%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP179^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:08:41 AM UTC 2026
% Result : Theorem 1.41s 0.52s
% Output : Refutation 1.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP179^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 20:12:51 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.43 % (1755615)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.59/0.43 % (1755621)lrs+10_16_si=on:nwc=1.5:random_seed=4195373414:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.59/0.43 % (1755626)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.59/0.43 % (1755626)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
% 0.59/0.43 % (1755621)Instruction limit reached!
% 0.59/0.43 % (1755621)------------------------------
% 0.59/0.43 % (1755621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.43 % (1755621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.43 % (1755621)CaDiCaL version: 2.1.3
% 0.59/0.43 % (1755621)Termination reason: Instruction limit
% 0.59/0.43 % (1755621)Termination phase: Property scanning
% 0.59/0.43 % (1755621)Time elapsed: 0.006 s
% 0.59/0.43 % (1755621)Peak memory usage: 10 MB
% 0.59/0.43 % (1755621)Instructions burned: 22 (million)
% 0.59/0.43 % (1755622)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4216525048:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.59/0.43 % (1755623)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=4024260969: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)
% 0.59/0.43 % (1755624)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=86981232:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.59/0.43 % (1755626)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=1301887030:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.59/0.43 % (1755625)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=990964725:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.59/0.43 % (1755622)Instruction limit reached!
% 0.59/0.43 % (1755622)------------------------------
% 0.59/0.43 % (1755622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.43 % (1755622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.43 % (1755622)CaDiCaL version: 2.1.3
% 0.59/0.43 % (1755622)Termination reason: Instruction limit
% 0.59/0.43 % (1755622)Termination phase: shuffling
% 0.59/0.43 % (1755622)Time elapsed: 0.003 s
% 0.59/0.43 % (1755622)Peak memory usage: 10 MB
% 0.59/0.43 % (1755622)Instructions burned: 5 (million)
% 0.59/0.43 % (1755628)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1827577128:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.59/0.43 % (1755628)Instruction limit reached!
% 0.59/0.43 % (1755628)------------------------------
% 0.59/0.43 % (1755628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.43 % (1755628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.43 % (1755628)CaDiCaL version: 2.1.3
% 0.59/0.43 % (1755628)Termination reason: Instruction limit
% 0.59/0.43 % (1755628)Termination phase: shuffling
% 0.59/0.43 % (1755628)Time elapsed: 0.001 s
% 0.59/0.43 % (1755628)Peak memory usage: 10 MB
% 0.59/0.43 % (1755628)Instructions burned: 4 (million)
% 0.59/0.43 % (1755620)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1343343258:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.59/0.43 % (1755624)Instruction limit reached!
% 0.59/0.43 % (1755624)------------------------------
% 0.59/0.43 % (1755624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.43 % (1755624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.43 % (1755624)CaDiCaL version: 2.1.3
% 0.59/0.43 % (1755624)Termination reason: Instruction limit
% 0.59/0.43 % (1755624)Termination phase: Property scanning
% 0.59/0.43 % (1755624)Time elapsed: 0.011 s
% 0.59/0.43 % (1755624)Peak memory usage: 10 MB
% 0.59/0.43 % (1755624)Instructions burned: 25 (million)
% 0.59/0.43 % (1755636)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.46 % (1755636)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=965045603:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.59/0.46 % (1755634)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=128094692:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.59/0.46 % (1755636)Instruction limit reached!
% 0.59/0.46 % (1755636)------------------------------
% 0.59/0.46 % (1755636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1755636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1755636)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1755636)Termination reason: Instruction limit
% 0.59/0.46 % (1755636)Termination phase: shuffling
% 0.59/0.46 % (1755636)Time elapsed: 0.002 s
% 0.59/0.46 % (1755636)Peak memory usage: 10 MB
% 0.59/0.46 % (1755636)Instructions burned: 10 (million)
% 0.59/0.46 % (1755634)Instruction limit reached!
% 0.59/0.46 % (1755634)------------------------------
% 0.59/0.46 % (1755634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1755634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1755634)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1755634)Termination reason: Instruction limit
% 0.59/0.46 % (1755634)Termination phase: shuffling
% 0.59/0.46 % (1755634)Time elapsed: 0.003 s
% 0.59/0.46 % (1755634)Peak memory usage: 10 MB
% 0.59/0.46 % (1755634)Instructions burned: 6 (million)
% 0.59/0.46 % (1755638)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3943065082:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.59/0.46 % (1755641)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
% 0.59/0.46 % (1755641)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.46 % (1755641)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=552436427:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.59/0.46 % (1755625)Instruction limit reached!
% 0.59/0.46 % (1755625)------------------------------
% 0.59/0.46 % (1755625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1755625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1755625)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1755625)Termination reason: Instruction limit
% 0.59/0.46 % (1755625)Termination phase: Function definition elimination
% 0.59/0.46 % (1755625)Time elapsed: 0.035 s
% 0.59/0.46 % (1755625)Peak memory usage: 12 MB
% 0.59/0.46 % (1755625)Instructions burned: 75 (million)
% 0.59/0.46 % (1755638)Instruction limit reached!
% 0.59/0.46 % (1755638)------------------------------
% 0.59/0.46 % (1755638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1755638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1755638)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1755638)Termination reason: Instruction limit
% 0.59/0.46 % (1755638)Termination phase: shuffling
% 0.59/0.46 % (1755638)Time elapsed: 0.006 s
% 0.59/0.46 % (1755638)Peak memory usage: 10 MB
% 0.59/0.46 % (1755638)Instructions burned: 13 (million)
% 0.59/0.46 % (1755641)Instruction limit reached!
% 0.59/0.46 % (1755641)------------------------------
% 0.59/0.46 % (1755641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1755641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1755641)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1755641)Termination reason: Instruction limit
% 0.59/0.46 % (1755641)Termination phase: shuffling
% 0.59/0.46 % (1755641)Time elapsed: 0.007 s
% 0.59/0.46 % (1755641)Peak memory usage: 10 MB
% 0.59/0.46 % (1755641)Instructions burned: 30 (million)
% 0.59/0.46 % (1755642)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=2134666844:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.59/0.46 % (1755646)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.59/0.49 % (1755645)lrs+10_1_si=on:cs=on:random_seed=628000111:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.59/0.49 % (1755646)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=2209138730:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.59/0.49 % (1755645)Instruction limit reached!
% 0.59/0.49 % (1755645)------------------------------
% 0.59/0.49 % (1755645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.49 % (1755645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.49 % (1755645)CaDiCaL version: 2.1.3
% 0.59/0.49 % (1755645)Termination reason: Instruction limit
% 0.59/0.49 % (1755645)Termination phase: shuffling
% 0.59/0.49 % (1755645)Time elapsed: 0.004 s
% 0.59/0.49 % (1755645)Peak memory usage: 10 MB
% 0.59/0.49 % (1755645)Instructions burned: 8 (million)
% 0.59/0.49 % (1755646)Instruction limit reached!
% 0.59/0.49 % (1755646)------------------------------
% 0.59/0.49 % (1755646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.49 % (1755646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.49 % (1755646)CaDiCaL version: 2.1.3
% 0.59/0.49 % (1755646)Termination reason: Instruction limit
% 0.59/0.49 % (1755646)Termination phase: shuffling
% 0.59/0.49 % (1755646)Time elapsed: 0.002 s
% 0.59/0.49 % (1755646)Peak memory usage: 10 MB
% 0.59/0.49 % (1755646)Instructions burned: 3 (million)
% 0.59/0.49 % (1755647)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2924022006:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.59/0.49 % (1755626)Instruction limit reached!
% 0.59/0.49 % (1755626)------------------------------
% 0.59/0.49 % (1755626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.49 % (1755626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.49 % (1755626)CaDiCaL version: 2.1.3
% 0.59/0.49 % (1755626)Termination reason: Instruction limit
% 0.59/0.49 % (1755626)Termination phase: Saturation
% 0.59/0.49 % (1755626)Time elapsed: 0.079 s
% 0.59/0.49 % (1755626)Peak memory usage: 14 MB
% 0.59/0.49 % (1755626)Instructions burned: 158 (million)
% 0.59/0.49 % (1755652)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=672623941:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.59/0.49 % (1755651)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=690841908:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.59/0.49 % (1755647)Instruction limit reached!
% 0.59/0.49 % (1755647)------------------------------
% 0.59/0.49 % (1755647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.49 % (1755647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.49 % (1755647)CaDiCaL version: 2.1.3
% 0.59/0.49 % (1755647)Termination reason: Instruction limit
% 0.59/0.49 % (1755647)Termination phase: Preprocessing 3
% 0.59/0.49 % (1755647)Time elapsed: 0.018 s
% 0.59/0.49 % (1755647)Peak memory usage: 11 MB
% 0.59/0.49 % (1755647)Instructions burned: 39 (million)
% 0.59/0.49 % (1755642)Instruction limit reached!
% 0.59/0.49 % (1755642)------------------------------
% 0.59/0.49 % (1755642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.49 % (1755642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.49 % (1755642)CaDiCaL version: 2.1.3
% 0.59/0.49 % (1755642)Termination reason: Instruction limit
% 0.59/0.49 % (1755642)Termination phase: Property scanning
% 0.59/0.49 % (1755642)Time elapsed: 0.036 s
% 0.59/0.49 % (1755642)Peak memory usage: 11 MB
% 0.59/0.49 % (1755642)Instructions burned: 86 (million)
% 0.59/0.49 % (1755620)Instruction limit reached!
% 0.59/0.49 % (1755620)------------------------------
% 0.59/0.49 % (1755620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.49 % (1755620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.49 % (1755620)CaDiCaL version: 2.1.3
% 0.59/0.49 % (1755620)Termination reason: Instruction limit
% 0.59/0.49 % (1755620)Termination phase: Property scanning
% 0.59/0.49 % (1755620)Time elapsed: 0.071 s
% 0.59/0.49 % (1755620)Peak memory usage: 12 MB
% 0.59/0.49 % (1755620)Instructions burned: 87 (million)
% 0.59/0.49 % (1755652)Instruction limit reached!
