%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP028^2 : 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 : n005.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 08:08:01 AM UTC 2026
% Result : Theorem 0.49s 0.43s
% Output : Refutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP028^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n005.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 19:38:16 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.27 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
% 0.49/0.42 % (2114056)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.49/0.42 % (2114071)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3162286314:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.49/0.42 % (2114077)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.49/0.42 % (2114077)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
% 0.49/0.42 % (2114072)lrs+10_16_si=on:nwc=1.5:random_seed=158482335:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.49/0.42 % (2114076)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3366973101:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.49/0.42 % (2114077)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=989067277:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.49/0.42 % (2114074)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=2900212307: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)
% 0.49/0.42 % (2114075)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3074177055:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.49/0.42 % (2114073)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=228831644:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.49/0.42 % (2114073)Instruction limit reached!
% 0.49/0.42 % (2114073)------------------------------
% 0.49/0.42 % (2114073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114073)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114073)Termination reason: Instruction limit
% 0.49/0.42 % (2114073)Termination phase: shuffling
% 0.49/0.42 % (2114073)Time elapsed: 0.003 s
% 0.49/0.42 % (2114073)Peak memory usage: 10 MB
% 0.49/0.42 % (2114073)Instructions burned: 4 (million)
% 0.49/0.42 % (2114072)Instruction limit reached!
% 0.49/0.42 % (2114072)------------------------------
% 0.49/0.42 % (2114072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114072)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114072)Termination reason: Instruction limit
% 0.49/0.42 % (2114072)Termination phase: shuffling
% 0.49/0.42 % (2114072)Time elapsed: 0.010 s
% 0.49/0.42 % (2114072)Peak memory usage: 10 MB
% 0.49/0.42 % (2114072)Instructions burned: 19 (million)
% 0.49/0.42 % (2114075)Instruction limit reached!
% 0.49/0.42 % (2114075)------------------------------
% 0.49/0.42 % (2114075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114075)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114075)Termination reason: Instruction limit
% 0.49/0.42 % (2114075)Termination phase: Property scanning
% 0.49/0.42 % (2114075)Time elapsed: 0.013 s
% 0.49/0.42 % (2114075)Peak memory usage: 10 MB
% 0.49/0.42 % (2114075)Instructions burned: 25 (million)
% 0.49/0.42 % (2114071)Instruction limit reached!
% 0.49/0.42 % (2114071)------------------------------
% 0.49/0.42 % (2114071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114071)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114071)Termination reason: Instruction limit
% 0.49/0.42 % (2114071)Termination phase: Property scanning
% 0.49/0.42 % (2114071)Time elapsed: 0.025 s
% 0.49/0.42 % (2114071)Peak memory usage: 12 MB
% 0.49/0.42 % (2114071)Instructions burned: 91 (million)
% 0.49/0.42 % (2114094)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=54234826:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.42 % (2114101)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=844469846:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.49/0.42 % (2114097)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=867573964:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.49/0.42 % (2114094)Instruction limit reached!
% 0.49/0.42 % (2114094)------------------------------
% 0.49/0.42 % (2114094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114094)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114094)Termination reason: Instruction limit
% 0.49/0.42 % (2114094)Termination phase: shuffling
% 0.49/0.42 % (2114094)Time elapsed: 0.002 s
% 0.49/0.42 % (2114098)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.42 % (2114094)Peak memory usage: 10 MB
% 0.49/0.42 % (2114094)Instructions burned: 3 (million)
% 0.49/0.42 % (2114101)Instruction limit reached!
% 0.49/0.42 % (2114101)------------------------------
% 0.49/0.42 % (2114101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114101)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114101)Termination reason: Instruction limit
% 0.49/0.42 % (2114101)Termination phase: shuffling
% 0.49/0.42 % (2114101)Time elapsed: 0.003 s
% 0.49/0.42 % (2114101)Peak memory usage: 10 MB
% 0.49/0.42 % (2114101)Instructions burned: 12 (million)
% 0.49/0.42 % (2114098)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1002208964:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.49/0.42 % (2114097)Instruction limit reached!
% 0.49/0.42 % (2114097)------------------------------
% 0.49/0.42 % (2114097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114097)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114097)Termination reason: Instruction limit
% 0.49/0.42 % (2114097)Termination phase: shuffling
% 0.49/0.42 % (2114097)Time elapsed: 0.006 s
% 0.49/0.42 % (2114097)Peak memory usage: 10 MB
% 0.49/0.42 % (2114097)Instructions burned: 11 (million)
% 0.49/0.42 % (2114098)Instruction limit reached!
% 0.49/0.42 % (2114098)------------------------------
% 0.49/0.42 % (2114098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114098)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114098)Termination reason: Instruction limit
% 0.49/0.42 % (2114098)Termination phase: shuffling
% 0.49/0.42 % (2114098)Time elapsed: 0.004 s
% 0.49/0.42 % (2114098)Peak memory usage: 10 MB
% 0.49/0.42 % (2114098)Instructions burned: 8 (million)
% 0.49/0.42 % (2114076)Instruction limit reached!
