @ X2 @ X0 > X2))).
% 1.83/0.61 thf(func_def_138, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > $o) > (X2 > X0 > X1) > product_prod @ X2 @ X0 > X0))).
% 1.83/0.61 thf(func_def_139, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1 > $o) > product_prod @ X0 @ X2 > X1 > X2))).
% 1.83/0.61 thf(func_def_140, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1 > $o) > product_prod @ X0 @ X2 > X1 > X0))).
% 1.83/0.61 thf(func_def_141, type, sK70: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_142, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X0 > X2) > (X1 > X2 > $o) > (X1 > X2 > $o) > X1))).
% 1.83/0.61 thf(func_def_143, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X0 > X2) > (X1 > X2 > $o) > (X1 > X2 > $o) > X2))).
% 1.83/0.61 thf(func_def_144, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X5))).
% 1.83/0.61 thf(func_def_145, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X2))).
% 1.83/0.61 thf(func_def_146, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X3))).
% 1.83/0.61 thf(func_def_147, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X6))).
% 1.83/0.61 thf(func_def_148, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X0))).
% 1.83/0.61 thf(func_def_149, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X1))).
% 1.83/0.61 thf(func_def_150, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X4))).
% 1.83/0.61 thf(func_def_151, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X2 @ X0 @ X1 > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 1.83/0.61 thf(func_def_152, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X2 @ X0 @ X1 > denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit))).
% 1.83/0.61 thf(func_def_153, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > set @ X2) > X2 > X0))).
% 1.83/0.61 thf(func_def_154, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > set @ X2) > X2 > X1))).
% 1.83/0.61 thf(func_def_155, type, sK84: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 1.83/0.61 thf(func_def_156, type, sK85: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 1.83/0.61 thf(func_def_157, type, sK86: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X1 > X0) > X1))).
% 1.83/0.61 thf(func_def_158, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ X2 > (X1 > X2 > set @ X0) > X0 > X1))).
% 1.83/0.61 thf(func_def_159, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ X2 > (X1 > X2 > set @ X0) > X0 > X2))).
% 1.83/0.61 thf(func_def_160, type, sK89: !>[X0: $tType, X1: $tType]:((frechet_strm @ X1 @ X0 > trm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_161, type, sK90: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 1.83/0.61 thf(func_def_162, type, sK91: !>[X0: $tType, X1: $tType]:((frechet_strm @ X0 @ X1 > trm @ X0 @ X1))).
% 1.83/0.61 thf(func_def_163, type, sK92: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > X1))).
% 1.83/0.61 thf(func_def_164, type, sK93: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > trm @ X0 @ X1))).
% 1.83/0.61 thf(func_def_165, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType]:(((frechet_good_interp @ X1 @ X2 @ X0 > $o) > denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit))).
% 1.83/0.61 thf(func_def_166, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ X2 > set @ product_prod @ X3 @ X0 > (X0 > X2) > (X3 > X1) > X3))).
% 1.83/0.61 thf(func_def_167, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ X2 > set @ product_prod @ X3 @ X0 > (X0 > X2) > (X3 > X1) > X0))).
% 1.83/0.61 thf(func_def_168, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit))).
% 1.83/0.61 thf(func_def_169, type, sK98: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_170, type, sK99: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_171, type, sK100: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > X0) > set @ X1 > X1))).
% 1.83/0.61 thf(func_def_172, type, sK101: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_173, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0))).
% 1.83/0.61 thf(func_def_174, type, sK103: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1))).
% 1.83/0.61 thf(func_def_175, type, sK104: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > set @ X0 > X0))).
% 1.83/0.61 thf(func_def_176, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit))).
% 1.83/0.61 thf(func_def_177, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit @ X1 > X1))).
% 1.83/0.61 thf(func_def_178, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit @ X1 > denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit))).
% 1.83/0.61 thf(func_def_179, type, sK108: !>[X0: $tType, X1: $tType]:(((frechet_strm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 1.83/0.61 thf(func_def_180, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X2))).
% 1.83/0.61 thf(func_def_181, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X0))).
% 1.83/0.61 thf(func_def_182, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X1))).
% 1.83/0.61 thf(func_def_183, type, sK112: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.83/0.61 thf(func_def_184, type, sK113: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 1.83/0.61 thf(func_def_185, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > $o) > (X1 > X2) > (X0 > X2 > $o) > (X1 > X0) > X0))).
% 1.83/0.61 thf(func_def_186, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > $o) > (X1 > X2) > (X0 > X2 > $o) > (X1 > X0) > X2))).
% 1.83/0.61 thf(func_def_187, type, sK116: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 1.83/0.61 thf(func_def_188, type, sK117: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > set @ X1) > set @ X0 > X0))).
% 1.83/0.61 thf(func_def_189, type, sK118: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > set @ X1) > set @ X0 > X1))).
% 1.83/0.61 thf(func_def_190, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1))).
% 1.83/0.61 thf(func_def_191, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X5))).
% 1.83/0.61 thf(func_def_192, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X3))).
% 1.83/0.61 thf(func_def_193, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2))).
% 1.83/0.61 thf(func_def_194, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X0))).
% 1.83/0.61 thf(func_def_195, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X4))).
% 1.83/0.61 thf(func_def_196, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit > frechet_good_interp @ X2 @ X0 @ X1))).
% 1.83/0.61 thf(func_def_197, type, sK126: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.83/0.61 thf(func_def_198, type, sK127: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 1.83/0.61 thf(func_def_199, type, sK128: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 1.83/0.61 thf(func_def_200, type, sK129: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 1.83/0.61 thf(func_def_201, type, sK130: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 1.83/0.61 thf(func_def_202, type, sK131: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 1.83/0.61 thf(func_def_203, type, sK132: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 1.83/0.61 thf(func_def_204, type, sK133: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 1.83/0.61 thf(func_def_205, type, sK134: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 1.83/0.61 thf(func_def_206, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.83/0.61 thf(func_def_207, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.83/0.61 thf(func_def_208, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.83/0.61 thf(func_def_209, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 1.83/0.61 thf(func_def_210, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 1.83/0.61 thf(func_def_211, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.83/0.61 thf(func_def_212, type, sK141: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 1.83/0.61 thf(func_def_213, type, sK142: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_214, type, sK143: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_215, type, sK144: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_216, type, sK145: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_217, type, sK146: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_218, type, sK147: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 1.83/0.61 thf(func_def_219, type, sK148: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 1.83/0.61 thf(func_def_220, type, sK149: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1))).
% 1.83/0.61 thf(func_def_221, type, sK150: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0))).
% 1.83/0.61 thf(func_def_223, type, sK152: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 1.83/0.61 thf(func_def_224, type, sK153: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 1.83/0.61 thf(func_def_225, type, sK154: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X0 @ X2 > denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit))).
% 1.83/0.61 thf(func_def_226, type, sK155: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X1 @ X0 @ X2 > denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit))).
% 1.83/0.61 thf(f3,axiom,(
% 1.83/0.61 ! [X2 : $tType,X0 : $tType,X1 : $tType] : ((finite_finite @ X1 & finite_finite @ X0 & finite_finite @ X2) => ! [X4 : denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit,X3 : denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit,X5 : set @ sum_sum @ X2 @ sum_sum @ X1 @ X0] : ((denotational_Iagree @ X2 @ X1 @ X0 @ X3 @ X4 @ X5) => (denotational_Iagree @ X2 @ X1 @ X0 @ X4 @ X3 @ X5)))),
% 1.83/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Iagree__comm)).
% 1.83/0.61 thf(f5,axiom,(
% 1.83/0.61 ! [X0 : $tType] : (finite_finite @ X0 => ! [X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X1 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X3 : set @ sum_sum @ X0 @ X0] : ((denotational_Vagree @ X0 @ X1 @ X2 @ X3) => (denotational_Vagree @ X0 @ X2 @ X1 @ X3)))),
% 1.83/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_agree__comm)).
% 1.83/0.61 thf(f279,axiom,(
% 1.83/0.61 finite_finite @ b),
% 1.83/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_4)).