% 0.59/0.49 % (1755652)------------------------------
% 1.41/0.52 % (1755652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755652)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755652)Termination reason: Instruction limit
% 1.41/0.52 % (1755652)Termination phase: Property scanning
% 1.41/0.52 % (1755652)Time elapsed: 0.011 s
% 1.41/0.52 % (1755652)Peak memory usage: 10 MB
% 1.41/0.52 % (1755652)Instructions burned: 26 (million)
% 1.41/0.52 % (1755659)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=367163671: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)
% 1.41/0.52 % (1755659)Instruction limit reached!
% 1.41/0.52 % (1755659)------------------------------
% 1.41/0.52 % (1755659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755659)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755659)Termination reason: Instruction limit
% 1.41/0.52 % (1755659)Termination phase: shuffling
% 1.41/0.52 % (1755659)Time elapsed: 0.001 s
% 1.41/0.52 % (1755659)Peak memory usage: 10 MB
% 1.41/0.52 % (1755659)Instructions burned: 6 (million)
% 1.41/0.52 % (1755656)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=810974789:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.41/0.52 % (1755657)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4272613552:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.41/0.52 % (1755658)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2605303296:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.41/0.52 % (1755656)Instruction limit reached!
% 1.41/0.52 % (1755656)------------------------------
% 1.41/0.52 % (1755656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755656)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755656)Termination reason: Instruction limit
% 1.41/0.52 % (1755656)Termination phase: shuffling
% 1.41/0.52 % (1755656)Time elapsed: 0.007 s
% 1.41/0.52 % (1755656)Peak memory usage: 10 MB
% 1.41/0.52 % (1755656)Instructions burned: 15 (million)
% 1.41/0.52 % (1755660)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3403336227:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.41/0.52 % (1755658)Instruction limit reached!
% 1.41/0.52 % (1755658)------------------------------
% 1.41/0.52 % (1755658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755658)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755658)Termination reason: Instruction limit
% 1.41/0.52 % (1755658)Termination phase: shuffling
% 1.41/0.52 % (1755658)Time elapsed: 0.007 s
% 1.41/0.52 % (1755658)Peak memory usage: 10 MB
% 1.41/0.52 % (1755658)Instructions burned: 17 (million)
% 1.41/0.52 % (1755662)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1461696705:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.41/0.52 % (1755668)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
% 1.41/0.52 % (1755668)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.41/0.52 % (1755668)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=176351957:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.41/0.52 % (1755660)Instruction limit reached!
% 1.41/0.52 % (1755660)------------------------------
% 1.41/0.52 % (1755660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755660)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755660)Termination reason: Instruction limit
% 1.41/0.52 % (1755660)Termination phase: shuffling
% 1.41/0.52 % (1755660)Time elapsed: 0.012 s
% 1.41/0.52 % (1755660)Peak memory usage: 11 MB
% 1.41/0.52 % (1755660)Instructions burned: 26 (million)
% 1.41/0.52 % (1755666)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3275539231:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.41/0.52 % (1755668)Instruction limit reached!
% 1.41/0.52 % (1755668)------------------------------
% 1.41/0.52 % (1755668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755668)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755668)Termination reason: Instruction limit
% 1.41/0.52 % (1755668)Termination phase: shuffling
% 1.41/0.52 % (1755668)Time elapsed: 0.003 s
% 1.41/0.52 % (1755668)Peak memory usage: 10 MB
% 1.41/0.52 % (1755668)Instructions burned: 14 (million)
% 1.41/0.52 % (1755662)Instruction limit reached!
% 1.41/0.52 % (1755662)------------------------------
% 1.41/0.52 % (1755662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755662)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755662)Termination reason: Instruction limit
% 1.41/0.52 % (1755662)Termination phase: Property scanning
% 1.41/0.52 % (1755662)Time elapsed: 0.011 s
% 1.41/0.52 % (1755662)Peak memory usage: 10 MB
% 1.41/0.52 % (1755662)Instructions burned: 25 (million)
% 1.41/0.52 % (1755673)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=3378887041:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.41/0.52 % (1755671)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.41/0.52 % (1755671)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=2598032379:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.41/0.52 % (1755673)Instruction limit reached!
% 1.41/0.52 % (1755673)------------------------------
% 1.41/0.52 % (1755673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755673)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755673)Termination reason: Instruction limit
% 1.41/0.52 % (1755673)Termination phase: shuffling
% 1.41/0.52 % (1755673)Time elapsed: 0.008 s
% 1.41/0.52 % (1755673)Peak memory usage: 10 MB
% 1.41/0.52 % (1755673)Instructions burned: 35 (million)
% 1.41/0.52 % (1755671)Instruction limit reached!
% 1.41/0.52 % (1755671)------------------------------
% 1.41/0.52 % (1755671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755671)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755671)Termination reason: Instruction limit
% 1.41/0.52 % (1755671)Termination phase: shuffling
% 1.41/0.52 % (1755671)Time elapsed: 0.005 s
% 1.41/0.52 % (1755671)Peak memory usage: 10 MB
% 1.41/0.52 % (1755671)Instructions burned: 10 (million)
% 1.41/0.52 % (1755674)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3540667340:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.41/0.52 % (1755666)Instruction limit reached!
% 1.41/0.52 % (1755666)------------------------------
% 1.41/0.52 % (1755666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755674)Instruction limit reached!
% 1.41/0.52 % (1755674)------------------------------
% 1.41/0.52 % (1755674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755666)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755666)Termination reason: Instruction limit
% 1.41/0.52 % (1755666)Termination phase: Property scanning
% 1.41/0.52 % (1755666)Time elapsed: 0.027 s
% 1.41/0.52 % (1755674)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755674)Termination reason: Instruction limit
% 1.41/0.52 % (1755674)Termination phase: shuffling
% 1.41/0.52 % (1755666)Peak memory usage: 11 MB
% 1.41/0.52 % (1755674)Time elapsed: 0.004 s
% 1.41/0.52 % (1755674)Peak memory usage: 10 MB
% 1.41/0.52 % (1755666)Instructions burned: 61 (million)
% 1.41/0.52 % (1755674)Instructions burned: 8 (million)
% 1.41/0.52 % (1755677)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3014324980:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.41/0.52 % (1755677)Instruction limit reached!
% 1.41/0.52 % (1755677)------------------------------
% 1.41/0.52 % (1755677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755677)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755677)Termination reason: Instruction limit
% 1.41/0.52 % (1755677)Termination phase: shuffling
% 1.41/0.52 % (1755677)Time elapsed: 0.010 s
% 1.41/0.52 % (1755677)Peak memory usage: 10 MB
% 1.41/0.52 % (1755677)Instructions burned: 26 (million)
% 1.41/0.52 % (1755678)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2855446353:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.41/0.52 % (1755623) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1755615-1755623"...
% 1.41/0.52 % (1755680)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4220778846:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.41/0.52 % (1755681)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=766943679:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.41/0.52 % (1755623)...printing done.
% 1.41/0.52 % (1755678)Instruction limit reached!
% 1.41/0.52 % (1755678)------------------------------
% 1.41/0.52 % (1755678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755678)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755678)Termination reason: Instruction limit
% 1.41/0.52 % (1755678)Termination phase: Property scanning
% 1.41/0.52 % (1755678)Time elapsed: 0.009 s
% 1.41/0.52 % (1755678)Peak memory usage: 10 MB
% 1.41/0.52 % (1755678)Instructions burned: 21 (million)
% 1.41/0.52 % (1755684)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4167440624:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.41/0.52 % (1755623)Refutation found. Thanks to Tanya!
% 1.41/0.52 % SZS status Theorem for theBenchmark
% 1.41/0.52 % SZS output start Proof for theBenchmark
% 1.41/0.52 thf(type_def_5, type, set_Pr1355257963at_nat: $tType).
% 1.41/0.52 thf(type_def_6, type, set_Pr1429673827um_a_b: $tType).
% 1.41/0.52 thf(type_def_7, type, set_Pr2065572323um_a_b: $tType).
% 1.41/0.52 thf(type_def_8, type, set_Pr1558970842um_a_b: $tType).
% 1.41/0.52 thf(type_def_9, type, set_Pr1121389018um_a_b: $tType).
% 1.41/0.52 thf(type_def_10, type, produc1733247354um_a_b: $tType).
% 1.41/0.52 thf(type_def_11, type, produc1681803642um_a_b: $tType).
% 1.41/0.52 thf(type_def_12, type, produc1871334759_a_nat: $tType).
% 1.41/0.52 thf(type_def_13, type, labele498606060at_nat: $tType).
% 1.41/0.52 thf(type_def_14, type, set_Pr304595758um_a_b: $tType).
% 1.41/0.52 thf(type_def_15, type, set_Pr409224873um_a_b: $tType).
% 1.41/0.52 thf(type_def_16, type, set_Pr45173959um_a_b: $tType).
% 1.41/0.52 thf(type_def_17, type, set_Pr689416536at_nat: $tType).
% 1.41/0.52 thf(type_def_18, type, set_Pr1134469976at_nat: $tType).
% 1.41/0.52 thf(type_def_19, type, labele1191284958um_a_b: $tType).
% 1.41/0.52 thf(type_def_20, type, produc1963079155um_a_b: $tType).
% 1.41/0.52 thf(type_def_21, type, produc1918750183um_a_b: $tType).
% 1.41/0.52 thf(type_def_22, type, set_Pr55236280um_a_b: $tType).
% 1.41/0.52 thf(type_def_23, type, set_Pr326391507um_a_b: $tType).
% 1.41/0.52 thf(type_def_24, type, set_Pr386468381um_a_b: $tType).
% 1.41/0.52 thf(type_def_25, type, labele261019144um_a_b: $tType).
% 1.41/0.52 thf(type_def_26, type, produc1003469085um_a_b: $tType).
% 1.41/0.52 thf(type_def_27, type, produc1546082365um_a_b: $tType).
% 1.41/0.52 thf(type_def_28, type, set_Pr1783309276um_a_b: $tType).