% 0.49/0.42 % (2114076)------------------------------
% 0.49/0.42 % (2114076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114076)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114076)Termination reason: Instruction limit
% 0.49/0.42 % (2114076)Termination phase: Property scanning
% 0.49/0.42 % (2114076)Time elapsed: 0.040 s
% 0.49/0.42 % (2114076)Peak memory usage: 12 MB
% 0.49/0.42 % (2114076)Instructions burned: 76 (million)
% 0.49/0.42 % (2114113)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=2259898102:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.49/0.42 % (2114111)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
% 0.49/0.42 % (2114111)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.42 % (2114111)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3846072356:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.49/0.42 % (2114117)lrs+10_1_si=on:cs=on:random_seed=542536996:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.49/0.42 % (2114119)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.49/0.42 % (2114119)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=2811344912:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.42 % (2114117)Instruction limit reached!
% 0.49/0.42 % (2114117)------------------------------
% 0.49/0.42 % (2114117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114117)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114117)Termination reason: Instruction limit
% 0.49/0.42 % (2114117)Termination phase: shuffling
% 0.49/0.42 % (2114117)Time elapsed: 0.004 s
% 0.49/0.42 % (2114117)Peak memory usage: 10 MB
% 0.49/0.42 % (2114117)Instructions burned: 8 (million)
% 0.49/0.42 % (2114121)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2735401561:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.49/0.42 % (2114119)Instruction limit reached!
% 0.49/0.42 % (2114119)------------------------------
% 0.49/0.42 % (2114119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114119)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114119)Termination reason: Instruction limit
% 0.49/0.42 % (2114119)Termination phase: shuffling
% 0.49/0.42 % (2114119)Time elapsed: 0.002 s
% 0.49/0.42 % (2114119)Peak memory usage: 10 MB
% 0.49/0.42 % (2114119)Instructions burned: 3 (million)
% 0.49/0.42 % (2114111)Instruction limit reached!
% 0.49/0.42 % (2114111)------------------------------
% 0.49/0.42 % (2114111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114111)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114111)Termination reason: Instruction limit
% 0.49/0.42 % (2114111)Termination phase: shuffling
% 0.49/0.42 % (2114111)Time elapsed: 0.014 s
% 0.49/0.42 % (2114111)Peak memory usage: 11 MB
% 0.49/0.42 % (2114111)Instructions burned: 28 (million)
% 0.49/0.42 % (2114113)Instruction limit reached!
% 0.49/0.42 % (2114113)------------------------------
% 0.49/0.42 % (2114113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114113)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114113)Termination reason: Instruction limit
% 0.49/0.42 % (2114113)Termination phase: Preprocessing 3
% 0.49/0.42 % (2114113)Time elapsed: 0.021 s
% 0.49/0.42 % (2114113)Peak memory usage: 11 MB
% 0.49/0.42 % (2114113)Instructions burned: 89 (million)
% 0.49/0.42 % (2114131)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1232067405:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.49/0.42 % (2114127)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=419562641:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.49/0.42 % (2114121)Instruction limit reached!
% 0.49/0.42 % (2114121)------------------------------
% 0.49/0.42 % (2114121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (2114121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (2114121)CaDiCaL version: 2.1.3
% 0.49/0.42 % (2114121)Termination reason: Instruction limit
% 0.49/0.42 % (2114121)Termination phase: Preprocessing 3
% 0.49/0.42 % (2114121)Time elapsed: 0.019 s
% 0.49/0.42 % (2114121)Peak memory usage: 11 MB
% 0.49/0.42 % (2114121)Instructions burned: 38 (million)
% 0.49/0.42 % (2114129)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1844104991:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.49/0.42 % (2114074) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2114056-2114074"...
% 0.49/0.42 % (2114130)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2309452023:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.49/0.42 % (2114077)Instruction limit reached!
% 0.49/0.42 % (2114077)------------------------------
% 0.49/0.42 % (2114077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.43 % (2114077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.43 % (2114077)CaDiCaL version: 2.1.3
% 0.49/0.43 % (2114077)Termination reason: Instruction limit
% 0.49/0.43 % (2114077)Termination phase: Saturation
% 0.49/0.43 % (2114077)Time elapsed: 0.083 s
% 0.49/0.43 % (2114077)Peak memory usage: 14 MB
% 0.49/0.43 % (2114077)Instructions burned: 157 (million)
% 0.49/0.43 % (2114074)...printing done.
% 0.49/0.43 % (2114074)Refutation found. Thanks to Tanya!