% 1.83/0.61 thf(f280,axiom,(
% 1.83/0.61 finite_finite @ a),
% 1.83/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_5)).
% 1.83/0.61 thf(f281,axiom,(
% 1.83/0.61 finite_finite @ c),
% 1.83/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_6)).
% 1.83/0.61 thf(f282,conjecture,(
% 1.83/0.61 (! [X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X3 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((denotational_Iagree @ a @ b @ c @ X2 @ X3 @ (static_SIGF @ a @ b @ c @ phi)) => ((denotational_Vagree @ c @ X0 @ X1 @ (static_FVF @ a @ b @ c @ phi)) => (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X3 @ phi)))))) = ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X3 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((denotational_Iagree @ a @ b @ c @ X2 @ X3 @ (static_SIGF @ a @ b @ c @ phi)) => ((denotational_Vagree @ c @ X0 @ X1 @ (static_FVF @ a @ b @ c @ phi)) => (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X3 @ phi)))))))),
% 1.83/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.83/0.61 thf(f283,negated_conjecture,(
% 1.83/0.61 ~ (! [X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X3 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((denotational_Iagree @ a @ b @ c @ X2 @ X3 @ (static_SIGF @ a @ b @ c @ phi)) => ((denotational_Vagree @ c @ X0 @ X1 @ (static_FVF @ a @ b @ c @ phi)) => (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X3 @ phi)))))) = ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X3 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((denotational_Iagree @ a @ b @ c @ X2 @ X3 @ (static_SIGF @ a @ b @ c @ phi)) => ((denotational_Vagree @ c @ X0 @ X1 @ (static_FVF @ a @ b @ c @ phi)) => (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X3 @ phi)))))))),
% 1.83/0.61 inference(negated_conjecture,[status(cth)],[f282])).
% 1.83/0.61 thf(f290,plain,(
% 1.83/0.61 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite @ X2 & finite_finite @ X1 & finite_finite @ X0) => ! [X3 : denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit,X4 : denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit,X5 : set @ sum_sum @ X0 @ sum_sum @ X2 @ X1] : ((denotational_Iagree @ X0 @ X2 @ X1 @ X4 @ X3 @ X5) => (denotational_Iagree @ X0 @ X2 @ X1 @ X3 @ X4 @ X5)))),
% 1.83/0.61 inference(rectify,[],[f3])).
% 1.83/0.61 thf(f291,plain,(
% 1.83/0.61 ! [X1 : $tType,X2 : $tType,X0 : $tType] : (((finite_finite @ X2 = $true) & (finite_finite @ X0 = $true) & (finite_finite @ X1 = $true)) => ! [X5 : set @ sum_sum @ X0 @ sum_sum @ X2 @ X1,X4 : denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit,X3 : denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit] : (($true = ((denotational_Iagree @ X0 @ X2 @ X1 @ X4 @ X3 @ X5))) => ($true = ((denotational_Iagree @ X0 @ X2 @ X1 @ X3 @ X4 @ X5)))))),
% 1.83/0.61 inference(fool_elimination,[],[f290])).
% 1.83/0.61 thf(f429,plain,(
% 1.83/0.61 finite_finite @ a),
% 1.83/0.61 inference(rectify,[],[f280])).
% 1.83/0.61 thf(f430,plain,(
% 1.83/0.61 (finite_finite @ a = $true)),
% 1.83/0.61 inference(fool_elimination,[],[f429])).
% 1.83/0.61 thf(f461,plain,(
% 1.83/0.61 ! [X0 : $tType] : (finite_finite @ X0 => ! [X1 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X3 : set @ sum_sum @ X0 @ X0] : ((denotational_Vagree @ X0 @ X2 @ X1 @ X3) => (denotational_Vagree @ X0 @ X1 @ X2 @ X3)))),
% 1.83/0.61 inference(rectify,[],[f5])).
% 1.83/0.61 thf(f462,plain,(
% 1.83/0.61 ! [X0 : $tType] : ((finite_finite @ X0 = $true) => ! [X3 : set @ sum_sum @ X0 @ X0,X1 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0] : ((((denotational_Vagree @ X0 @ X2 @ X1 @ X3)) = $true) => (((denotational_Vagree @ X0 @ X1 @ X2 @ X3)) = $true)))),
% 1.83/0.61 inference(fool_elimination,[],[f461])).
% 1.83/0.61 thf(f579,plain,(
% 1.83/0.61 finite_finite @ b),
% 1.83/0.61 inference(rectify,[],[f279])).
% 1.83/0.61 thf(f580,plain,(
% 1.83/0.61 (finite_finite @ b = $true)),
% 1.83/0.61 inference(fool_elimination,[],[f579])).
% 1.83/0.61 thf(f653,plain,(
% 1.83/0.61 ~ (! [X0 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X3 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((denotational_Iagree @ a @ b @ c @ X0 @ X2 @ (static_SIGF @ a @ b @ c @ phi)) => ((denotational_Vagree @ c @ X3 @ X1 @ (static_FVF @ a @ b @ c @ phi)) => (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X3 @ (denotational_fml_sem @ a @ b @ c @ X0 @ phi)))))) = ! [X4 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X5 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X6 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X7 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((denotational_Iagree @ a @ b @ c @ X7 @ X5 @ (static_SIGF @ a @ b @ c @ phi)) => ((denotational_Vagree @ c @ X4 @ X6 @ (static_FVF @ a @ b @ c @ phi)) => (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X4 @ (denotational_fml_sem @ a @ b @ c @ X7 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X6 @ (denotational_fml_sem @ a @ b @ c @ X5 @ phi)))))))),
% 1.83/0.61 inference(rectify,[],[f283])).
% 1.83/0.61 thf(f654,plain,(
% 1.83/0.61 ~(! [X5 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X4 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X6 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X7 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true = ((denotational_Iagree @ a @ b @ c @ X7 @ X5 @ (static_SIGF @ a @ b @ c @ phi)))) => (($true = ((denotational_Vagree @ c @ X4 @ X6 @ (static_FVF @ a @ b @ c @ phi)))) => (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X4 @ (denotational_fml_sem @ a @ b @ c @ X7 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X6 @ (denotational_fml_sem @ a @ b @ c @ X5 @ phi)))))) <=> ! [X0 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X3 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : (($true = ((denotational_Iagree @ a @ b @ c @ X0 @ X2 @ (static_SIGF @ a @ b @ c @ phi)))) => (($true = ((denotational_Vagree @ c @ X3 @ X1 @ (static_FVF @ a @ b @ c @ phi)))) => (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X3 @ (denotational_fml_sem @ a @ b @ c @ X0 @ phi)))))))),
% 1.83/0.61 inference(fool_elimination,[],[f653])).
% 1.83/0.61 thf(f667,plain,(
% 1.83/0.61 finite_finite @ c),
% 1.83/0.61 inference(rectify,[],[f281])).
% 1.83/0.61 thf(f668,plain,(
% 1.83/0.61 (finite_finite @ c = $true)),
% 1.83/0.61 inference(fool_elimination,[],[f667])).
% 1.83/0.61 thf(f888,plain,(
% 1.83/0.61 ! [X5 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X4 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X6 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X7 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X4 @ (denotational_fml_sem @ a @ b @ c @ X7 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X6 @ (denotational_fml_sem @ a @ b @ c @ X5 @ phi)))) | ($true != ((denotational_Vagree @ c @ X4 @ X6 @ (static_FVF @ a @ b @ c @ phi))))) | ($true != ((denotational_Iagree @ a @ b @ c @ X7 @ X5 @ (static_SIGF @ a @ b @ c @ phi))))) <~> ! [X0 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X3 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : (((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X3 @ (denotational_fml_sem @ a @ b @ c @ X0 @ phi)))) | ($true != ((denotational_Vagree @ c @ X3 @ X1 @ (static_FVF @ a @ b @ c @ phi))))) | ($true != ((denotational_Iagree @ a @ b @ c @ X0 @ X2 @ (static_SIGF @ a @ b @ c @ phi)))))),
% 1.83/0.61 inference(ennf_transformation,[],[f654])).