% 1.41/0.52 thf(type_def_29, type, set_Pr507214050_b_nat: $tType).
% 1.41/0.52 thf(type_def_30, type, set_Pr653770722um_a_b: $tType).
% 1.41/0.52 thf(type_def_31, type, set_Pr1155046920um_a_b: $tType).
% 1.41/0.52 thf(type_def_32, type, set_Pr1647387645at_nat: $tType).
% 1.41/0.52 thf(type_def_33, type, produc323101606um_a_b: $tType).
% 1.41/0.52 thf(type_def_34, type, produc585753260um_a_b: $tType).
% 1.41/0.52 thf(type_def_35, type, produc1032616263at_nat: $tType).
% 1.41/0.52 thf(type_def_36, type, set_Pr1994339542um_a_b: $tType).
% 1.41/0.52 thf(type_def_37, type, set_Pr1902304780_b_nat: $tType).
% 1.41/0.52 thf(type_def_38, type, set_Pr195945996um_a_b: $tType).
% 1.41/0.52 thf(type_def_39, type, set_Pr1618094130um_a_b: $tType).
% 1.41/0.52 thf(type_def_40, type, labele431970251um_a_b: $tType).
% 1.41/0.52 thf(type_def_41, type, produc1394389750um_a_b: $tType).
% 1.41/0.52 thf(type_def_42, type, produc1798470614um_a_b: $tType).
% 1.41/0.52 thf(type_def_43, type, produc204140796um_a_b: $tType).
% 1.41/0.52 thf(type_def_44, type, set_Pr1916610317um_a_b: $tType).
% 1.41/0.52 thf(type_def_45, type, labele935650037_a_nat: $tType).
% 1.41/0.52 thf(type_def_46, type, produc1548871597um_a_b: $tType).
% 1.41/0.52 thf(type_def_47, type, set_Pr375490359_b_nat: $tType).
% 1.41/0.52 thf(type_def_48, type, set_Pr1174980151um_a_b: $tType).
% 1.41/0.52 thf(type_def_49, type, produc1978941143_b_nat: $tType).
% 1.41/0.52 thf(type_def_50, type, produc1124793815um_a_b: $tType).
% 1.41/0.52 thf(type_def_51, type, set_St761939237tant_a: $tType).
% 1.41/0.52 thf(type_def_52, type, set_Pr1986765409at_nat: $tType).
% 1.41/0.52 thf(type_def_53, type, standard_Constant_a: $tType).
% 1.41/0.52 thf(type_def_54, type, product_prod_nat_nat: $tType).
% 1.41/0.52 thf(type_def_55, type, set_Sum_sum_a_b: $tType).
% 1.41/0.52 thf(type_def_56, type, sum_sum_a_b: $tType).
% 1.41/0.52 thf(type_def_57, type, set_nat: $tType).
% 1.41/0.52 thf(type_def_58, type, nat: $tType).
% 1.41/0.52 thf(type_def_59, type, sTfun: ($tType * $tType) > $tType).
% 1.41/0.52 thf(func_def_0, type, zero_zero_nat: nat).
% 1.41/0.52 thf(func_def_1, type, standard_S_Bot_a: standard_Constant_a).
% 1.41/0.52 thf(func_def_2, type, standard_S_Idt_a: standard_Constant_a).
% 1.41/0.52 thf(func_def_3, type, getRel1465196352um_a_b: (standard_Constant_a > labele431970251um_a_b > set_Pr1916610317um_a_b)).
% 1.41/0.52 thf(func_def_4, type, edge_p170421892tant_a: (set_Pr1986765409at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o)).
% 1.41/0.52 thf(func_def_5, type, edge_p1382426714tant_a: (set_Pr1174980151um_a_b > set_Pr1647387645at_nat > set_Pr409224873um_a_b > $o)).
% 1.41/0.52 thf(func_def_6, type, edge_p749155930tant_a: (set_Pr375490359_b_nat > set_Pr409224873um_a_b > set_Pr1647387645at_nat > $o)).
% 1.41/0.52 thf(func_def_7, type, edge_p1871801392tant_a: (set_Pr1916610317um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o)).
% 1.41/0.52 thf(func_def_8, type, graph_2130075512at_nat: (labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o)).
% 1.41/0.52 thf(func_def_9, type, graph_1452133198um_a_b: (labele935650037_a_nat > labele431970251um_a_b > set_Pr1174980151um_a_b > $o)).
% 1.41/0.52 thf(func_def_10, type, graph_149544303at_nat: (labele498606060at_nat > labele935650037_a_nat > set_Pr689416536at_nat > $o)).
% 1.41/0.52 thf(func_def_11, type, graph_166346565um_a_b: (labele498606060at_nat > labele431970251um_a_b > set_Pr304595758um_a_b > $o)).
% 1.41/0.52 thf(func_def_12, type, graph_1203757137_b_nat: (labele261019144um_a_b > labele935650037_a_nat > set_Pr1902304780_b_nat > $o)).
% 1.41/0.52 thf(func_def_13, type, graph_502887975um_a_b: (labele261019144um_a_b > labele431970251um_a_b > set_Pr653770722um_a_b > $o)).
% 1.41/0.52 thf(func_def_14, type, graph_1815313447_b_nat: (labele1191284958um_a_b > labele935650037_a_nat > set_Pr507214050_b_nat > $o)).
% 1.41/0.52 thf(func_def_15, type, graph_1763806717um_a_b: (labele1191284958um_a_b > labele431970251um_a_b > set_Pr55236280um_a_b > $o)).
% 1.41/0.52 thf(func_def_16, type, graph_165730638_b_nat: (labele431970251um_a_b > labele935650037_a_nat > set_Pr375490359_b_nat > $o)).
% 1.41/0.52 thf(func_def_17, type, graph_611893540um_a_b: (labele431970251um_a_b > labele431970251um_a_b > set_Pr1916610317um_a_b > $o)).
% 1.41/0.52 thf(func_def_18, type, labele16114835_a_nat: (set_Pr1647387645at_nat > set_nat > labele935650037_a_nat)).
% 1.41/0.52 thf(func_def_19, type, labele1813985418at_nat: (set_Pr1355257963at_nat > set_Pr1647387645at_nat > labele498606060at_nat)).
% 1.41/0.52 thf(func_def_20, type, labele2034032468um_a_b: (set_Pr2065572323um_a_b > set_Pr1174980151um_a_b > labele261019144um_a_b)).
% 1.41/0.52 thf(func_def_21, type, labele989994um_a_b: (set_Pr1429673827um_a_b > set_Pr1916610317um_a_b > labele1191284958um_a_b)).
% 1.41/0.52 thf(func_def_22, type, labele1729654377um_a_b: (set_Pr409224873um_a_b > set_Sum_sum_a_b > labele431970251um_a_b)).
% 1.41/0.52 thf(func_def_23, type, labele195203296_a_nat: (labele935650037_a_nat > set_Pr1647387645at_nat)).
% 1.41/0.52 thf(func_def_24, type, labele1939049654um_a_b: (labele431970251um_a_b > set_Pr409224873um_a_b)).
% 1.41/0.52 thf(func_def_25, type, labele1810595089_a_nat: (labele935650037_a_nat > set_nat)).
% 1.41/0.52 thf(func_def_26, type, labele577278695um_a_b: (labele431970251um_a_b > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_27, type, restri572569417_a_nat: (labele935650037_a_nat > labele935650037_a_nat)).
% 1.41/0.52 thf(func_def_28, type, restri1162247455um_a_b: (labele431970251um_a_b > labele431970251um_a_b)).
% 1.41/0.52 thf(func_def_29, type, unival860567212at_nat: (set_Pr1647387645at_nat > $o)).
% 1.41/0.52 thf(func_def_30, type, unival1487587672um_a_b: (set_Pr409224873um_a_b > $o)).
% 1.41/0.52 thf(func_def_31, type, unival2092813468um_a_b: (set_Pr1174980151um_a_b > $o)).
% 1.41/0.52 thf(func_def_32, type, unival118648434um_a_b: (set_Pr1916610317um_a_b > $o)).
% 1.41/0.52 thf(func_def_33, type, bot_bot_nat: nat).
% 1.41/0.52 thf(func_def_34, type, bot_bo1160111033tant_a: set_St761939237tant_a).
% 1.41/0.52 thf(func_def_35, type, bot_bot_set_nat: set_nat).
% 1.41/0.52 thf(func_def_36, type, bot_bo810816657at_nat: set_Pr1647387645at_nat).
% 1.41/0.52 thf(func_def_37, type, bot_bo1524397311at_nat: set_Pr1355257963at_nat).
% 1.41/0.52 thf(func_def_38, type, bot_bo1208513655um_a_b: set_Pr2065572323um_a_b).
% 1.41/0.52 thf(func_def_39, type, bot_bo1262778871um_a_b: set_Pr1429673827um_a_b).
% 1.41/0.52 thf(func_def_40, type, bot_bo1262634813um_a_b: set_Pr409224873um_a_b).
% 1.41/0.52 thf(func_def_41, type, bot_bo2130386637at_nat: set_Pr1986765409at_nat).
% 1.41/0.52 thf(func_def_42, type, bot_bo575978147um_a_b: set_Pr1174980151um_a_b).
% 1.41/0.52 thf(func_def_43, type, bot_bo1582968772at_nat: set_Pr689416536at_nat).
% 1.41/0.52 thf(func_def_44, type, bot_bo627753370um_a_b: set_Pr304595758um_a_b).
% 1.41/0.52 thf(func_def_45, type, bot_bo949957280_b_nat: set_Pr1902304780_b_nat).
% 1.41/0.52 thf(func_def_46, type, bot_bo1892785270um_a_b: set_Pr653770722um_a_b).
% 1.41/0.52 thf(func_def_47, type, bot_bo1746228598_b_nat: set_Pr507214050_b_nat).
% 1.41/0.52 thf(func_def_48, type, bot_bo1217542988um_a_b: set_Pr55236280um_a_b).