% 0.49/0.43 % SZS status Theorem for theBenchmark
% 0.49/0.43 % SZS output start Proof for theBenchmark
% 0.49/0.43 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.49/0.43 thf(type_def_6, type, set: $tType > $tType).
% 0.49/0.43 thf(type_def_7, type, e: $tType).
% 0.49/0.43 thf(type_def_8, type, a: $tType).
% 0.49/0.43 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.49/0.43 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.49/0.43 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.49/0.43 thf(func_def_2, type, top: !>[X0: $tType]:($o)).
% 0.49/0.43 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.49/0.43 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 0.49/0.43 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 0.49/0.43 thf(func_def_6, type, order_top: !>[X0: $tType]:($o)).
% 0.49/0.43 thf(func_def_7, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.49/0.43 thf(func_def_8, type, bNF_csquare: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ X0 > (X1 > X2) > (X3 > X2) > (X0 > X1) > (X0 > X3) > $o))).
% 0.49/0.43 thf(func_def_9, type, bNF_fstOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X0 @ X1))).
% 0.49/0.43 thf(func_def_10, type, bNF_pick_middlep: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > X1))).
% 0.49/0.43 thf(func_def_11, type, bNF_sndOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 0.49/0.43 thf(func_def_12, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2))).
% 0.49/0.43 thf(func_def_13, type, finite_Fpow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 0.49/0.43 thf(func_def_14, type, fun_in_rel: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > X1 > $o))).
% 0.49/0.43 thf(func_def_15, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.49/0.43 thf(func_def_16, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_17, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.49/0.43 thf(func_def_18, type, top_top: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_19, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.49/0.43 thf(func_def_20, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 0.49/0.43 thf(func_def_21, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.49/0.43 thf(func_def_22, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.49/0.43 thf(func_def_23, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.49/0.43 thf(func_def_24, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.49/0.43 thf(func_def_25, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.49/0.43 thf(func_def_26, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.49/0.43 thf(func_def_27, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.49/0.43 thf(func_def_28, type, domain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0))).
% 0.49/0.43 thf(func_def_29, type, range: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X1))).
% 0.49/0.43 thf(func_def_30, type, converse: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X1 @ X0))).
% 0.49/0.43 thf(func_def_31, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 0.49/0.43 thf(func_def_32, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.49/0.43 thf(func_def_33, type, relcompp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > $o))).
% 0.49/0.43 thf(func_def_34, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.49/0.43 thf(func_def_35, type, pow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 0.49/0.43 thf(func_def_36, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.49/0.43 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.49/0.43 thf(func_def_38, type, c: set @ product_prod @ set @ a @ (a > e)).
% 0.49/0.43 thf(func_def_39, type, a1: set @ a).
% 0.49/0.43 thf(func_def_40, type, a2: set @ a).
% 0.49/0.43 thf(func_def_41, type, a3: set @ a).
% 0.49/0.43 thf(func_def_42, type, b1: (a > e)).
% 0.49/0.43 thf(func_def_43, type, b2: (a > e)).
% 0.49/0.43 thf(func_def_44, type, b3: (a > e)).
% 0.49/0.43 thf(func_def_45, type, thesis: $o).
% 0.49/0.43 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.49/0.43 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.49/0.43 thf(func_def_54, type, vAND: ($o > $o > $o)).
% 0.49/0.43 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.49/0.43 thf(func_def_56, type, db3: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_57, type, db4: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.49/0.43 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.49/0.43 thf(func_def_60, type, db5: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_61, type, db6: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_62, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.49/0.43 thf(func_def_63, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.49/0.43 thf(func_def_64, type, sK2: !>[X0: $tType, X1: $tType]:((X1 > product_prod @ X0 @ X1 > X0))).
% 0.49/0.43 thf(func_def_65, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X1))).
% 0.49/0.43 thf(func_def_66, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X0))).
% 0.49/0.43 thf(func_def_67, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X4))).
% 0.49/0.43 thf(func_def_68, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X3))).
% 0.49/0.43 thf(func_def_69, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X2))).
% 0.49/0.43 thf(func_def_70, type, sK8: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.49/0.43 thf(func_def_71, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_72, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X1 @ X0 > X0))).
% 0.49/0.43 thf(func_def_73, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.49/0.43 thf(func_def_74, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.49/0.43 thf(func_def_75, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.49/0.43 thf(func_def_76, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > set @ X2) > product_prod @ X1 @ X0 > X2 > X1))).
% 0.49/0.43 thf(func_def_77, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > set @ X2) > product_prod @ X1 @ X0 > X2 > X0))).
% 0.49/0.43 thf(func_def_78, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X0))).
% 0.49/0.43 thf(func_def_79, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X2))).
% 0.49/0.43 thf(func_def_80, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X1))).
% 0.49/0.43 thf(func_def_81, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X3))).
% 0.49/0.43 thf(func_def_82, type, sK20: set @ a).
% 0.49/0.43 thf(func_def_83, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X0))).