% 1.83/0.61 thf(f889,plain,(
% 1.83/0.61 ! [X5 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X6 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X4 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X7 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X4 @ (denotational_fml_sem @ a @ b @ c @ X7 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X6 @ (denotational_fml_sem @ a @ b @ c @ X5 @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ X7 @ X5 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true != ((denotational_Vagree @ c @ X4 @ X6 @ (static_FVF @ a @ b @ c @ phi))))) <~> ! [X3 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X0 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true != ((denotational_Vagree @ c @ X3 @ X1 @ (static_FVF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X3 @ (denotational_fml_sem @ a @ b @ c @ X0 @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ X0 @ X2 @ (static_SIGF @ a @ b @ c @ phi)))))),
% 1.83/0.61 inference(flattening,[],[f888])).
% 1.83/0.61 thf(f890,plain,(
% 1.83/0.61 ! [X0 : $tType] : ((finite_finite @ X0 != $true) | ! [X3 : set @ sum_sum @ X0 @ X0,X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X1 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0] : ((((denotational_Vagree @ X0 @ X1 @ X2 @ X3)) = $true) | (((denotational_Vagree @ X0 @ X2 @ X1 @ X3)) != $true)))),
% 1.83/0.61 inference(ennf_transformation,[],[f462])).
% 1.83/0.61 thf(f891,plain,(
% 1.83/0.61 ! [X1 : $tType,X2 : $tType,X0 : $tType] : (! [X4 : denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit,X5 : set @ sum_sum @ X0 @ sum_sum @ X2 @ X1,X3 : denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit] : (($true = ((denotational_Iagree @ X0 @ X2 @ X1 @ X3 @ X4 @ X5))) | ($true != ((denotational_Iagree @ X0 @ X2 @ X1 @ X4 @ X3 @ X5)))) | ((finite_finite @ X2 != $true) | (finite_finite @ X0 != $true) | (finite_finite @ X1 != $true)))),
% 1.83/0.61 inference(ennf_transformation,[],[f291])).
% 1.83/0.61 thf(f892,plain,(
% 1.83/0.61 ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((finite_finite @ X2 != $true) | (finite_finite @ X1 != $true) | (finite_finite @ X0 != $true) | ! [X4 : denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit,X5 : set @ sum_sum @ X0 @ sum_sum @ X2 @ X1,X3 : denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit] : (($true = ((denotational_Iagree @ X0 @ X2 @ X1 @ X3 @ X4 @ X5))) | ($true != ((denotational_Iagree @ X0 @ X2 @ X1 @ X4 @ X3 @ X5)))))),
% 1.83/0.61 inference(flattening,[],[f891])).
% 1.83/0.61 thf(f1278,plain,(
% 1.83/0.61 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((finite_finite @ X2 != $true) | (finite_finite @ X0 != $true) | (finite_finite @ X1 != $true) | ! [X3 : denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit,X4 : set @ sum_sum @ X1 @ sum_sum @ X2 @ X0,X5 : denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit] : (($true = ((denotational_Iagree @ X1 @ X2 @ X0 @ X5 @ X3 @ X4))) | ($true != ((denotational_Iagree @ X1 @ X2 @ X0 @ X3 @ X5 @ X4)))))),
% 1.83/0.61 inference(rectify,[],[f892])).
% 1.83/0.61 thf(f1286,plain,(
% 1.83/0.61 ! [X0 : $tType] : ((finite_finite @ X0 != $true) | ! [X1 : set @ sum_sum @ X0 @ X0,X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X3 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0] : (($true = ((denotational_Vagree @ X0 @ X3 @ X2 @ X1))) | (((denotational_Vagree @ X0 @ X2 @ X3 @ X1)) != $true)))),
% 1.83/0.61 inference(rectify,[],[f890])).
% 1.83/0.61 thf(f1426,plain,(
% 1.83/0.61 (? [X3 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X0 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true = ((denotational_Vagree @ c @ X3 @ X1 @ (static_FVF @ a @ b @ c @ phi)))) & (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X3 @ (denotational_fml_sem @ a @ b @ c @ X0 @ phi)))) & ($true = ((denotational_Iagree @ a @ b @ c @ X0 @ X2 @ (static_SIGF @ a @ b @ c @ phi))))) | ? [X5 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X6 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X4 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X7 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X4 @ (denotational_fml_sem @ a @ b @ c @ X7 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X6 @ (denotational_fml_sem @ a @ b @ c @ X5 @ phi)))) & ($true = ((denotational_Iagree @ a @ b @ c @ X7 @ X5 @ (static_SIGF @ a @ b @ c @ phi)))) & ($true = ((denotational_Vagree @ c @ X4 @ X6 @ (static_FVF @ a @ b @ c @ phi)))))) & (! [X3 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X0 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true != ((denotational_Vagree @ c @ X3 @ X1 @ (static_FVF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X3 @ (denotational_fml_sem @ a @ b @ c @ X0 @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ X0 @ X2 @ (static_SIGF @ a @ b @ c @ phi))))) | ! [X5 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X6 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X4 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X7 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X4 @ (denotational_fml_sem @ a @ b @ c @ X7 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X6 @ (denotational_fml_sem @ a @ b @ c @ X5 @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ X7 @ X5 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true != ((denotational_Vagree @ c @ X4 @ X6 @ (static_FVF @ a @ b @ c @ phi))))))),
% 1.83/0.61 inference(nnf_transformation,[],[f889])).
% 1.83/0.61 thf(f1427,plain,(
% 1.83/0.61 (? [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X2 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X3 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((((denotational_Vagree @ c @ X0 @ X1 @ (static_FVF @ a @ b @ c @ phi))) = $true) & (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X2 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X1 @ (denotational_fml_sem @ a @ b @ c @ X3 @ phi)))) & (((denotational_Iagree @ a @ b @ c @ X2 @ X3 @ (static_SIGF @ a @ b @ c @ phi))) = $true)) | ? [X4 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X5 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X6 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X7 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X6 @ (denotational_fml_sem @ a @ b @ c @ X7 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X5 @ (denotational_fml_sem @ a @ b @ c @ X4 @ phi)))) & ($true = ((denotational_Iagree @ a @ b @ c @ X7 @ X4 @ (static_SIGF @ a @ b @ c @ phi)))) & ($true = ((denotational_Vagree @ c @ X6 @ X5 @ (static_FVF @ a @ b @ c @ phi)))))) & (! [X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true)) | ! [X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true)))),
% 1.83/0.61 inference(rectify,[],[f1426])).
% 1.83/0.61 thf(f1428,plain,(
% 1.83/0.61 ((($true = ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi)))) & (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) & ($true = ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi))))) | ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) & ($true = ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) & ($true = ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))))) & (! [X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true)) | ! [X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true)))),
% 1.83/0.61 inference(skolemize,[status(esa),new_symbols(skolem,[sK127,sK128,sK129,sK130,sK131,sK132,sK133,sK134]),skolemize(X0,sK127),skolemize(X1,sK128),skolemize(X2,sK129),skolemize(X3,sK130),skolemize(X4,sK131),skolemize(X5,sK132),skolemize(X6,sK133),skolemize(X7,sK134)],[f1427])).
% 1.83/0.61 thf(f1467,plain,(
% 1.83/0.61 (finite_finite @ c = $true)),
% 1.83/0.61 inference(cnf_transformation,[],[f668])).
% 1.83/0.61 thf(f1605,plain,(
% 1.83/0.61 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit,X4 : set @ sum_sum @ X1 @ sum_sum @ X2 @ X0,X5 : denota1663640101rp_ext @ X1 @ X2 @ X0 @ product_unit] : (($true = ((denotational_Iagree @ X1 @ X2 @ X0 @ X5 @ X3 @ X4))) | (finite_finite @ X0 != $true) | (finite_finite @ X1 != $true) | ($true != ((denotational_Iagree @ X1 @ X2 @ X0 @ X3 @ X5 @ X4))) | (finite_finite @ X2 != $true)) )),
% 1.83/0.61 inference(cnf_transformation,[],[f1278])).