% 1.41/0.52 thf(func_def_49, type, bot_bo1923972003_b_nat: set_Pr375490359_b_nat).
% 1.41/0.52 thf(func_def_50, type, bot_bo225809273um_a_b: set_Pr1916610317um_a_b).
% 1.41/0.52 thf(func_def_51, type, bot_bo1491243248um_a_b: set_Sum_sum_a_b).
% 1.41/0.52 thf(func_def_52, type, ord_less_eq_nat: (nat > nat > $o)).
% 1.41/0.52 thf(func_def_53, type, ord_le1739761029tant_a: (set_St761939237tant_a > set_St761939237tant_a > $o)).
% 1.41/0.52 thf(func_def_54, type, ord_less_eq_set_nat: (set_nat > set_nat > $o)).
% 1.41/0.52 thf(func_def_55, type, ord_le1909159005at_nat: (set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o)).
% 1.41/0.52 thf(func_def_56, type, ord_le615126793um_a_b: (set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o)).
% 1.41/0.52 thf(func_def_57, type, ord_le841296385at_nat: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o)).
% 1.41/0.52 thf(func_def_58, type, ord_le823954903um_a_b: (set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > $o)).
% 1.41/0.52 thf(func_def_59, type, ord_le1059794605um_a_b: (set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > $o)).
% 1.41/0.52 thf(func_def_60, type, ord_le192794300um_a_b: (set_Sum_sum_a_b > set_Sum_sum_a_b > $o)).
% 1.41/0.52 thf(func_def_61, type, produc407553657at_nat: (standard_Constant_a > product_prod_nat_nat > produc1032616263at_nat)).
% 1.41/0.52 thf(func_def_62, type, produc414524239um_a_b: (standard_Constant_a > produc1124793815um_a_b > produc1003469085um_a_b)).
% 1.41/0.52 thf(func_def_63, type, produc1697725733um_a_b: (standard_Constant_a > produc1548871597um_a_b > produc1963079155um_a_b)).
% 1.41/0.52 thf(func_def_64, type, produc584843310um_a_b: (standard_Constant_a > sum_sum_a_b > produc1394389750um_a_b)).
% 1.41/0.52 thf(func_def_65, type, produc1676969687_a_nat: (labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat)).
% 1.41/0.52 thf(func_def_66, type, product_Pair_nat_nat: (nat > nat > product_prod_nat_nat)).
% 1.41/0.52 thf(func_def_67, type, produc1346373166um_a_b: (nat > produc1124793815um_a_b > produc204140796um_a_b)).
% 1.41/0.52 thf(func_def_68, type, produc1808556047um_a_b: (nat > sum_sum_a_b > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_69, type, produc522766386um_a_b: (produc1963079155um_a_b > sum_sum_a_b > produc1681803642um_a_b)).
% 1.41/0.52 thf(func_def_70, type, produc335036333um_a_b: (product_prod_nat_nat > produc1124793815um_a_b > produc1546082365um_a_b)).
% 1.41/0.52 thf(func_def_71, type, produc1872245072um_a_b: (product_prod_nat_nat > sum_sum_a_b > produc1798470614um_a_b)).
% 1.41/0.52 thf(func_def_72, type, produc27163479um_a_b: (produc1124793815um_a_b > produc1124793815um_a_b > produc1918750183um_a_b)).
% 1.41/0.52 thf(func_def_73, type, produc831476262um_a_b: (produc1124793815um_a_b > sum_sum_a_b > produc585753260um_a_b)).
% 1.41/0.52 thf(func_def_74, type, produc522153487_b_nat: (sum_sum_a_b > nat > produc1978941143_b_nat)).
% 1.41/0.52 thf(func_def_75, type, produc230853810um_a_b: (sum_sum_a_b > produc1963079155um_a_b > produc1733247354um_a_b)).
% 1.41/0.52 thf(func_def_76, type, produc1637282520um_a_b: (sum_sum_a_b > produc1124793815um_a_b > produc323101606um_a_b)).
% 1.41/0.52 thf(func_def_77, type, produc176426981um_a_b: (sum_sum_a_b > sum_sum_a_b > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_78, type, domain1060562500at_nat: (set_Pr1647387645at_nat > set_St761939237tant_a)).
% 1.41/0.52 thf(func_def_79, type, domain1362581744um_a_b: (set_Pr409224873um_a_b > set_St761939237tant_a)).
% 1.41/0.52 thf(func_def_80, type, domain_nat_nat: (set_Pr1986765409at_nat > set_nat)).
% 1.41/0.52 thf(func_def_81, type, domain1368163076um_a_b: (set_Pr1174980151um_a_b > set_nat)).
% 1.41/0.52 thf(func_def_82, type, domain2069673178um_a_b: (set_Pr1916610317um_a_b > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_83, type, id_on_Sum_sum_a_b: (set_Sum_sum_a_b > set_Pr1916610317um_a_b)).
% 1.41/0.52 thf(func_def_84, type, image_127502653at_nat: (set_Pr1647387645at_nat > set_St761939237tant_a > set_Pr1986765409at_nat)).
% 1.41/0.52 thf(func_def_85, type, image_1179143699um_a_b: (set_Pr326391507um_a_b > set_St761939237tant_a > set_Pr1174980151um_a_b)).
% 1.41/0.52 thf(func_def_86, type, image_2023280617um_a_b: (set_Pr409224873um_a_b > set_St761939237tant_a > set_Pr1916610317um_a_b)).
% 1.41/0.52 thf(func_def_87, type, image_2129435242um_a_b: (set_Pr1994339542um_a_b > set_St761939237tant_a > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_88, type, image_nat_nat: (set_Pr1986765409at_nat > set_nat > set_nat)).
% 1.41/0.52 thf(func_def_89, type, image_489788268at_nat: (set_Pr1134469976at_nat > set_nat > set_Pr1647387645at_nat)).
% 1.41/0.52 thf(func_def_90, type, image_1228479730um_a_b: (set_Pr1618094130um_a_b > set_nat > set_Pr1174980151um_a_b)).
% 1.41/0.52 thf(func_def_91, type, image_166667464um_a_b: (set_Pr1155046920um_a_b > set_nat > set_Pr1916610317um_a_b)).
% 1.41/0.52 thf(func_def_92, type, image_256773707um_a_b: (set_Pr1174980151um_a_b > set_nat > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_93, type, image_452296684at_nat: (set_Pr689416536at_nat > set_Pr1647387645at_nat > set_nat)).
% 1.41/0.52 thf(func_def_94, type, image_1774897262um_a_b: (set_Pr1121389018um_a_b > set_Pr409224873um_a_b > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_95, type, image_320480233um_a_b: (set_Pr386468381um_a_b > set_Pr1986765409at_nat > set_Pr1174980151um_a_b)).
% 1.41/0.52 thf(func_def_96, type, image_1754351636um_a_b: (set_Pr195945996um_a_b > set_Pr1986765409at_nat > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_97, type, image_128716052_b_nat: (set_Pr1902304780_b_nat > set_Pr1174980151um_a_b > set_nat)).
% 1.41/0.52 thf(func_def_98, type, image_1464989587um_a_b: (set_Pr45173959um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b)).
% 1.41/0.52 thf(func_def_99, type, image_869585130um_a_b: (set_Pr653770722um_a_b > set_Pr1174980151um_a_b > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_100, type, image_1117854795_b_nat: (set_Pr375490359_b_nat > set_Sum_sum_a_b > set_nat)).
% 1.41/0.52 thf(func_def_101, type, image_1482984686um_a_b: (set_Pr1558970842um_a_b > set_Sum_sum_a_b > set_Pr409224873um_a_b)).
% 1.41/0.52 thf(func_def_102, type, image_1675391388um_a_b: (set_Pr1783309276um_a_b > set_Sum_sum_a_b > set_Pr1174980151um_a_b)).
% 1.41/0.52 thf(func_def_103, type, image_1918588449um_a_b: (set_Pr1916610317um_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_104, type, mainta522127984um_a_b: (produc1871334759_a_nat > labele431970251um_a_b > $o)).
% 1.41/0.52 thf(func_def_105, type, collect_nat: ((nat > $o) > set_nat)).
% 1.41/0.52 thf(func_def_106, type, collec52779676at_nat: ((produc1032616263at_nat > $o) > set_Pr1647387645at_nat)).
% 1.41/0.52 thf(func_def_107, type, collec1254333256um_a_b: ((produc1963079155um_a_b > $o) > set_Pr409224873um_a_b)).
% 1.41/0.52 thf(func_def_108, type, collec492052930um_a_b: ((produc1124793815um_a_b > $o) > set_Pr1174980151um_a_b)).
% 1.41/0.52 thf(func_def_109, type, collec1769032088um_a_b: ((produc1548871597um_a_b > $o) > set_Pr1916610317um_a_b)).
% 1.41/0.52 thf(func_def_110, type, collect_Sum_sum_a_b: ((sum_sum_a_b > $o) > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_111, type, insert1909710879tant_a: (standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a)).
% 1.41/0.52 thf(func_def_112, type, insert_nat: (nat > set_nat > set_nat)).
% 1.41/0.52 thf(func_def_113, type, insert1625259895at_nat: (produc1032616263at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat)).
% 1.41/0.52 thf(func_def_114, type, insert323157027um_a_b: (produc1963079155um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b)).
% 1.41/0.52 thf(func_def_115, type, insert271595217at_nat: (product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat)).
% 1.41/0.52 thf(func_def_116, type, insert983991207um_a_b: (produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b)).
% 1.41/0.52 thf(func_def_117, type, insert1435405693um_a_b: (produc1548871597um_a_b > set_Pr1916610317um_a_b > set_Pr1916610317um_a_b)).
% 1.41/0.52 thf(func_def_118, type, insert_Sum_sum_a_b: (sum_sum_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_119, type, standa1343274079tant_a: (standard_Constant_a > standard_Constant_a > produc1871334759_a_nat)).
% 1.41/0.52 thf(func_def_120, type, standa1410829644tant_a: produc1871334759_a_nat).