% 0.49/0.43 thf(func_def_84, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X1))).
% 0.49/0.43 thf(func_def_85, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X2))).
% 0.49/0.43 thf(func_def_86, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ X1 > $o) > X1))).
% 0.49/0.43 thf(func_def_87, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ X1 > $o) > X4))).
% 0.49/0.43 thf(func_def_88, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ X1 > $o) > X5))).
% 0.49/0.43 thf(func_def_89, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ X1 > $o) > X0))).
% 0.49/0.43 thf(func_def_90, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ X1 > $o) > X3))).
% 0.49/0.43 thf(func_def_91, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X4 @ X1 > $o) > X2))).
% 0.49/0.43 thf(func_def_92, type, sK30: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_93, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > (X0 > X2 > X1) > product_prod @ X0 @ X2 > X0))).
% 0.49/0.43 thf(func_def_94, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > (X0 > X2 > X1) > product_prod @ X0 @ X2 > X2))).
% 0.49/0.43 thf(func_def_95, type, sK33: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X1 > X0) > set @ X1))).
% 0.49/0.43 thf(func_def_96, type, sK34: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X1 > X0))).
% 0.49/0.43 thf(func_def_97, type, sK35: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > product_prod @ X1 @ X0 > X1))).
% 0.49/0.43 thf(func_def_98, type, sK36: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > product_prod @ X1 @ X0 > X0))).
% 0.49/0.43 thf(func_def_99, type, sK37: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X0 > set @ X1 > X1))).
% 0.49/0.43 thf(func_def_100, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > (X1 > X0 > $o) > set @ X0 > X1))).
% 0.49/0.43 thf(func_def_101, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > (X1 > X0 > $o) > set @ X0 > X0))).
% 0.49/0.43 thf(func_def_102, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X3))).
% 0.49/0.43 thf(func_def_103, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X2))).
% 0.49/0.43 thf(func_def_104, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X4))).
% 0.49/0.43 thf(func_def_105, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X0))).
% 0.49/0.43 thf(func_def_106, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X5))).
% 0.49/0.43 thf(func_def_107, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X1))).
% 0.49/0.43 thf(func_def_108, type, sK46: !>[X0: $tType, X1: $tType]:((X0 > X1 > set @ product_prod @ X0 @ X1 > X1))).
% 0.49/0.43 thf(func_def_109, type, sK47: !>[X0: $tType, X1: $tType]:((X0 > X1 > set @ product_prod @ X0 @ X1 > X0))).
% 0.49/0.43 thf(func_def_110, type, sK48: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_111, type, sK49: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.49/0.43 thf(func_def_112, type, sK50: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_113, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X0 > set @ X1 > X1))).
% 0.49/0.43 thf(func_def_114, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X2 > X1 > $o) > X0 > (X1 > X0 > $o) > X1))).
% 0.49/0.43 thf(func_def_115, type, sK53: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X0 > X1 > $o) > X0))).
% 0.49/0.43 thf(func_def_116, type, sK54: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X0 > X1 > $o) > X1))).
% 0.49/0.43 thf(func_def_117, type, sK55: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.49/0.43 thf(func_def_118, type, sK56: !>[X0: $tType, X1: $tType]:(((set @ X0 > $o) > set @ X1 > (X1 > X0) > set @ X0))).
% 0.49/0.43 thf(func_def_119, type, sK57: !>[X0: $tType, X1: $tType]:(((set @ X0 > $o) > set @ X1 > (X1 > X0) > set @ X1))).
% 0.49/0.43 thf(func_def_120, type, sK58: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > X1))).
% 0.49/0.43 thf(func_def_121, type, sK59: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > set @ X0 > X0))).
% 0.49/0.43 thf(func_def_122, type, sK60: !>[X0: $tType, X1: $tType]:((set @ X0 > X1 > (X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_123, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0 > set @ X0))).
% 0.49/0.43 thf(func_def_124, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X6 @ X1 > $o) > X3))).
% 0.49/0.43 thf(func_def_125, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X6 @ X1 > $o) > X6))).
% 0.49/0.43 thf(func_def_126, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X6 @ X1 > $o) > X2))).
% 0.49/0.43 thf(func_def_127, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X6 @ X1 > $o) > X4))).
% 0.49/0.43 thf(func_def_128, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X6 @ X1 > $o) > X0))).
% 0.49/0.43 thf(func_def_129, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X6 @ X1 > $o) > X1))).
% 0.49/0.43 thf(func_def_130, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X6 @ X1 > $o) > X5))).
% 0.49/0.43 thf(func_def_131, type, sK69: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X0 @ X1 > X0))).
% 0.49/0.43 thf(func_def_132, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2))).
% 0.49/0.43 thf(func_def_133, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X3))).
% 0.49/0.43 thf(func_def_134, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X0))).
% 0.49/0.43 thf(func_def_135, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1))).