% 1.83/0.61 thf(f1612,plain,(
% 1.83/0.61 ( ! [X0 : $tType,X2 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X3 : product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0,X1 : set @ sum_sum @ X0 @ X0] : (($true = ((denotational_Vagree @ X0 @ X3 @ X2 @ X1))) | (finite_finite @ X0 != $true) | (((denotational_Vagree @ X0 @ X2 @ X3 @ X1)) != $true)) )),
% 1.83/0.61 inference(cnf_transformation,[],[f1286])).
% 1.83/0.61 thf(f1666,plain,(
% 1.83/0.61 (finite_finite @ a = $true)),
% 1.83/0.61 inference(cnf_transformation,[],[f430])).
% 1.83/0.61 thf(f1693,plain,(
% 1.83/0.61 (finite_finite @ b = $true)),
% 1.83/0.61 inference(cnf_transformation,[],[f580])).
% 1.83/0.61 thf(f1779,plain,(
% 1.83/0.61 ( ! [X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true) | ($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true)) )),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1780,plain,(
% 1.83/0.61 ($true = ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true = ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1781,plain,(
% 1.83/0.61 ($true = ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true = ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1782,plain,(
% 1.83/0.61 ($true = ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1783,plain,(
% 1.83/0.61 (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | ($true = ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1784,plain,(
% 1.83/0.61 ($true = ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1785,plain,(
% 1.83/0.61 (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1786,plain,(
% 1.83/0.61 ($true = ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))) | ($true = ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1787,plain,(
% 1.83/0.61 ($true = ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi)))) | ($true = ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1788,plain,(
% 1.83/0.61 ($true = ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi))))),
% 1.83/0.61 inference(cnf_transformation,[],[f1428])).
% 1.83/0.61 thf(f1889,plain,(
% 1.83/0.61 ( ! [X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = $true) | ($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi))))) )),
% 1.83/0.61 inference(iff_proxy_clausification,[],[f1779])).
% 1.83/0.61 thf(f1890,plain,(
% 1.83/0.61 ( ! [X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi)))) | ($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = $false) | (((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi))))) )),
% 1.83/0.61 inference(iff_proxy_clausification,[],[f1779])).
% 1.83/0.61 thf(f1891,plain,(
% 1.83/0.61 ( ! [X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = $false) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = $true) | ($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi))) = $false)) )),
% 1.83/0.61 inference(iff_proxy_clausification,[],[f1890])).
% 1.83/0.61 thf(f1894,plain,(
% 1.83/0.61 ( ! [X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | ($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi)))) | (((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = $false) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = $true)) )),
% 1.83/0.61 inference(iff_proxy_clausification,[],[f1889])).
% 1.83/0.61 thf(f1895,plain,(
% 1.83/0.61 ($true = ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $true)),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1782])).
% 1.83/0.61 thf(f1896,plain,(
% 1.83/0.61 ($true = ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $false)),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1782])).
% 1.83/0.61 thf(f1911,plain,(
% 1.83/0.61 ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | ($true = ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1784])).
% 1.83/0.61 thf(f1912,plain,(
% 1.83/0.61 ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi)))) | ($true = ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1784])).
% 1.83/0.61 thf(f1915,plain,(
% 1.83/0.61 (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $true) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | ($true = ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1788])).
% 1.83/0.61 thf(f1916,plain,(
% 1.83/0.61 ($true = ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $false)),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1788])).
% 1.83/0.61 thf(f1922,plain,(
% 1.83/0.61 (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $true) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1785])).
% 1.83/0.61 thf(f1923,plain,(
% 1.83/0.61 (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))) != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $false) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1785])).
% 1.83/0.61 thf(f1924,plain,(
% 1.83/0.61 ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $false) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1923])).
% 1.83/0.61 thf(f1925,plain,(
% 1.83/0.61 (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $false) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1923])).
% 1.83/0.61 thf(f1926,plain,(
% 1.83/0.61 ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $true) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1922])).
% 1.83/0.61 thf(f1927,plain,(
% 1.83/0.61 ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $true) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1922])).
% 1.83/0.61 thf(f1952,plain,(
% 1.83/0.61 ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi)))) | ($true = ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1783])).
% 1.83/0.61 thf(f1953,plain,(
% 1.83/0.61 ($true = ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))))),
% 1.83/0.61 inference(xor_proxy_clausification,[],[f1783])).
% 1.83/0.61 thf(f1966,definition,(
% 1.83/0.61 spl151_1 <=> ($true = ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_1])],[avatar_definition])).
% 1.83/0.61 thf(f1968,plain,(
% 1.83/0.61 ($true = ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))) | ~spl151_1),
% 1.83/0.61 inference(avatar_component_clause,[],[f1966])).
% 1.83/0.61 thf(f1970,definition,(
% 1.83/0.61 spl151_2 <=> ($true = ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_2])],[avatar_definition])).
% 1.83/0.61 thf(f1972,plain,(
% 1.83/0.61 ($true = ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi)))) | ~spl151_2),
% 1.83/0.61 inference(avatar_component_clause,[],[f1970])).
% 1.83/0.61 thf(f1973,plain,(
% 1.83/0.61 spl151_1 | spl151_2),
% 1.83/0.61 inference(avatar_split_clause,[],[f1786,f1970,f1966])).
% 1.83/0.61 thf(f1982,definition,(
% 1.83/0.61 spl151_5 <=> ! [X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | ($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = $false) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi)))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_5])],[avatar_definition])).
% 1.83/0.61 thf(f1983,plain,(
% 1.83/0.61 ( ! [X10 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X11 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X8 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X9 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : (($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X8 @ (denotational_fml_sem @ a @ b @ c @ X10 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X9 @ (denotational_fml_sem @ a @ b @ c @ X11 @ phi))) = $false) | (((denotational_Iagree @ a @ b @ c @ X10 @ X11 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | ($true != ((denotational_Vagree @ c @ X8 @ X9 @ (static_FVF @ a @ b @ c @ phi))))) ) | ~spl151_5),
% 1.83/0.61 inference(avatar_component_clause,[],[f1982])).
% 1.83/0.61 thf(f1985,definition,(
% 1.83/0.61 spl151_6 <=> ! [X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : ((((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = $false) | (((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true) | ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_6])],[avatar_definition])).
% 1.83/0.61 thf(f1986,plain,(
% 1.83/0.61 ( ! [X14 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X15 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X12 : denota1663640101rp_ext @ a @ b @ c @ product_unit,X13 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : (($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X13 @ (denotational_fml_sem @ a @ b @ c @ X12 @ phi)))) | (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X14 @ (denotational_fml_sem @ a @ b @ c @ X15 @ phi))) = $false) | (((denotational_Iagree @ a @ b @ c @ X15 @ X12 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ X14 @ X13 @ (static_FVF @ a @ b @ c @ phi))) != $true)) ) | ~spl151_6),
% 1.83/0.61 inference(avatar_component_clause,[],[f1985])).
% 1.83/0.61 thf(f1988,plain,(
% 1.83/0.61 spl151_5 | spl151_5),
% 1.83/0.61 inference(avatar_split_clause,[],[f1891,f1982,f1982])).
% 1.83/0.61 thf(f1989,plain,(
% 1.83/0.61 spl151_6 | spl151_6),
% 1.83/0.61 inference(avatar_split_clause,[],[f1894,f1985,f1985])).
% 1.83/0.61 thf(f1992,definition,(
% 1.83/0.61 spl151_7 <=> ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_7])],[avatar_definition])).
% 1.83/0.61 thf(f1994,plain,(
% 1.83/0.61 ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | ~spl151_7),
% 1.83/0.61 inference(avatar_component_clause,[],[f1992])).
% 1.83/0.61 thf(f1996,definition,(
% 1.83/0.61 spl151_8 <=> ($true = ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_8])],[avatar_definition])).
% 1.83/0.61 thf(f1998,plain,(
% 1.83/0.61 ($true = ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | ~spl151_8),
% 1.83/0.61 inference(avatar_component_clause,[],[f1996])).
% 1.83/0.61 thf(f2000,definition,(
% 1.83/0.61 spl151_9 <=> (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $false)),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_9])],[avatar_definition])).
% 1.83/0.61 thf(f2002,plain,(
% 1.83/0.61 (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $false) | ~spl151_9),
% 1.83/0.61 inference(avatar_component_clause,[],[f2000])).