% 1.41/0.52 thf(func_def_121, type, standa63370785tant_a: (standard_Constant_a > produc1871334759_a_nat)).
% 1.41/0.52 thf(func_def_122, type, standa997693288tant_a: (standard_Constant_a > produc1871334759_a_nat)).
% 1.41/0.52 thf(func_def_123, type, standa1795879409tant_a: (standard_Constant_a > produc1871334759_a_nat)).
% 1.41/0.52 thf(func_def_124, type, member1632892294tant_a: (standard_Constant_a > set_St761939237tant_a > $o)).
% 1.41/0.52 thf(func_def_125, type, member_nat: (nat > set_nat > $o)).
% 1.41/0.52 thf(func_def_126, type, member1696759390at_nat: (produc1032616263at_nat > set_Pr1647387645at_nat > $o)).
% 1.41/0.52 thf(func_def_127, type, member1502344244um_a_b: (produc1003469085um_a_b > set_Pr326391507um_a_b > $o)).
% 1.41/0.52 thf(func_def_128, type, member1998628618um_a_b: (produc1963079155um_a_b > set_Pr409224873um_a_b > $o)).
% 1.41/0.52 thf(func_def_129, type, member1641046175um_a_b: (produc1394389750um_a_b > set_Pr1994339542um_a_b > $o)).
% 1.41/0.52 thf(func_def_130, type, member701585322at_nat: (product_prod_nat_nat > set_Pr1986765409at_nat > $o)).
% 1.41/0.52 thf(func_def_131, type, member1139034387um_a_b: (produc204140796um_a_b > set_Pr1618094130um_a_b > $o)).
% 1.41/0.52 thf(func_def_132, type, member1294585472um_a_b: (produc1124793815um_a_b > set_Pr1174980151um_a_b > $o)).
% 1.41/0.52 thf(func_def_133, type, member1590479267um_a_b: (produc1681803642um_a_b > set_Pr1121389018um_a_b > $o)).
% 1.41/0.52 thf(func_def_134, type, member834135910um_a_b: (produc1546082365um_a_b > set_Pr386468381um_a_b > $o)).
% 1.41/0.52 thf(func_def_135, type, member585880557um_a_b: (produc1798470614um_a_b > set_Pr195945996um_a_b > $o)).
% 1.41/0.52 thf(func_def_136, type, member429827856um_a_b: (produc1918750183um_a_b > set_Pr45173959um_a_b > $o)).
% 1.41/0.52 thf(func_def_137, type, member748122307um_a_b: (produc585753260um_a_b > set_Pr653770722um_a_b > $o)).
% 1.41/0.52 thf(func_def_138, type, member1249152_b_nat: (produc1978941143_b_nat > set_Pr375490359_b_nat > $o)).
% 1.41/0.52 thf(func_def_139, type, member1641922979um_a_b: (produc1733247354um_a_b > set_Pr1558970842um_a_b > $o)).
% 1.41/0.52 thf(func_def_140, type, member485470653um_a_b: (produc323101606um_a_b > set_Pr1783309276um_a_b > $o)).
% 1.41/0.52 thf(func_def_141, type, member947389014um_a_b: (produc1548871597um_a_b > set_Pr1916610317um_a_b > $o)).
% 1.41/0.52 thf(func_def_142, type, member_Sum_sum_a_b: (sum_sum_a_b > set_Sum_sum_a_b > $o)).
% 1.41/0.52 thf(func_def_143, type, g: labele431970251um_a_b).
% 1.41/0.52 thf(func_def_144, type, f: set_Pr1174980151um_a_b).
% 1.41/0.52 thf(func_def_145, type, l: standard_Constant_a).
% 1.41/0.52 thf(func_def_146, type, v: sum_sum_a_b).
% 1.41/0.52 thf(func_def_150, type, vAND: ($o > $o > $o)).
% 1.41/0.52 thf(func_def_151, type, db1: !>[X0: $tType]:(X0)).
% 1.41/0.52 thf(func_def_152, type, db0: !>[X0: $tType]:(X0)).
% 1.41/0.52 thf(func_def_153, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.41/0.52 thf(func_def_154, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.41/0.52 thf(func_def_155, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.41/0.52 thf(func_def_156, type, vIMP: ($o > $o > $o)).
% 1.41/0.52 thf(func_def_157, type, db2: !>[X0: $tType]:(X0)).
% 1.41/0.52 thf(func_def_158, type, sK0: (set_St761939237tant_a > set_Pr1647387645at_nat > product_prod_nat_nat > standard_Constant_a)).
% 1.41/0.52 thf(func_def_159, type, sK1: ((sum_sum_a_b > $o) > (sum_sum_a_b > $o) > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_160, type, sK2: (nat > set_Pr1986765409at_nat > nat)).
% 1.41/0.52 thf(func_def_161, type, sK3: (nat > set_Pr1174980151um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_162, type, sK4: (set_Pr409224873um_a_b > standard_Constant_a > standard_Constant_a)).
% 1.41/0.52 thf(func_def_163, type, sK5: (set_Pr409224873um_a_b > standard_Constant_a > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_164, type, sK6: ((produc1032616263at_nat > $o) > produc1032616263at_nat)).
% 1.41/0.52 thf(func_def_165, type, sK7: (standard_Constant_a > set_Pr1647387645at_nat > product_prod_nat_nat)).
% 1.41/0.52 thf(func_def_166, type, sK8: (set_Pr1783309276um_a_b > produc1124793815um_a_b > set_Sum_sum_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_167, type, sK9: (nat > set_Pr1174980151um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_168, type, sK10: (sum_sum_a_b > set_Pr1916610317um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_169, type, sK11: (set_Pr409224873um_a_b > (standard_Constant_a > $o) > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_170, type, sK12: (set_Pr409224873um_a_b > (standard_Constant_a > $o) > standard_Constant_a)).
% 1.41/0.52 thf(func_def_171, type, sK13: ((sum_sum_a_b > $o) > set_Pr1916610317um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_172, type, sK14: ((sum_sum_a_b > $o) > set_Pr1916610317um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_173, type, sK15: (sum_sum_a_b > set_Pr1916610317um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_174, type, sK16: (set_Pr45173959um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_175, type, sK17: (set_Pr1916610317um_a_b > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_176, type, sK18: ((produc1548871597um_a_b > $o) > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_177, type, sK19: (set_Pr1916610317um_a_b > sum_sum_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_178, type, sK20: (set_Pr1647387645at_nat > standard_Constant_a > product_prod_nat_nat)).
% 1.41/0.52 thf(func_def_179, type, sK21: ((produc1548871597um_a_b > $o) > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_180, type, sK22: (set_Pr1647387645at_nat > set_Pr1647387645at_nat > standard_Constant_a)).
% 1.41/0.52 thf(func_def_181, type, sK23: (set_Pr1647387645at_nat > set_Pr1647387645at_nat > product_prod_nat_nat)).
% 1.41/0.52 thf(func_def_182, type, sK24: (set_Pr409224873um_a_b > set_St761939237tant_a > produc1548871597um_a_b > standard_Constant_a)).
% 1.41/0.52 thf(func_def_183, type, sK25: (set_Sum_sum_a_b > set_Pr1916610317um_a_b > sum_sum_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_184, type, sK26: (set_Pr409224873um_a_b > standard_Constant_a > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_185, type, sK27: (set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_186, type, sK28: (set_Pr1986765409at_nat > nat > set_nat > nat)).
% 1.41/0.52 thf(func_def_187, type, sK29: (set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_188, type, sK30: (set_Pr409224873um_a_b > standard_Constant_a > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_189, type, sK31: (set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_190, type, sK32: (set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > nat)).
% 1.41/0.52 thf(func_def_191, type, sK33: (set_Pr1986765409at_nat > (nat > $o) > nat)).
% 1.41/0.52 thf(func_def_192, type, sK34: (set_Pr1986765409at_nat > (nat > $o) > nat)).
% 1.41/0.52 thf(func_def_193, type, sK35: (sum_sum_a_b > set_nat > set_Pr1174980151um_a_b > nat)).
% 1.41/0.52 thf(func_def_194, type, sK36: (set_Pr409224873um_a_b > produc1963079155um_a_b)).
% 1.41/0.52 thf(func_def_195, type, sK37: (set_Pr1174980151um_a_b > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_196, type, sK38: (set_Sum_sum_a_b > set_Pr1558970842um_a_b > produc1963079155um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_197, type, sK39: (nat > set_Pr1174980151um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_198, type, sK40: (set_Pr1121389018um_a_b > sum_sum_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b)).
% 1.41/0.52 thf(func_def_199, type, sK41: (labele935650037_a_nat > set_Pr1647387645at_nat)).
% 1.41/0.52 thf(func_def_200, type, sK42: (labele935650037_a_nat > set_nat)).
% 1.41/0.52 thf(func_def_201, type, sK43: (set_Pr1174980151um_a_b > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_202, type, sK44: (set_Pr1647387645at_nat > produc1032616263at_nat)).
% 1.41/0.52 thf(func_def_203, type, sK45: ((sum_sum_a_b > $o) > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_204, type, sK46: (set_Pr1647387645at_nat > produc1032616263at_nat)).
% 1.41/0.52 thf(func_def_205, type, sK47: (set_Pr409224873um_a_b > standard_Constant_a > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_206, type, sK48: (sum_sum_a_b > set_Pr1916610317um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_207, type, sK49: (sum_sum_a_b > set_Pr1916610317um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_208, type, sK50: (labele431970251um_a_b > set_Pr409224873um_a_b)).
% 1.41/0.52 thf(func_def_209, type, sK51: (labele431970251um_a_b > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_210, type, sK52: (set_Pr1174980151um_a_b > (nat > $o) > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_211, type, sK53: (set_Pr1174980151um_a_b > (nat > $o) > nat)).
% 1.41/0.52 thf(func_def_212, type, sK54: (produc1548871597um_a_b > set_Pr409224873um_a_b > set_St761939237tant_a > standard_Constant_a)).