% 0.49/0.43 thf(func_def_136, type, sK74: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.49/0.43 thf(func_def_137, type, sK75: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.49/0.43 thf(func_def_138, type, sK76: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_139, type, sK77: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 0.49/0.43 thf(func_def_140, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X5))).
% 0.49/0.43 thf(func_def_141, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X0))).
% 0.49/0.43 thf(func_def_142, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X3))).
% 0.49/0.43 thf(func_def_143, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X4))).
% 0.49/0.43 thf(func_def_144, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X6))).
% 0.49/0.43 thf(func_def_145, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X2))).
% 0.49/0.43 thf(func_def_146, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X6 @ X4 > X1))).
% 0.49/0.43 thf(func_def_147, type, sK85: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.49/0.43 thf(func_def_148, type, sK86: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.49/0.43 thf(func_def_149, type, sK87: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 0.49/0.43 thf(func_def_150, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > $o) > (X2 > X1 > $o) > (X2 > X0 > $o) > X2))).
% 0.49/0.43 thf(func_def_151, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > $o) > (X2 > X1 > $o) > (X2 > X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_152, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > $o) > (X2 > X1 > $o) > (X2 > X0 > $o) > X1))).
% 0.49/0.43 thf(func_def_153, type, sK91: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 0.49/0.43 thf(func_def_154, type, sK92: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_155, type, sK93: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_156, type, sK94: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.49/0.43 thf(func_def_157, type, sK95: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X1 > X0))).
% 0.49/0.43 thf(func_def_158, type, sK96: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.49/0.43 thf(func_def_159, type, sK97: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.49/0.43 thf(func_def_160, type, sK98: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_161, type, sK99: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_162, type, sK100: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_163, type, sK101: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_164, type, sK102: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_165, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > set @ product_prod @ X2 @ X0 > product_prod @ X3 @ X1 > (X2 > X3) > X0))).
% 0.49/0.43 thf(func_def_166, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > set @ product_prod @ X2 @ X0 > product_prod @ X3 @ X1 > (X2 > X3) > X2))).
% 0.49/0.43 thf(func_def_167, type, sK105: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_168, type, sK106: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.49/0.43 thf(func_def_169, type, sK107: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X1))).
% 0.49/0.43 thf(func_def_170, type, sK108: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 0.49/0.43 thf(func_def_171, type, sK109: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.49/0.43 thf(func_def_172, type, sK110: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.49/0.43 thf(func_def_173, type, sK111: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_174, type, sK112: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.43 thf(func_def_175, type, sK113: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_176, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0 > (X1 > X0 > $o) > (X2 > X1 > $o) > X1))).
% 0.49/0.43 thf(func_def_177, type, sK115: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_178, type, sK116: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_179, type, sK117: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X1 > $o) > X1))).
% 0.49/0.43 thf(func_def_180, type, sK118: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X1 > $o) > X0))).
% 0.49/0.43 thf(func_def_181, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X3))).
% 0.49/0.43 thf(func_def_182, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X2))).
% 0.49/0.43 thf(func_def_183, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X1))).
% 0.49/0.43 thf(func_def_184, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X4))).
% 0.49/0.43 thf(func_def_185, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X0))).
% 0.49/0.43 thf(func_def_186, type, sK124: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X0 @ X1 > X1))).
% 0.49/0.43 thf(func_def_187, type, sK125: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X0 @ X1 > X0))).
% 0.49/0.43 thf(func_def_188, type, sK126: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.49/0.43 thf(func_def_189, type, sK127: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.49/0.43 thf(func_def_190, type, sK128: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_191, type, sK129: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 0.49/0.43 thf(func_def_192, type, sK130: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 0.49/0.43 thf(func_def_193, type, sK131: !>[X0: $tType, X1: $tType]:((X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.49/0.43 thf(func_def_194, type, sK132: !>[X0: $tType, X1: $tType]:((X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.49/0.43 thf(func_def_195, type, sK133: !>[X0: $tType]:(X0)).
% 0.49/0.43 thf(func_def_196, type, sK134: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.49/0.43 thf(func_def_197, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X1 > (X0 > X3) > (X3 > X1 > $o) > (X2 > X3 > $o) > X2 > X0))).
% 0.49/0.43 thf(func_def_198, type, sK136: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.49/0.43 thf(func_def_199, type, sK137: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.49/0.43 thf(func_def_200, type, sK138: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_201, type, sK139: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_202, type, sK140: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_203, type, sK141: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.49/0.43 thf(func_def_204, type, sK142: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_205, type, sK143: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.43 thf(func_def_206, type, sK144: !>[X0: $tType, X1: $tType]:((set @ X1 > X0 > (X1 > X0) > X1))).
% 0.49/0.43 thf(func_def_207, type, sK145: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.49/0.43 thf(func_def_208, type, sK146: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.49/0.43 thf(func_def_209, type, sK147: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1 > X0))).