% 1.83/0.61 thf(f2003,plain,(
% 1.83/0.61 spl151_7 | spl151_8 | spl151_9),
% 1.83/0.61 inference(avatar_split_clause,[],[f1896,f2000,f1996,f1992])).
% 1.83/0.61 thf(f2005,definition,(
% 1.83/0.61 spl151_10 <=> ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_10])],[avatar_definition])).
% 1.83/0.61 thf(f2006,plain,(
% 1.83/0.61 ($true != ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | spl151_10),
% 1.83/0.61 inference(avatar_component_clause,[],[f2005])).
% 1.83/0.61 thf(f2007,plain,(
% 1.83/0.61 ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK132 @ (denotational_fml_sem @ a @ b @ c @ sK131 @ phi)))) | ~spl151_10),
% 1.83/0.61 inference(avatar_component_clause,[],[f2005])).
% 1.83/0.61 thf(f2009,definition,(
% 1.83/0.61 spl151_11 <=> (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $true)),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_11])],[avatar_definition])).
% 1.83/0.61 thf(f2011,plain,(
% 1.83/0.61 (((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK133 @ (denotational_fml_sem @ a @ b @ c @ sK134 @ phi))) = $true) | ~spl151_11),
% 1.83/0.61 inference(avatar_component_clause,[],[f2009])).
% 1.83/0.61 thf(f2012,plain,(
% 1.83/0.61 spl151_8 | spl151_10 | spl151_11),
% 1.83/0.61 inference(avatar_split_clause,[],[f1895,f2009,f2005,f1996])).
% 1.83/0.61 thf(f2033,plain,(
% 1.83/0.61 spl151_8 | spl151_1),
% 1.83/0.61 inference(avatar_split_clause,[],[f1780,f1966,f1996])).
% 1.83/0.61 thf(f2056,definition,(
% 1.83/0.61 spl151_22 <=> (finite_finite @ c = $true)),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_22])],[avatar_definition])).
% 1.83/0.61 thf(f2058,plain,(
% 1.83/0.61 (finite_finite @ c = $true) | ~spl151_22),
% 1.83/0.61 inference(avatar_component_clause,[],[f2056])).
% 1.83/0.61 thf(f2059,plain,(
% 1.83/0.61 spl151_22),
% 1.83/0.61 inference(avatar_split_clause,[],[f1467,f2056])).
% 1.83/0.61 thf(f2073,definition,(
% 1.83/0.61 spl151_26 <=> ($true = ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_26])],[avatar_definition])).
% 1.83/0.61 thf(f2075,plain,(
% 1.83/0.61 ($true = ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | ~spl151_26),
% 1.83/0.61 inference(avatar_component_clause,[],[f2073])).
% 1.83/0.61 thf(f2077,definition,(
% 1.83/0.61 spl151_27 <=> ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_27])],[avatar_definition])).
% 1.83/0.61 thf(f2079,plain,(
% 1.83/0.61 ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | ~spl151_27),
% 1.83/0.61 inference(avatar_component_clause,[],[f2077])).
% 1.83/0.61 thf(f2081,definition,(
% 1.83/0.61 spl151_28 <=> ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_28])],[avatar_definition])).
% 1.83/0.61 thf(f2083,plain,(
% 1.83/0.61 ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi)))) | ~spl151_28),
% 1.83/0.61 inference(avatar_component_clause,[],[f2081])).
% 1.83/0.61 thf(f2084,plain,(
% 1.83/0.61 spl151_26 | spl151_27 | spl151_28),
% 1.83/0.61 inference(avatar_split_clause,[],[f1912,f2081,f2077,f2073])).
% 1.83/0.61 thf(f2086,definition,(
% 1.83/0.61 spl151_29 <=> ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_29])],[avatar_definition])).
% 1.83/0.61 thf(f2088,plain,(
% 1.83/0.61 ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK127 @ (denotational_fml_sem @ a @ b @ c @ sK129 @ phi)))) | ~spl151_29),
% 1.83/0.61 inference(avatar_component_clause,[],[f2086])).
% 1.83/0.61 thf(f2090,definition,(
% 1.83/0.61 spl151_30 <=> ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi))))),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_30])],[avatar_definition])).
% 1.83/0.61 thf(f2092,plain,(
% 1.83/0.61 ($true = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ sK128 @ (denotational_fml_sem @ a @ b @ c @ sK130 @ phi)))) | ~spl151_30),
% 1.83/0.61 inference(avatar_component_clause,[],[f2090])).
% 1.83/0.61 thf(f2093,plain,(
% 1.83/0.61 spl151_29 | spl151_30 | spl151_26),
% 1.83/0.61 inference(avatar_split_clause,[],[f1911,f2073,f2090,f2086])).
% 1.83/0.61 thf(f2103,plain,(
% 1.83/0.61 spl151_26 | spl151_2),
% 1.83/0.61 inference(avatar_split_clause,[],[f1787,f1970,f2073])).
% 1.83/0.61 thf(f2104,plain,(
% 1.83/0.61 spl151_9 | spl151_7 | spl151_2),
% 1.83/0.61 inference(avatar_split_clause,[],[f1916,f1970,f1992,f2000])).
% 1.83/0.61 thf(f2105,plain,(
% 1.83/0.61 spl151_11 | spl151_10 | spl151_2),
% 1.83/0.61 inference(avatar_split_clause,[],[f1915,f1970,f2005,f2009])).
% 1.83/0.61 thf(f2110,plain,(
% 1.83/0.61 spl151_9 | spl151_27 | spl151_28 | spl151_7),
% 1.83/0.61 inference(avatar_split_clause,[],[f1925,f1992,f2081,f2077,f2000])).
% 1.83/0.61 thf(f2111,plain,(
% 1.83/0.61 spl151_9 | spl151_30 | spl151_7 | spl151_29),
% 1.83/0.61 inference(avatar_split_clause,[],[f1924,f2086,f1992,f2090,f2000])).
% 1.83/0.61 thf(f2112,plain,(
% 1.83/0.61 spl151_28 | spl151_27 | spl151_11 | spl151_10),
% 1.83/0.61 inference(avatar_split_clause,[],[f1927,f2005,f2009,f2077,f2081])).
% 1.83/0.61 thf(f2113,plain,(
% 1.83/0.61 spl151_10 | spl151_29 | spl151_30 | spl151_11),
% 1.83/0.61 inference(avatar_split_clause,[],[f1926,f2009,f2090,f2086,f2005])).
% 1.83/0.61 thf(f2147,definition,(
% 1.83/0.61 spl151_41 <=> (finite_finite @ b = $true)),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_41])],[avatar_definition])).
% 1.83/0.61 thf(f2149,plain,(
% 1.83/0.61 (finite_finite @ b = $true) | ~spl151_41),
% 1.83/0.61 inference(avatar_component_clause,[],[f2147])).
% 1.83/0.61 thf(f2150,plain,(
% 1.83/0.61 spl151_41),
% 1.83/0.61 inference(avatar_split_clause,[],[f1693,f2147])).
% 1.83/0.61 thf(f2232,definition,(
% 1.83/0.61 spl151_58 <=> (finite_finite @ a = $true)),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_58])],[avatar_definition])).
% 1.83/0.61 thf(f2234,plain,(
% 1.83/0.61 (finite_finite @ a = $true) | ~spl151_58),
% 1.83/0.61 inference(avatar_component_clause,[],[f2232])).
% 1.83/0.61 thf(f2235,plain,(
% 1.83/0.61 spl151_58),
% 1.83/0.61 inference(avatar_split_clause,[],[f1666,f2232])).
% 1.83/0.61 thf(f2265,plain,(
% 1.83/0.61 spl151_26 | spl151_8),
% 1.83/0.61 inference(avatar_split_clause,[],[f1781,f1996,f2073])).
% 1.83/0.61 thf(f2267,plain,(
% 1.83/0.61 spl151_1 | spl151_28 | spl151_27),
% 1.83/0.61 inference(avatar_split_clause,[],[f1953,f2077,f2081,f1966])).