% 1.41/0.52 thf(func_def_213, type, sK55: (set_Sum_sum_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_214, type, sK56: ((produc1124793815um_a_b > $o) > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_215, type, sK57: (product_prod_nat_nat > set_Pr1647387645at_nat > set_St761939237tant_a > standard_Constant_a)).
% 1.41/0.52 thf(func_def_216, type, sK58: (set_Pr409224873um_a_b > produc1963079155um_a_b)).
% 1.41/0.52 thf(func_def_217, type, sK59: (set_nat > nat)).
% 1.41/0.52 thf(func_def_218, type, sK60: ((nat > $o) > nat)).
% 1.41/0.52 thf(func_def_219, type, sK61: ((produc1963079155um_a_b > $o) > produc1963079155um_a_b)).
% 1.41/0.52 thf(func_def_220, type, sK62: (set_Pr1986765409at_nat > set_nat > nat > nat)).
% 1.41/0.52 thf(func_def_221, type, sK63: (set_Pr1986765409at_nat > nat > nat)).
% 1.41/0.52 thf(func_def_222, type, sK64: (set_Pr1174980151um_a_b > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_223, type, sK65: ((produc1032616263at_nat > $o) > produc1032616263at_nat)).
% 1.41/0.52 thf(func_def_224, type, sK66: ((sum_sum_a_b > $o) > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_225, type, sK67: sum_sum_a_b).
% 1.41/0.52 thf(func_def_226, type, sK68: (set_Pr1647387645at_nat > standard_Constant_a > product_prod_nat_nat)).
% 1.41/0.52 thf(func_def_227, type, sK69: (set_Sum_sum_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_228, type, sK70: (nat > set_Pr1986765409at_nat > nat)).
% 1.41/0.52 thf(func_def_229, type, sK71: (nat > set_Pr1986765409at_nat > nat)).
% 1.41/0.52 thf(func_def_230, type, sK72: (set_Pr1986765409at_nat > nat > nat)).
% 1.41/0.52 thf(func_def_231, type, sK73: (set_Pr1916610317um_a_b > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_232, type, sK74: ((sum_sum_a_b > $o) > (sum_sum_a_b > $o) > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_233, type, sK75: (nat > set_Pr1174980151um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_234, type, sK76: (nat > set_Pr1174980151um_a_b > nat)).
% 1.41/0.52 thf(func_def_235, type, sK77: (set_Pr1174980151um_a_b > set_nat > sum_sum_a_b > nat)).
% 1.41/0.52 thf(func_def_236, type, sK78: (set_Pr409224873um_a_b > produc1963079155um_a_b)).
% 1.41/0.52 thf(func_def_237, type, sK79: ((nat > $o) > nat)).
% 1.41/0.52 thf(func_def_238, type, sK80: ((labele431970251um_a_b > $o) > set_Sum_sum_a_b)).
% 1.41/0.52 thf(func_def_239, type, sK81: ((labele431970251um_a_b > $o) > set_Pr409224873um_a_b)).
% 1.41/0.52 thf(func_def_240, type, sK82: (set_Pr409224873um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b)).
% 1.41/0.52 thf(func_def_241, type, sK83: (set_Pr409224873um_a_b > set_Pr409224873um_a_b > standard_Constant_a)).
% 1.41/0.52 thf(func_def_242, type, sK84: (set_Pr409224873um_a_b > set_Pr409224873um_a_b > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_243, type, sK85: ((produc1963079155um_a_b > $o) > produc1963079155um_a_b)).
% 1.41/0.52 thf(func_def_244, type, sK86: ((labele935650037_a_nat > $o) > set_Pr1647387645at_nat)).
% 1.41/0.52 thf(func_def_245, type, sK87: ((labele935650037_a_nat > $o) > set_nat)).
% 1.41/0.52 thf(func_def_246, type, sK88: (set_Pr1916610317um_a_b > produc1548871597um_a_b)).
% 1.41/0.52 thf(func_def_247, type, sK89: (set_Pr1647387645at_nat > produc1032616263at_nat)).
% 1.41/0.52 thf(func_def_248, type, sK90: (standard_Constant_a > set_Pr1647387645at_nat > product_prod_nat_nat)).
% 1.41/0.52 thf(func_def_249, type, sK91: (standard_Constant_a > set_Pr1647387645at_nat > standard_Constant_a)).
% 1.41/0.52 thf(func_def_250, type, sK92: (set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_251, type, sK93: (set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_252, type, sK94: (set_Sum_sum_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_253, type, sK95: ((produc1124793815um_a_b > $o) > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_254, type, sK96: (set_nat > nat)).
% 1.41/0.52 thf(func_def_255, type, sK97: (sum_sum_a_b > set_Pr1174980151um_a_b > set_Pr653770722um_a_b > produc1124793815um_a_b)).
% 1.41/0.52 thf(func_def_256, type, sK98: (set_Pr1916610317um_a_b > sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b)).
% 1.41/0.52 thf(func_def_257, type, sK99: (set_nat > nat)).
% 1.41/0.52 thf(func_def_258, type, sK100: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat)).
% 1.41/0.52 thf(func_def_259, type, sK101: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat)).
% 1.41/0.52 thf(func_def_260, type, sK102: ((nat > $o) > nat)).
% 1.41/0.52 thf(func_def_261, type, sK103: (nat > (nat > $o) > nat)).
% 1.41/0.52 thf(func_def_262, type, sK104: ((standard_Constant_a > $o) > set_Pr1647387645at_nat > product_prod_nat_nat)).
% 1.41/0.52 thf(func_def_263, type, sK105: ((standard_Constant_a > $o) > set_Pr1647387645at_nat > standard_Constant_a)).
% 1.41/0.52 thf(func_def_264, type, vNOT: ($o > $o)).
% 1.41/0.52 thf(f1,axiom,(
% 1.41/0.52 (g = ((restri1162247455um_a_b @ g)))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_g)).
% 1.41/0.52 thf(f3,axiom,(
% 1.41/0.52 (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062)).
% 1.41/0.52 thf(f4,axiom,(
% 1.41/0.52 (ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_r)).
% 1.41/0.52 thf(f5,axiom,(
% 1.41/0.52 (f = ((insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_f)).
% 1.41/0.52 thf(f6,axiom,(
% 1.41/0.52 (((domain1368163076um_a_b @ f)) = ((insert_nat @ zero_zero_nat @ bot_bot_set_nat)))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_d)).
% 1.41/0.52 thf(f8,axiom,(
% 1.41/0.52 ! [X0 : standard_Constant_a,X2 : nat,X1 : nat] : (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X0 @ (product_Pair_nat_nat @ X1 @ X2)) @ bot_bo810816657at_nat) @ (insert_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)))) = ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X0 @ (product_Pair_nat_nat @ X1 @ X2)) @ bot_bo810816657at_nat) @ (insert_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat))))))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_graph__single)).
% 1.41/0.52 thf(f10,axiom,(
% 1.41/0.52 (unival2092813468um_a_b @ f)),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_u)).
% 1.41/0.52 thf(f129,axiom,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b,X1 : set_Pr1174980151um_a_b] : ((ord_le823954903um_a_b @ X0 @ X1) => (ord_less_eq_set_nat @ (domain1368163076um_a_b @ X0) @ (domain1368163076um_a_b @ X1)))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Domain__mono)).
% 1.41/0.52 thf(f136,axiom,(
% 1.41/0.52 ! [X1 : set_nat,X0 : set_Pr1647387645at_nat] : (((labele1810595089_a_nat @ (labele16114835_a_nat @ X0 @ X1))) = X1)),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_labeled__graph_Osel_I2_J)).
% 1.41/0.52 thf(f138,axiom,(
% 1.41/0.52 ! [X0 : set_Pr1647387645at_nat,X1 : set_nat] : (((labele195203296_a_nat @ (labele16114835_a_nat @ X0 @ X1))) = X0)),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_labeled__graph_Osel_I1_J)).
% 1.41/0.52 thf(f154,axiom,(
% 1.41/0.52 ! [X1 : set_nat,X0 : nat,X2 : nat] : ((((insert_nat @ X0 @ X1)) = ((insert_nat @ X2 @ bot_bot_set_nat))) = (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)) & (X0 = X2))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_singleton__insert__inj__eq_H)).
% 1.41/0.52 thf(f161,axiom,(
% 1.41/0.52 ! [X0 : produc1032616263at_nat,X2 : set_Pr1647387645at_nat,X1 : produc1032616263at_nat] : ((((insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)) = ((insert1625259895at_nat @ X1 @ X2))) = (X1 = X0) & (ord_le1909159005at_nat @ X2 @ (insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_singleton__insert__inj__eq)).
% 1.41/0.52 thf(f182,axiom,(
% 1.41/0.52 ! [X2 : set_Pr1174980151um_a_b,X0 : produc1124793815um_a_b,X1 : set_Pr1174980151um_a_b] : (((ord_le823954903um_a_b @ (insert983991207um_a_b @ X0 @ X1) @ X2)) = (ord_le823954903um_a_b @ X1 @ X2) & (member1294585472um_a_b @ X0 @ X2))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_insert__subset)).
% 1.41/0.52 thf(f193,axiom,(
% 1.41/0.52 ! [X0 : set_Pr1647387645at_nat] : (ord_le1909159005at_nat @ bot_bo810816657at_nat @ X0)),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_empty__subsetI)).
% 1.41/0.52 thf(f195,axiom,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b] : (ord_le823954903um_a_b @ bot_bo575978147um_a_b @ X0)),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_empty__subsetI)).
% 1.41/0.52 thf(f253,axiom,(
% 1.41/0.52 ! [X0 : nat,X1 : set_nat] : (((insert_nat @ X0 @ (insert_nat @ X0 @ X1))) = ((insert_nat @ X0 @ X1)))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_insert__absorb2)).
% 1.41/0.52 thf(f333,axiom,(
% 1.41/0.52 ! [X0 : produc1124793815um_a_b,X1 : set_Pr1174980151um_a_b] : (member1294585472um_a_b @ X0 @ (insert983991207um_a_b @ X0 @ X1))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_insertI1)).