% 0.49/0.43 thf(func_def_210, type, sK148: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.49/0.43 thf(func_def_211, type, sK149: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.49/0.43 thf(func_def_212, type, sK150: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.49/0.43 thf(func_def_213, type, vNOT: ($o > $o)).
% 0.49/0.43 thf(f2,axiom,(
% 0.49/0.43 ? [X0 : set @ a] : ((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c)) & (ord_less_eq @ set @ a @ a3 @ X0) & (ord_less_eq @ set @ a @ a1 @ X0) & (ord_less_eq @ set @ a @ a2 @ X0))),
% 0.49/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062)).
% 0.49/0.43 thf(f271,axiom,(
% 0.49/0.43 ! [X0 : set @ a] : ((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c)) => ((ord_less_eq @ set @ a @ a1 @ X0) => ((ord_less_eq @ set @ a @ a2 @ X0) => ((ord_less_eq @ set @ a @ a3 @ X0) => thesis))))),
% 0.49/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.49/0.43 thf(f272,conjecture,(
% 0.49/0.43 thesis),
% 0.49/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.49/0.43 thf(f273,negated_conjecture,(
% 0.49/0.43 ~thesis),
% 0.49/0.43 inference(negated_conjecture,[status(cth)],[f272])).
% 0.49/0.43 thf(f304,plain,(
% 0.49/0.43 ! [X0 : set @ a] : ((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c)) => ((ord_less_eq @ set @ a @ a1 @ X0) => ((ord_less_eq @ set @ a @ a2 @ X0) => ((ord_less_eq @ set @ a @ a3 @ X0) => thesis))))),
% 0.49/0.43 inference(rectify,[],[f271])).
% 0.49/0.43 thf(f305,plain,(
% 0.49/0.43 ! [X0 : set @ a] : ((((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true) => ((((ord_less_eq @ set @ a @ a1 @ X0)) = $true) => ((((ord_less_eq @ set @ a @ a2 @ X0)) = $true) => ((((ord_less_eq @ set @ a @ a3 @ X0)) = $true) => (thesis = $true)))))),
% 0.49/0.43 inference(fool_elimination,[],[f304])).
% 0.49/0.43 thf(f537,plain,(
% 0.49/0.43 ? [X0 : set @ a] : ((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c)) & (ord_less_eq @ set @ a @ a3 @ X0) & (ord_less_eq @ set @ a @ a1 @ X0) & (ord_less_eq @ set @ a @ a2 @ X0))),
% 0.49/0.43 inference(rectify,[],[f2])).
% 0.49/0.43 thf(f538,plain,(
% 0.49/0.43 ? [X0 : set @ a] : ((((ord_less_eq @ set @ a @ a2 @ X0)) = $true) & (((ord_less_eq @ set @ a @ a3 @ X0)) = $true) & (((ord_less_eq @ set @ a @ a1 @ X0)) = $true) & (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true))),
% 0.49/0.43 inference(fool_elimination,[],[f537])).
% 0.49/0.43 thf(f615,plain,(
% 0.49/0.43 ~thesis),
% 0.49/0.43 inference(rectify,[],[f273])).
% 0.49/0.43 thf(f616,plain,(
% 0.49/0.43 ~ (thesis = $true)),
% 0.49/0.43 inference(fool_elimination,[],[f615])).
% 0.49/0.43 thf(f746,plain,(
% 0.49/0.43 (thesis != $true)),
% 0.49/0.43 inference(flattening,[],[f616])).
% 0.49/0.43 thf(f933,plain,(
% 0.49/0.43 ! [X0 : set @ a] : (((((thesis = $true) | (((ord_less_eq @ set @ a @ a3 @ X0)) != $true)) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true)) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true)) | (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true))),
% 0.49/0.43 inference(ennf_transformation,[],[f305])).
% 0.49/0.43 thf(f934,plain,(
% 0.49/0.43 ! [X0 : set @ a] : ((((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true) | (thesis = $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a3 @ X0)) != $true))),
% 0.49/0.43 inference(flattening,[],[f933])).
% 0.49/0.43 thf(f1014,plain,(
% 0.49/0.43 (((ord_less_eq @ set @ a @ a2 @ sK20)) = $true) & (((ord_less_eq @ set @ a @ a3 @ sK20)) = $true) & ($true = ((ord_less_eq @ set @ a @ a1 @ sK20))) & ($true = ((member @ set @ a @ sK20 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))))),
% 0.49/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f538])).
% 0.49/0.43 thf(f1299,plain,(
% 0.49/0.43 ($true = ((member @ set @ a @ sK20 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))))),
% 0.49/0.43 inference(cnf_transformation,[],[f1014])).