% 1.83/0.61 thf(f2268,plain,(
% 1.83/0.61 spl151_29 | spl151_1 | spl151_30),
% 1.83/0.61 inference(avatar_split_clause,[],[f1952,f2090,f1966,f2086])).
% 1.83/0.61 thf(f2309,plain,(
% 1.83/0.61 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X1 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ sK130 @ X1 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ sK128 @ X0 @ (static_FVF @ a @ b @ c @ phi))) != $true) | ($true = $false)) ) | (~spl151_5 | ~spl151_27)),
% 1.83/0.61 inference(superposition,[],[f2079,f1983])).
% 1.83/0.61 thf(f2311,plain,(
% 1.83/0.61 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X1 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ sK130 @ X1 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ sK128 @ X0 @ (static_FVF @ a @ b @ c @ phi))) != $true)) ) | (~spl151_5 | ~spl151_27)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2309])).
% 1.83/0.61 thf(f2322,plain,(
% 1.83/0.61 (((denotational_Vagree @ c @ sK128 @ sK127 @ (static_FVF @ a @ b @ c @ phi))) != $true) | ($true = $false) | (((denotational_Iagree @ a @ b @ c @ sK130 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (~spl151_5 | ~spl151_27 | ~spl151_29)),
% 1.83/0.61 inference(superposition,[],[f2311,f2088])).
% 1.83/0.61 thf(f2328,plain,(
% 1.83/0.61 (((denotational_Vagree @ c @ sK128 @ sK127 @ (static_FVF @ a @ b @ c @ phi))) != $true) | (((denotational_Iagree @ a @ b @ c @ sK130 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (~spl151_5 | ~spl151_27 | ~spl151_29)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2322])).
% 1.83/0.61 thf(f2331,definition,(
% 1.83/0.61 spl151_71 <=> (((denotational_Vagree @ c @ sK128 @ sK127 @ (static_FVF @ a @ b @ c @ phi))) = $true)),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_71])],[avatar_definition])).
% 1.83/0.61 thf(f2332,plain,(
% 1.83/0.61 (((denotational_Vagree @ c @ sK128 @ sK127 @ (static_FVF @ a @ b @ c @ phi))) = $true) | ~spl151_71),
% 1.83/0.61 inference(avatar_component_clause,[],[f2331])).
% 1.83/0.61 thf(f2333,plain,(
% 1.83/0.61 (((denotational_Vagree @ c @ sK128 @ sK127 @ (static_FVF @ a @ b @ c @ phi))) != $true) | spl151_71),
% 1.83/0.61 inference(avatar_component_clause,[],[f2331])).
% 1.83/0.61 thf(f2335,definition,(
% 1.83/0.61 spl151_72 <=> (((denotational_Iagree @ a @ b @ c @ sK130 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) = $true)),
% 1.83/0.61 introduced(definition,[new_symbols(definition,[spl151_72])],[avatar_definition])).
% 1.83/0.61 thf(f2336,plain,(
% 1.83/0.61 (((denotational_Iagree @ a @ b @ c @ sK130 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) = $true) | ~spl151_72),
% 1.83/0.61 inference(avatar_component_clause,[],[f2335])).
% 1.83/0.61 thf(f2337,plain,(
% 1.83/0.61 (((denotational_Iagree @ a @ b @ c @ sK130 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | spl151_72),
% 1.83/0.61 inference(avatar_component_clause,[],[f2335])).
% 1.83/0.61 thf(f2339,plain,(
% 1.83/0.61 ~spl151_72 | ~spl151_71 | ~spl151_5 | ~spl151_27 | ~spl151_29),
% 1.83/0.61 inference(avatar_split_clause,[],[f2328,f2086,f2077,f1982,f2331,f2335])).
% 1.83/0.61 thf(f2364,plain,(
% 1.83/0.61 (finite_finite @ c != $true) | ($true != ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi)))) | ($true != $true) | spl151_71),
% 1.83/0.61 inference(superposition,[],[f2333,f1612])).
% 1.83/0.61 thf(f2365,plain,(
% 1.83/0.61 (finite_finite @ c != $true) | ($true != ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi)))) | spl151_71),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2364])).
% 1.83/0.61 thf(f2366,plain,(
% 1.83/0.61 ($true != ((denotational_Vagree @ c @ sK127 @ sK128 @ (static_FVF @ a @ b @ c @ phi)))) | (~spl151_22 | spl151_71)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f2365,f2058])).
% 1.83/0.61 thf(f2367,plain,(
% 1.83/0.61 $false | (~spl151_2 | ~spl151_22 | spl151_71)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f2366,f1972])).
% 1.83/0.61 thf(f2368,plain,(
% 1.83/0.61 ~spl151_2 | ~spl151_22 | spl151_71),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f2367])).
% 1.83/0.61 thf(f2369,plain,(
% 1.83/0.61 (finite_finite @ a != $true) | (finite_finite @ b != $true) | (finite_finite @ c != $true) | ($true != ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true != $true) | spl151_72),
% 1.83/0.61 inference(superposition,[],[f2337,f1605])).
% 1.83/0.61 thf(f2370,plain,(
% 1.83/0.61 (finite_finite @ a != $true) | (finite_finite @ c != $true) | ($true != ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | (finite_finite @ b != $true) | spl151_72),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2369])).
% 1.83/0.61 thf(f2371,plain,(
% 1.83/0.61 (finite_finite @ c != $true) | ($true != ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | (finite_finite @ b != $true) | (~spl151_58 | spl151_72)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f2370,f2234])).
% 1.83/0.61 thf(f2372,plain,(
% 1.83/0.61 (finite_finite @ b != $true) | ($true != ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | (~spl151_22 | ~spl151_58 | spl151_72)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f2371,f2058])).
% 1.83/0.61 thf(f2373,plain,(
% 1.83/0.61 ($true != ((denotational_Iagree @ a @ b @ c @ sK129 @ sK130 @ (static_SIGF @ a @ b @ c @ phi)))) | (~spl151_22 | ~spl151_41 | ~spl151_58 | spl151_72)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f2372,f2149])).
% 1.83/0.61 thf(f2374,plain,(
% 1.83/0.61 $false | (~spl151_8 | ~spl151_22 | ~spl151_41 | ~spl151_58 | spl151_72)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f2373,f1998])).
% 1.83/0.61 thf(f2375,plain,(
% 1.83/0.61 ~spl151_8 | ~spl151_22 | ~spl151_41 | ~spl151_58 | spl151_72),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f2374])).
% 1.83/0.61 thf(f2378,plain,(
% 1.83/0.61 ($true = $false) | (~spl151_28 | ~spl151_29)),
% 1.83/0.61 inference(superposition,[],[f2083,f2088])).
% 1.83/0.61 thf(f2387,plain,(
% 1.83/0.61 $false | (~spl151_28 | ~spl151_29)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2378])).
% 1.83/0.61 thf(f2388,plain,(
% 1.83/0.61 ~spl151_28 | ~spl151_29),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f2387])).
% 1.83/0.61 thf(f2400,plain,(
% 1.83/0.61 ($true = $false) | (~spl151_27 | ~spl151_30)),
% 1.83/0.61 inference(forward_demodulation,[],[f2092,f2079])).
% 1.83/0.61 thf(f2401,plain,(
% 1.83/0.61 $false | (~spl151_27 | ~spl151_30)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2400])).
% 1.83/0.61 thf(f2402,plain,(
% 1.83/0.61 ~spl151_27 | ~spl151_30),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f2401])).
% 1.83/0.61 thf(f2408,plain,(
% 1.83/0.61 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true = $false) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X1 @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ sK134 @ X1 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true != ((denotational_Vagree @ c @ sK133 @ X0 @ (static_FVF @ a @ b @ c @ phi))))) ) | (~spl151_5 | ~spl151_9)),
% 1.83/0.61 inference(superposition,[],[f1983,f2002])).
% 1.83/0.61 thf(f2409,plain,(
% 1.83/0.61 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X1 @ phi)))) | ($true != ((denotational_Vagree @ c @ sK133 @ X0 @ (static_FVF @ a @ b @ c @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ sK134 @ X1 @ (static_SIGF @ a @ b @ c @ phi))))) ) | (~spl151_5 | ~spl151_9)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2408])).