% 1.41/0.52 thf(f353,conjecture,(
% 1.41/0.52 (ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) & (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) = ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) & (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) & (g = ((restri1162247455um_a_b @ g))) & (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g)) & (unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))),
% 1.41/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.41/0.52 thf(f354,negated_conjecture,(
% 1.41/0.52 ~((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) & (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) = ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) & (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) & (g = ((restri1162247455um_a_b @ g))) & (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g)) & (unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))),
% 1.41/0.52 inference(negated_conjecture,[status(cth)],[f353])).
% 1.41/0.52 thf(f435,plain,(
% 1.41/0.52 ! [X0 : produc1032616263at_nat,X1 : set_Pr1647387645at_nat,X2 : produc1032616263at_nat] : ((((insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)) = ((insert1625259895at_nat @ X2 @ X1))) = (X0 = X2) & (ord_le1909159005at_nat @ X1 @ (insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)))),
% 1.41/0.52 inference(rectify,[],[f161])).
% 1.41/0.52 thf(f436,plain,(
% 1.41/0.52 ! [X2 : produc1032616263at_nat,X0 : produc1032616263at_nat,X1 : set_Pr1647387645at_nat] : ((((insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)) = ((insert1625259895at_nat @ X2 @ X1))) <=> ((X0 = X2) & ($true = ((ord_le1909159005at_nat @ X1 @ (insert1625259895at_nat @ X0 @ bot_bo810816657at_nat))))))),
% 1.41/0.52 inference(fool_elimination,[],[f435])).
% 1.41/0.52 thf(f475,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b,X1 : produc1124793815um_a_b,X2 : set_Pr1174980151um_a_b] : (((ord_le823954903um_a_b @ (insert983991207um_a_b @ X1 @ X2) @ X0)) = (ord_le823954903um_a_b @ X2 @ X0) & (member1294585472um_a_b @ X1 @ X0))),
% 1.41/0.52 inference(rectify,[],[f182])).
% 1.41/0.52 thf(f476,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b,X1 : produc1124793815um_a_b,X2 : set_Pr1174980151um_a_b] : ((((ord_le823954903um_a_b @ (insert983991207um_a_b @ X1 @ X2) @ X0)) = $true) <=> ((((member1294585472um_a_b @ X1 @ X0)) = $true) & ($true = ((ord_le823954903um_a_b @ X2 @ X0)))))),
% 1.41/0.52 inference(fool_elimination,[],[f475])).
% 1.41/0.52 thf(f488,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b,X1 : set_Pr1174980151um_a_b] : ((ord_le823954903um_a_b @ X0 @ X1) => (ord_less_eq_set_nat @ (domain1368163076um_a_b @ X0) @ (domain1368163076um_a_b @ X1)))),
% 1.41/0.52 inference(rectify,[],[f129])).
% 1.41/0.52 thf(f489,plain,(
% 1.41/0.52 ! [X1 : set_Pr1174980151um_a_b,X0 : set_Pr1174980151um_a_b] : ((((ord_le823954903um_a_b @ X0 @ X1)) = $true) => (((ord_less_eq_set_nat @ (domain1368163076um_a_b @ X0) @ (domain1368163076um_a_b @ X1))) = $true))),
% 1.41/0.52 inference(fool_elimination,[],[f488])).
% 1.41/0.52 thf(f624,plain,(
% 1.41/0.52 (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g))),
% 1.41/0.52 inference(rectify,[],[f3])).
% 1.41/0.52 thf(f625,plain,(
% 1.41/0.52 (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g))) = $true)),
% 1.41/0.52 inference(fool_elimination,[],[f624])).
% 1.41/0.52 thf(f661,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b] : (ord_le823954903um_a_b @ bot_bo575978147um_a_b @ X0)),
% 1.41/0.52 inference(rectify,[],[f195])).
% 1.41/0.52 thf(f662,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b] : (((ord_le823954903um_a_b @ bot_bo575978147um_a_b @ X0)) = $true)),
% 1.41/0.52 inference(fool_elimination,[],[f661])).
% 1.41/0.52 thf(f739,plain,(
% 1.41/0.52 (unival2092813468um_a_b @ f)),
% 1.41/0.52 inference(rectify,[],[f10])).
% 1.41/0.52 thf(f740,plain,(
% 1.41/0.52 (((unival2092813468um_a_b @ f)) = $true)),
% 1.41/0.52 inference(fool_elimination,[],[f739])).
% 1.41/0.52 thf(f744,plain,(
% 1.41/0.52 (ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g))),
% 1.41/0.52 inference(rectify,[],[f4])).
% 1.41/0.52 thf(f745,plain,(
% 1.41/0.52 (((ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g))) = $true)),
% 1.41/0.52 inference(fool_elimination,[],[f744])).
% 1.41/0.52 thf(f781,plain,(
% 1.41/0.52 ! [X0 : produc1124793815um_a_b,X1 : set_Pr1174980151um_a_b] : (member1294585472um_a_b @ X0 @ (insert983991207um_a_b @ X0 @ X1))),
% 1.41/0.52 inference(rectify,[],[f333])).
% 1.41/0.52 thf(f782,plain,(
% 1.41/0.52 ! [X1 : set_Pr1174980151um_a_b,X0 : produc1124793815um_a_b] : (((member1294585472um_a_b @ X0 @ (insert983991207um_a_b @ X0 @ X1))) = $true)),
% 1.41/0.52 inference(fool_elimination,[],[f781])).
% 1.41/0.52 thf(f820,plain,(
% 1.41/0.52 ! [X0 : set_nat,X1 : nat,X2 : nat] : ((((insert_nat @ X2 @ bot_bot_set_nat)) = ((insert_nat @ X1 @ X0))) = (ord_less_eq_set_nat @ X0 @ (insert_nat @ X2 @ bot_bot_set_nat)) & (X1 = X2))),
% 1.41/0.52 inference(rectify,[],[f154])).
% 1.41/0.52 thf(f821,plain,(
% 1.41/0.52 ! [X2 : nat,X0 : set_nat,X1 : nat] : ((($true = ((ord_less_eq_set_nat @ X0 @ (insert_nat @ X2 @ bot_bot_set_nat)))) & (X1 = X2)) <=> (((insert_nat @ X2 @ bot_bot_set_nat)) = ((insert_nat @ X1 @ X0))))),
% 1.41/0.52 inference(fool_elimination,[],[f820])).
% 1.41/0.52 thf(f822,plain,(
% 1.41/0.52 ! [X0 : set_Pr1647387645at_nat] : (ord_le1909159005at_nat @ bot_bo810816657at_nat @ X0)),
% 1.41/0.52 inference(rectify,[],[f193])).
% 1.41/0.52 thf(f823,plain,(
% 1.41/0.52 ! [X0 : set_Pr1647387645at_nat] : (((ord_le1909159005at_nat @ bot_bo810816657at_nat @ X0)) = $true)),
% 1.41/0.52 inference(fool_elimination,[],[f822])).
% 1.41/0.52 thf(f828,plain,(
% 1.41/0.52 ~((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) & (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) = ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) & (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) & (g = ((restri1162247455um_a_b @ g))) & (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g)) & (unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))),
% 1.41/0.52 inference(rectify,[],[f354])).
% 1.41/0.52 thf(f829,plain,(
% 1.41/0.52 ~((((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) & (((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g))) = $true) & (g = ((restri1162247455um_a_b @ g))) & (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) = ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) & (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g))) = $true) & (((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) = $true))),
% 1.41/0.52 inference(fool_elimination,[],[f828])).
% 1.41/0.52 thf(f952,plain,(
% 1.41/0.52 ! [X0 : set_nat,X1 : set_Pr1647387645at_nat] : (((labele1810595089_a_nat @ (labele16114835_a_nat @ X1 @ X0))) = X0)),
% 1.41/0.52 inference(rectify,[],[f136])).
% 1.41/0.52 thf(f1000,plain,(
% 1.41/0.52 ! [X1 : set_Pr1174980151um_a_b,X0 : set_Pr1174980151um_a_b] : ((((ord_le823954903um_a_b @ X0 @ X1)) != $true) | (((ord_less_eq_set_nat @ (domain1368163076um_a_b @ X0) @ (domain1368163076um_a_b @ X1))) = $true))),
% 1.41/0.52 inference(ennf_transformation,[],[f489])).
% 1.41/0.52 thf(f1055,plain,(
% 1.41/0.52 (g != ((restri1162247455um_a_b @ g))) | (((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) != $true) | (((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g))) != $true) | (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g))) != $true) | (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) != ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) | (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) != ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))))),
% 1.41/0.52 inference(ennf_transformation,[],[f829])).
% 1.41/0.52 thf(f1233,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b,X1 : produc1124793815um_a_b] : ($true = ((member1294585472um_a_b @ X1 @ (insert983991207um_a_b @ X1 @ X0))))),
% 1.41/0.52 inference(rectify,[],[f782])).
% 1.41/0.52 thf(f1274,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b,X1 : produc1124793815um_a_b,X2 : set_Pr1174980151um_a_b] : (((((ord_le823954903um_a_b @ (insert983991207um_a_b @ X1 @ X2) @ X0)) = $true) | ((((member1294585472um_a_b @ X1 @ X0)) != $true) | ($true != ((ord_le823954903um_a_b @ X2 @ X0))))) & (((((member1294585472um_a_b @ X1 @ X0)) = $true) & ($true = ((ord_le823954903um_a_b @ X2 @ X0)))) | (((ord_le823954903um_a_b @ (insert983991207um_a_b @ X1 @ X2) @ X0)) != $true)))),
% 1.41/0.52 inference(nnf_transformation,[],[f476])).
% 1.41/0.52 thf(f1275,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b,X1 : produc1124793815um_a_b,X2 : set_Pr1174980151um_a_b] : (((((ord_le823954903um_a_b @ (insert983991207um_a_b @ X1 @ X2) @ X0)) = $true) | (((member1294585472um_a_b @ X1 @ X0)) != $true) | ($true != ((ord_le823954903um_a_b @ X2 @ X0)))) & (((((member1294585472um_a_b @ X1 @ X0)) = $true) & ($true = ((ord_le823954903um_a_b @ X2 @ X0)))) | (((ord_le823954903um_a_b @ (insert983991207um_a_b @ X1 @ X2) @ X0)) != $true)))),
% 1.41/0.52 inference(flattening,[],[f1274])).