% 0.49/0.43 thf(f1300,plain,(
% 0.49/0.43 ($true = ((ord_less_eq @ set @ a @ a1 @ sK20)))),
% 0.49/0.43 inference(cnf_transformation,[],[f1014])).
% 0.49/0.43 thf(f1301,plain,(
% 0.49/0.43 (((ord_less_eq @ set @ a @ a3 @ sK20)) = $true)),
% 0.49/0.43 inference(cnf_transformation,[],[f1014])).
% 0.49/0.43 thf(f1302,plain,(
% 0.49/0.43 (((ord_less_eq @ set @ a @ a2 @ sK20)) = $true)),
% 0.49/0.43 inference(cnf_transformation,[],[f1014])).
% 0.49/0.43 thf(f1383,plain,(
% 0.49/0.43 (thesis != $true)),
% 0.49/0.43 inference(cnf_transformation,[],[f746])).
% 0.49/0.43 thf(f1500,plain,(
% 0.49/0.43 ( ! [X0 : set @ a] : ((((ord_less_eq @ set @ a @ a3 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true) | (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true) | (thesis = $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true)) )),
% 0.49/0.43 inference(cnf_transformation,[],[f934])).
% 0.49/0.43 thf(f1775,definition,(
% 0.49/0.43 spl151_5 <=> ($true = ((member @ set @ a @ sK20 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))))),
% 0.49/0.43 introduced(definition,[new_symbols(definition,[spl151_5])],[avatar_definition])).
% 0.49/0.43 thf(f1777,plain,(
% 0.49/0.43 ($true = ((member @ set @ a @ sK20 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c)))) | ~spl151_5),
% 0.49/0.43 inference(avatar_component_clause,[],[f1775])).
% 0.49/0.43 thf(f1778,plain,(
% 0.49/0.43 spl151_5),
% 0.49/0.43 inference(avatar_split_clause,[],[f1299,f1775])).
% 0.49/0.43 thf(f1794,definition,(
% 0.49/0.43 spl151_9 <=> (((ord_less_eq @ set @ a @ a3 @ sK20)) = $true)),
% 0.49/0.43 introduced(definition,[new_symbols(definition,[spl151_9])],[avatar_definition])).
% 0.49/0.43 thf(f1796,plain,(
% 0.49/0.43 (((ord_less_eq @ set @ a @ a3 @ sK20)) = $true) | ~spl151_9),
% 0.49/0.43 inference(avatar_component_clause,[],[f1794])).
% 0.49/0.43 thf(f1797,plain,(
% 0.49/0.43 spl151_9),
% 0.49/0.43 inference(avatar_split_clause,[],[f1301,f1794])).
% 0.49/0.43 thf(f1809,definition,(
% 0.49/0.43 spl151_12 <=> (thesis = $true)),
% 0.49/0.43 introduced(definition,[new_symbols(definition,[spl151_12])],[avatar_definition])).
% 0.49/0.43 thf(f1812,plain,(
% 0.49/0.43 ~spl151_12),
% 0.49/0.43 inference(avatar_split_clause,[],[f1383,f1809])).
% 0.49/0.43 thf(f1843,definition,(
% 0.49/0.43 spl151_19 <=> ($true = ((ord_less_eq @ set @ a @ a1 @ sK20)))),
% 0.49/0.43 introduced(definition,[new_symbols(definition,[spl151_19])],[avatar_definition])).
% 0.49/0.43 thf(f1845,plain,(
% 0.49/0.43 ($true = ((ord_less_eq @ set @ a @ a1 @ sK20))) | ~spl151_19),
% 0.49/0.43 inference(avatar_component_clause,[],[f1843])).
% 0.49/0.43 thf(f1846,plain,(
% 0.49/0.43 spl151_19),
% 0.49/0.43 inference(avatar_split_clause,[],[f1300,f1843])).
% 0.49/0.43 thf(f1848,definition,(
% 0.49/0.43 spl151_20 <=> (((ord_less_eq @ set @ a @ a2 @ sK20)) = $true)),
% 0.49/0.43 introduced(definition,[new_symbols(definition,[spl151_20])],[avatar_definition])).
% 0.49/0.43 thf(f1850,plain,(
% 0.49/0.43 (((ord_less_eq @ set @ a @ a2 @ sK20)) = $true) | ~spl151_20),
% 0.49/0.43 inference(avatar_component_clause,[],[f1848])).
% 0.49/0.43 thf(f1851,plain,(
% 0.49/0.43 spl151_20),
% 0.49/0.43 inference(avatar_split_clause,[],[f1302,f1848])).
% 0.49/0.43 thf(f1853,definition,(
% 0.49/0.43 spl151_21 <=> ! [X0 : set @ a] : ((((ord_less_eq @ set @ a @ a3 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true) | (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true))),
% 0.49/0.43 introduced(definition,[new_symbols(definition,[spl151_21])],[avatar_definition])).