% 1.83/0.61 thf(f2535,plain,(
% 1.83/0.61 ($true = $false) | ($true != ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | (~spl151_5 | ~spl151_9 | ~spl151_10)),
% 1.83/0.61 inference(superposition,[],[f2409,f2007])).
% 1.83/0.61 thf(f2543,plain,(
% 1.83/0.61 ($true != ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | ($true != ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))) | (~spl151_5 | ~spl151_9 | ~spl151_10)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2535])).
% 1.83/0.61 thf(f2546,plain,(
% 1.83/0.61 ($true != ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))) | (~spl151_5 | ~spl151_9 | ~spl151_10 | ~spl151_26)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f2543,f2075])).
% 1.83/0.61 thf(f2549,plain,(
% 1.83/0.61 $false | (~spl151_1 | ~spl151_5 | ~spl151_9 | ~spl151_10 | ~spl151_26)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f2546,f1968])).
% 1.83/0.61 thf(f2550,plain,(
% 1.83/0.61 ~spl151_1 | ~spl151_5 | ~spl151_9 | ~spl151_10 | ~spl151_26),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f2549])).
% 1.83/0.61 thf(f2551,plain,(
% 1.83/0.61 ($true = $false) | (~spl151_9 | ~spl151_11)),
% 1.83/0.61 inference(forward_demodulation,[],[f2011,f2002])).
% 1.83/0.61 thf(f2552,plain,(
% 1.83/0.61 $false | (~spl151_9 | ~spl151_11)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2551])).
% 1.83/0.61 thf(f2553,plain,(
% 1.83/0.61 ~spl151_9 | ~spl151_11),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f2552])).
% 1.83/0.61 thf(f2557,plain,(
% 1.83/0.61 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true = $false) | (((denotational_Iagree @ a @ b @ c @ X1 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X1 @ phi)))) | ($true != ((denotational_Vagree @ c @ X0 @ sK127 @ (static_FVF @ a @ b @ c @ phi))))) ) | (~spl151_6 | ~spl151_28)),
% 1.83/0.61 inference(superposition,[],[f1986,f2083])).
% 1.83/0.61 thf(f2559,plain,(
% 1.83/0.61 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X1 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X1 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | ($true != ((denotational_Vagree @ c @ X0 @ sK127 @ (static_FVF @ a @ b @ c @ phi))))) ) | (~spl151_6 | ~spl151_28)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2557])).
% 1.83/0.61 thf(f2606,plain,(
% 1.83/0.61 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($true != $true) | (((denotational_Iagree @ a @ b @ c @ X1 @ sK131 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ X0 @ sK132 @ (static_FVF @ a @ b @ c @ phi))) != $true) | ($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X1 @ phi))))) ) | (~spl151_6 | spl151_10)),
% 1.83/0.61 inference(superposition,[],[f2006,f1986])).
% 1.83/0.61 thf(f2609,plain,(
% 1.83/0.61 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c,X1 : denota1663640101rp_ext @ a @ b @ c @ product_unit] : (($false = ((member @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ X0 @ (denotational_fml_sem @ a @ b @ c @ X1 @ phi)))) | (((denotational_Iagree @ a @ b @ c @ X1 @ sK131 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ X0 @ sK132 @ (static_FVF @ a @ b @ c @ phi))) != $true)) ) | (~spl151_6 | spl151_10)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f2606])).
% 1.83/0.61 thf(f3203,plain,(
% 1.83/0.61 (((denotational_Vagree @ c @ sK128 @ sK127 @ (static_FVF @ a @ b @ c @ phi))) != $true) | ($true = $false) | (((denotational_Iagree @ a @ b @ c @ sK130 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (~spl151_6 | ~spl151_28 | ~spl151_30)),
% 1.83/0.61 inference(superposition,[],[f2092,f2559])).
% 1.83/0.61 thf(f3215,plain,(
% 1.83/0.61 (((denotational_Iagree @ a @ b @ c @ sK130 @ sK129 @ (static_SIGF @ a @ b @ c @ phi))) != $true) | (((denotational_Vagree @ c @ sK128 @ sK127 @ (static_FVF @ a @ b @ c @ phi))) != $true) | (~spl151_6 | ~spl151_28 | ~spl151_30)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f3203])).
% 1.83/0.61 thf(f3222,plain,(
% 1.83/0.61 (((denotational_Vagree @ c @ sK128 @ sK127 @ (static_FVF @ a @ b @ c @ phi))) != $true) | (~spl151_6 | ~spl151_28 | ~spl151_30 | ~spl151_72)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f3215,f2336])).
% 1.83/0.61 thf(f3225,plain,(
% 1.83/0.61 $false | (~spl151_6 | ~spl151_28 | ~spl151_30 | ~spl151_71 | ~spl151_72)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f3222,f2332])).
% 1.83/0.61 thf(f3226,plain,(
% 1.83/0.61 ~spl151_6 | ~spl151_28 | ~spl151_30 | ~spl151_71 | ~spl151_72),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f3225])).
% 1.83/0.61 thf(f3318,plain,(
% 1.83/0.61 ($true = $false) | ($true != ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | (~spl151_6 | spl151_10 | ~spl151_11)),
% 1.83/0.61 inference(superposition,[],[f2011,f2609])).
% 1.83/0.61 thf(f3335,plain,(
% 1.83/0.61 ($true != ((denotational_Vagree @ c @ sK133 @ sK132 @ (static_FVF @ a @ b @ c @ phi)))) | ($true != ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | (~spl151_6 | spl151_10 | ~spl151_11)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f3318])).
% 1.83/0.61 thf(f3338,plain,(
% 1.83/0.61 ($true != ((denotational_Iagree @ a @ b @ c @ sK134 @ sK131 @ (static_SIGF @ a @ b @ c @ phi)))) | (~spl151_1 | ~spl151_6 | spl151_10 | ~spl151_11)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f3335,f1968])).
% 1.83/0.61 thf(f3341,plain,(
% 1.83/0.61 $false | (~spl151_1 | ~spl151_6 | spl151_10 | ~spl151_11 | ~spl151_26)),
% 1.83/0.61 inference(forward_subsumption_resolution,[],[f3338,f2075])).
% 1.83/0.61 thf(f3342,plain,(
% 1.83/0.61 ~spl151_1 | ~spl151_6 | spl151_10 | ~spl151_11 | ~spl151_26),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f3341])).
% 1.83/0.61 thf(f3344,plain,(
% 1.83/0.61 ($true = $false) | (~spl151_7 | ~spl151_10)),
% 1.83/0.61 inference(forward_demodulation,[],[f2007,f1994])).
% 1.83/0.61 thf(f3345,plain,(
% 1.83/0.61 $false | (~spl151_7 | ~spl151_10)),
% 1.83/0.61 inference(trivial_inequality_removal,[],[f3344])).
% 1.83/0.61 thf(f3346,plain,(
% 1.83/0.61 ~spl151_7 | ~spl151_10),
% 1.83/0.61 inference(avatar_contradiction_clause,[],[f3345])).
% 1.83/0.61 cnf(s1, plain, spl151_1 | spl151_2, inference(sat_conversion,[],[f1973])).
% 1.83/0.61 cnf(s4, plain, spl151_5 | spl151_5, inference(sat_conversion,[],[f1988])).
% 1.83/0.61 cnf(s5, plain, spl151_5, inference(rat,[],[s4])).
% 1.83/0.61 cnf(s6, plain, spl151_6 | spl151_6, inference(sat_conversion,[],[f1989])).
% 1.83/0.61 cnf(s7, plain, spl151_6, inference(rat,[],[s6])).
% 1.83/0.61 cnf(s9, plain, spl151_7 | spl151_8 | spl151_9, inference(sat_conversion,[],[f2003])).
% 1.83/0.61 cnf(s10, plain, spl151_8 | spl151_10 | spl151_11, inference(sat_conversion,[],[f2012])).
% 1.83/0.61 cnf(s16, plain, spl151_1 | spl151_8, inference(sat_conversion,[],[f2033])).
% 1.83/0.61 cnf(s22, plain, spl151_22, inference(sat_conversion,[],[f2059])).
% 1.83/0.61 cnf(s26, plain, spl151_26 | spl151_27 | spl151_28, inference(sat_conversion,[],[f2084])).
% 1.83/0.61 cnf(s27, plain, spl151_26 | spl151_29 | spl151_30, inference(sat_conversion,[],[f2093])).
% 1.83/0.61 cnf(s30, plain, spl151_2 | spl151_26, inference(sat_conversion,[],[f2103])).
% 1.83/0.61 cnf(s31, plain, spl151_2 | spl151_7 | spl151_9, inference(sat_conversion,[],[f2104])).
% 1.83/0.61 cnf(s32, plain, spl151_2 | spl151_10 | spl151_11, inference(sat_conversion,[],[f2105])).
% 1.83/0.61 cnf(s34, plain, spl151_7 | spl151_9 | spl151_27 | spl151_28, inference(sat_conversion,[],[f2110])).
% 1.83/0.61 cnf(s35, plain, spl151_7 | spl151_9 | spl151_29 | spl151_30, inference(sat_conversion,[],[f2111])).
% 1.83/0.61 cnf(s36, plain, spl151_10 | spl151_11 | spl151_27 | spl151_28, inference(sat_conversion,[],[f2112])).
% 1.83/0.61 cnf(s37, plain, spl151_10 | spl151_11 | spl151_29 | spl151_30, inference(sat_conversion,[],[f2113])).
% 1.83/0.61 cnf(s49, plain, spl151_41, inference(sat_conversion,[],[f2150])).
% 1.83/0.61 cnf(s74, plain, spl151_58, inference(sat_conversion,[],[f2235])).
% 1.83/0.61 cnf(s82, plain, spl151_8 | spl151_26, inference(sat_conversion,[],[f2265])).
% 1.83/0.61 cnf(s84, plain, spl151_1 | spl151_27 | spl151_28, inference(sat_conversion,[],[f2267])).
% 1.83/0.61 cnf(s85, plain, spl151_1 | spl151_29 | spl151_30, inference(sat_conversion,[],[f2268])).
% 1.83/0.61 cnf(s93, plain, ~spl151_5 | ~spl151_27 | ~spl151_29 | ~spl151_71 | ~spl151_72, inference(sat_conversion,[],[f2339])).
% 1.83/0.61 cnf(s94, plain, ~spl151_2 | ~spl151_22 | spl151_71, inference(sat_conversion,[],[f2368])).
% 1.83/0.61 cnf(s95, plain, ~spl151_8 | ~spl151_22 | ~spl151_41 | ~spl151_58 | spl151_72, inference(sat_conversion,[],[f2375])).
% 1.83/0.61 cnf(s97, plain, ~spl151_28 | ~spl151_29, inference(sat_conversion,[],[f2388])).
% 1.83/0.61 cnf(s98, plain, ~spl151_27 | ~spl151_30, inference(sat_conversion,[],[f2402])).
% 1.83/0.61 cnf(s106, plain, ~spl151_1 | ~spl151_5 | ~spl151_9 | ~spl151_10 | ~spl151_26, inference(sat_conversion,[],[f2550])).
% 1.83/0.61 cnf(s107, plain, ~spl151_9 | ~spl151_11, inference(sat_conversion,[],[f2553])).
% 1.83/0.61 cnf(s114, plain, ~spl151_6 | ~spl151_28 | ~spl151_30 | ~spl151_71 | ~spl151_72, inference(sat_conversion,[],[f3226])).
% 1.83/0.61 cnf(s119, plain, ~spl151_1 | ~spl151_6 | spl151_10 | ~spl151_11 | ~spl151_26, inference(sat_conversion,[],[f3342])).
% 1.83/0.61 cnf(s121, plain, ~spl151_7 | ~spl151_10, inference(sat_conversion,[],[f3346])).
% 1.83/0.61 cnf(s122, plain, ~spl151_28 | spl151_1, inference(rat,[],[s85,s97,s114,s95,s16,s94,s1,s7,s22,s74,s49])).
% 1.83/0.61 cnf(s123, plain, spl151_1, inference(rat,[],[s85,s93,s98,s84,s122,s94,s95,s1,s16,s5,s22,s49,s74])).
% 1.83/0.61 cnf(s124, plain, ~spl151_28 | spl151_9 | spl151_7, inference(rat,[],[s35,s97,s114,s94,s31,s95,s9,s7,s22,s74,s49])).
% 1.83/0.61 cnf(s125, plain, spl151_9 | spl151_7, inference(rat,[],[s35,s93,s98,s34,s124,s95,s94,s9,s31,s22,s74,s49,s5])).
% 1.83/0.61 cnf(s126, plain, spl151_30 | spl151_29 | ~spl151_9, inference(rat,[],[s106,s27,s37,s107,s5,s123])).
% 1.83/0.61 cnf(s127, plain, spl151_8 | ~spl151_9, inference(rat,[],[s106,s10,s82,s107,s5,s123])).
% 1.83/0.61 cnf(s128, plain, spl151_2 | ~spl151_9, inference(rat,[],[s106,s32,s30,s107,s5,s123])).
% 1.83/0.61 cnf(s129, plain, ~spl151_28 | ~spl151_9, inference(rat,[],[s126,s114,s97,s95,s127,s94,s128,s7,s22,s74,s49])).
% 1.83/0.61 cnf(s130, plain, spl151_27 | ~spl151_9, inference(rat,[],[s106,s26,s36,s107,s129,s5,s123])).
% 1.83/0.61 cnf(s131, plain, ~spl151_9, inference(rat,[],[s126,s93,s98,s130,s94,s128,s95,s127,s5,s22,s49,s74])).
% 1.83/0.61 cnf(s132, plain, spl151_7, inference(rat,[],[s125,s131])).
% 1.83/0.61 cnf(s133, plain, ~spl151_10, inference(rat,[],[s121,s132])).
% 1.83/0.61 cnf(s134, plain, spl151_30 | spl151_29, inference(rat,[],[s119,s27,s37,s133,s123,s7])).
% 1.83/0.61 cnf(s135, plain, spl151_8, inference(rat,[],[s119,s10,s82,s7,s123,s133])).
% 1.83/0.61 cnf(s136, plain, spl151_72, inference(rat,[],[s95,s22,s74,s49,s135])).
% 1.83/0.61 cnf(s137, plain, spl151_2, inference(rat,[],[s119,s32,s30,s7,s123,s133])).
% 1.83/0.61 cnf(s138, plain, spl151_71, inference(rat,[],[s94,s22,s137])).
% 1.83/0.61 cnf(s139, plain, ~spl151_28, inference(rat,[],[s134,s114,s97,s7,s138,s136])).
% 1.83/0.61 cnf(s140, plain, spl151_27, inference(rat,[],[s119,s26,s36,s7,s123,s133,s139])).
% 1.83/0.61 cnf(s141, plain, ~spl151_30, inference(rat,[],[s98,s140])).
% 1.83/0.61 cnf(s142, plain, ~spl151_29, inference(rat,[],[s93,s136,s138,s5,s140])).
% 1.83/0.61 cnf(s143, plain, $false, inference(rat,[],[s134,s142,s141])).
% 1.83/0.61 thf(f3347,plain,(
% 1.83/0.61 $false),
% 1.83/0.61 inference(avatar_sat_refutation,[],[s143])).
% 1.83/0.61 % SZS output end Proof for theBenchmark
% 1.83/0.61 % (2559937)------------------------------
% 1.83/0.61 % (2559937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (2559937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (2559937)CaDiCaL version: 2.1.3
% 1.83/0.61 % (2559937)Termination reason: Refutation
% 1.83/0.61 % (2559937)Time elapsed: 0.235 s
% 1.83/0.61 % (2559937)Peak memory usage: 17 MB
% 1.83/0.61 % (2559937)Instructions burned: 450 (million)
% 1.83/0.61 % (2559929)Success in time 0.304 s
% 1.83/0.61 % Vampire exiting
%------------------------------------------------------------------------------