% 0.49/0.43 thf(f1854,plain,(
% 0.49/0.43 ( ! [X0 : set @ a] : ((((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true) | (((ord_less_eq @ set @ a @ a3 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true)) ) | ~spl151_21),
% 0.49/0.43 inference(avatar_component_clause,[],[f1853])).
% 0.49/0.43 thf(f1855,plain,(
% 0.49/0.43 spl151_12 | spl151_21),
% 0.49/0.43 inference(avatar_split_clause,[],[f1500,f1853,f1809])).
% 0.49/0.43 thf(f2039,plain,(
% 0.49/0.43 (((ord_less_eq @ set @ a @ a2 @ sK20)) != $true) | (((ord_less_eq @ set @ a @ a3 @ sK20)) != $true) | ($true != $true) | ($true != ((ord_less_eq @ set @ a @ a1 @ sK20))) | (~spl151_5 | ~spl151_21)),
% 0.49/0.43 inference(superposition,[],[f1854,f1777])).
% 0.49/0.43 thf(f2040,plain,(
% 0.49/0.43 (((ord_less_eq @ set @ a @ a2 @ sK20)) != $true) | (((ord_less_eq @ set @ a @ a3 @ sK20)) != $true) | ($true != ((ord_less_eq @ set @ a @ a1 @ sK20))) | (~spl151_5 | ~spl151_21)),
% 0.49/0.43 inference(trivial_inequality_removal,[],[f2039])).
% 0.49/0.43 thf(f2041,plain,(
% 0.49/0.43 ($true != ((ord_less_eq @ set @ a @ a1 @ sK20))) | (((ord_less_eq @ set @ a @ a3 @ sK20)) != $true) | (~spl151_5 | ~spl151_20 | ~spl151_21)),
% 0.49/0.43 inference(forward_subsumption_resolution,[],[f2040,f1850])).
% 0.49/0.43 thf(f2042,plain,(
% 0.49/0.43 (((ord_less_eq @ set @ a @ a3 @ sK20)) != $true) | (~spl151_5 | ~spl151_19 | ~spl151_20 | ~spl151_21)),
% 0.49/0.43 inference(forward_subsumption_resolution,[],[f2041,f1845])).
% 0.49/0.43 thf(f2043,plain,(
% 0.49/0.43 $false | (~spl151_5 | ~spl151_9 | ~spl151_19 | ~spl151_20 | ~spl151_21)),
% 0.49/0.43 inference(forward_subsumption_resolution,[],[f2042,f1796])).
% 0.49/0.43 thf(f2044,plain,(
% 0.49/0.43 ~spl151_5 | ~spl151_9 | ~spl151_19 | ~spl151_20 | ~spl151_21),
% 0.49/0.43 inference(avatar_contradiction_clause,[],[f2043])).
% 0.49/0.43 cnf(s4, plain, spl151_5, inference(sat_conversion,[],[f1778])).
% 0.49/0.43 cnf(s7, plain, spl151_9, inference(sat_conversion,[],[f1797])).
% 0.49/0.43 cnf(s10, plain, ~spl151_12, inference(sat_conversion,[],[f1812])).
% 0.49/0.43 cnf(s16, plain, spl151_19, inference(sat_conversion,[],[f1846])).
% 0.49/0.43 cnf(s17, plain, spl151_20, inference(sat_conversion,[],[f1851])).
% 0.49/0.43 cnf(s18, plain, spl151_12 | spl151_21, inference(sat_conversion,[],[f1855])).
% 0.49/0.43 cnf(s29, plain, ~spl151_5 | ~spl151_9 | ~spl151_19 | ~spl151_20 | ~spl151_21, inference(sat_conversion,[],[f2044])).
% 0.49/0.43 cnf(s31, plain, spl151_21, inference(rat,[],[s18,s10])).
% 0.49/0.43 cnf(s32, plain, ~spl151_5, inference(rat,[],[s29,s31,s17,s16,s7])).
% 0.49/0.43 cnf(s33, plain, $false, inference(rat,[],[s4,s32])).
% 0.49/0.43 thf(f2045,plain,(
% 0.49/0.43 $false),
% 0.49/0.43 inference(avatar_sat_refutation,[],[s33])).
% 0.49/0.43 % SZS output end Proof for theBenchmark
% 0.49/0.43 % (2114074)------------------------------
% 0.49/0.43 % (2114074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.43 % (2114074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.43 % (2114074)CaDiCaL version: 2.1.3
% 0.49/0.43 % (2114074)Termination reason: Refutation
% 0.49/0.43 % (2114074)Time elapsed: 0.085 s
% 0.49/0.43 % (2114074)Peak memory usage: 15 MB
% 0.49/0.43 % (2114074)Instructions burned: 161 (million)
% 0.49/0.43 % (2114056)Success in time 0.145 s
% 0.49/0.43 % Vampire exiting
%------------------------------------------------------------------------------