% 1.41/0.52 thf(f1297,plain,(
% 1.41/0.52 ! [X0 : set_Pr1174980151um_a_b,X1 : set_Pr1174980151um_a_b] : (($true != ((ord_le823954903um_a_b @ X1 @ X0))) | ($true = ((ord_less_eq_set_nat @ (domain1368163076um_a_b @ X1) @ (domain1368163076um_a_b @ X0)))))),
% 1.41/0.52 inference(rectify,[],[f1000])).
% 1.41/0.52 thf(f1384,plain,(
% 1.41/0.52 ! [X0 : standard_Constant_a,X1 : nat,X2 : nat] : (((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X0 @ (product_Pair_nat_nat @ X2 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X2 @ (insert_nat @ X1 @ bot_bot_set_nat))))) = ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X0 @ (product_Pair_nat_nat @ X2 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X2 @ (insert_nat @ X1 @ bot_bot_set_nat)))))),
% 1.41/0.52 inference(rectify,[],[f8])).
% 1.41/0.52 thf(f1388,plain,(
% 1.41/0.52 ! [X2 : produc1032616263at_nat,X0 : produc1032616263at_nat,X1 : set_Pr1647387645at_nat] : (((((insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)) = ((insert1625259895at_nat @ X2 @ X1))) | ((X0 != X2) | ($true != ((ord_le1909159005at_nat @ X1 @ (insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)))))) & (((X0 = X2) & ($true = ((ord_le1909159005at_nat @ X1 @ (insert1625259895at_nat @ X0 @ bot_bo810816657at_nat))))) | (((insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)) != ((insert1625259895at_nat @ X2 @ X1)))))),
% 1.41/0.52 inference(nnf_transformation,[],[f436])).
% 1.41/0.52 thf(f1389,plain,(
% 1.41/0.52 ! [X2 : produc1032616263at_nat,X0 : produc1032616263at_nat,X1 : set_Pr1647387645at_nat] : (((((insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)) = ((insert1625259895at_nat @ X2 @ X1))) | (X0 != X2) | ($true != ((ord_le1909159005at_nat @ X1 @ (insert1625259895at_nat @ X0 @ bot_bo810816657at_nat))))) & (((X0 = X2) & ($true = ((ord_le1909159005at_nat @ X1 @ (insert1625259895at_nat @ X0 @ bot_bo810816657at_nat))))) | (((insert1625259895at_nat @ X0 @ bot_bo810816657at_nat)) != ((insert1625259895at_nat @ X2 @ X1)))))),
% 1.41/0.52 inference(flattening,[],[f1388])).
% 1.41/0.52 thf(f1390,plain,(
% 1.41/0.52 ! [X0 : produc1032616263at_nat,X1 : produc1032616263at_nat,X2 : set_Pr1647387645at_nat] : (((((insert1625259895at_nat @ X1 @ bot_bo810816657at_nat)) = ((insert1625259895at_nat @ X0 @ X2))) | (X0 != X1) | (((ord_le1909159005at_nat @ X2 @ (insert1625259895at_nat @ X1 @ bot_bo810816657at_nat))) != $true)) & (((X0 = X1) & (((ord_le1909159005at_nat @ X2 @ (insert1625259895at_nat @ X1 @ bot_bo810816657at_nat))) = $true)) | (((insert1625259895at_nat @ X1 @ bot_bo810816657at_nat)) != ((insert1625259895at_nat @ X0 @ X2)))))),
% 1.41/0.52 inference(rectify,[],[f1389])).
% 1.41/0.52 thf(f1451,plain,(
% 1.41/0.52 ! [X2 : nat,X0 : set_nat,X1 : nat] : (((($true = ((ord_less_eq_set_nat @ X0 @ (insert_nat @ X2 @ bot_bot_set_nat)))) & (X1 = X2)) | (((insert_nat @ X2 @ bot_bot_set_nat)) != ((insert_nat @ X1 @ X0)))) & ((((insert_nat @ X2 @ bot_bot_set_nat)) = ((insert_nat @ X1 @ X0))) | (($true != ((ord_less_eq_set_nat @ X0 @ (insert_nat @ X2 @ bot_bot_set_nat)))) | (X1 != X2))))),
% 1.41/0.52 inference(nnf_transformation,[],[f821])).
% 1.41/0.52 thf(f1452,plain,(
% 1.41/0.52 ! [X2 : nat,X0 : set_nat,X1 : nat] : (((($true = ((ord_less_eq_set_nat @ X0 @ (insert_nat @ X2 @ bot_bot_set_nat)))) & (X1 = X2)) | (((insert_nat @ X2 @ bot_bot_set_nat)) != ((insert_nat @ X1 @ X0)))) & ((((insert_nat @ X2 @ bot_bot_set_nat)) = ((insert_nat @ X1 @ X0))) | ($true != ((ord_less_eq_set_nat @ X0 @ (insert_nat @ X2 @ bot_bot_set_nat)))) | (X1 != X2)))),
% 1.41/0.52 inference(flattening,[],[f1451])).
% 1.41/0.52 thf(f1453,plain,(
% 1.41/0.52 ! [X0 : nat,X1 : set_nat,X2 : nat] : (((($true = ((ord_less_eq_set_nat @ X1 @ (insert_nat @ X0 @ bot_bot_set_nat)))) & (X0 = X2)) | (((insert_nat @ X0 @ bot_bot_set_nat)) != ((insert_nat @ X2 @ X1)))) & ((((insert_nat @ X0 @ bot_bot_set_nat)) = ((insert_nat @ X2 @ X1))) | ($true != ((ord_less_eq_set_nat @ X1 @ (insert_nat @ X0 @ bot_bot_set_nat)))) | (X0 != X2)))),
% 1.41/0.52 inference(rectify,[],[f1452])).
% 1.41/0.52 thf(f1663,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1174980151um_a_b,X1 : produc1124793815um_a_b] : (($true = ((member1294585472um_a_b @ X1 @ (insert983991207um_a_b @ X1 @ X0))))) )),
% 1.41/0.52 inference(cnf_transformation,[],[f1233])).
% 1.41/0.52 thf(f1711,plain,(
% 1.41/0.52 ( ! [X2 : set_Pr1174980151um_a_b,X0 : set_Pr1174980151um_a_b,X1 : produc1124793815um_a_b] : ((((ord_le823954903um_a_b @ (insert983991207um_a_b @ X1 @ X2) @ X0)) = $true) | ($true != ((ord_le823954903um_a_b @ X2 @ X0))) | (((member1294585472um_a_b @ X1 @ X0)) != $true)) )),
% 1.41/0.52 inference(cnf_transformation,[],[f1275])).
% 1.41/0.52 thf(f1726,plain,(
% 1.41/0.52 (((insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = ((domain1368163076um_a_b @ f)))),
% 1.41/0.52 inference(cnf_transformation,[],[f6])).
% 1.41/0.52 thf(f1737,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1174980151um_a_b,X1 : set_Pr1174980151um_a_b] : (($true = ((ord_less_eq_set_nat @ (domain1368163076um_a_b @ X1) @ (domain1368163076um_a_b @ X0)))) | ($true != ((ord_le823954903um_a_b @ X1 @ X0)))) )),
% 1.41/0.52 inference(cnf_transformation,[],[f1297])).
% 1.41/0.52 thf(f1746,plain,(
% 1.41/0.52 ( ! [X0 : set_nat,X1 : set_Pr1647387645at_nat] : ((((labele1810595089_a_nat @ (labele16114835_a_nat @ X1 @ X0))) = X0)) )),
% 1.41/0.52 inference(cnf_transformation,[],[f952])).
% 1.41/0.52 thf(f1747,plain,(
% 1.41/0.52 (((insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) = f)),
% 1.41/0.52 inference(cnf_transformation,[],[f5])).
% 1.41/0.52 thf(f1776,plain,(
% 1.41/0.52 (((ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g))) = $true)),
% 1.41/0.52 inference(cnf_transformation,[],[f745])).
% 1.41/0.52 thf(f1847,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1647387645at_nat,X1 : set_nat] : ((((labele195203296_a_nat @ (labele16114835_a_nat @ X0 @ X1))) = X0)) )),
% 1.41/0.52 inference(cnf_transformation,[],[f138])).
% 1.41/0.52 thf(f1850,plain,(
% 1.41/0.52 (((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g))) != $true) | (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) != ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) | (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g))) != $true) | (((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) != $true) | (g != ((restri1162247455um_a_b @ g))) | (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) != ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))))),
% 1.41/0.52 inference(cnf_transformation,[],[f1055])).
% 1.41/0.52 thf(f1866,plain,(
% 1.41/0.52 (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g))) = $true)),
% 1.41/0.52 inference(cnf_transformation,[],[f625])).
% 1.41/0.52 thf(f1878,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1174980151um_a_b] : ((((ord_le823954903um_a_b @ bot_bo575978147um_a_b @ X0)) = $true)) )),
% 1.41/0.52 inference(cnf_transformation,[],[f662])).
% 1.41/0.52 thf(f1879,plain,(
% 1.41/0.52 ( ! [X2 : nat,X0 : standard_Constant_a,X1 : nat] : ((((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X0 @ (product_Pair_nat_nat @ X2 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X2 @ (insert_nat @ X1 @ bot_bot_set_nat))))) = ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X0 @ (product_Pair_nat_nat @ X2 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X2 @ (insert_nat @ X1 @ bot_bot_set_nat)))))) )),
% 1.41/0.52 inference(cnf_transformation,[],[f1384])).
% 1.41/0.52 thf(f1885,plain,(
% 1.41/0.52 ( ! [X2 : set_Pr1647387645at_nat,X0 : produc1032616263at_nat,X1 : produc1032616263at_nat] : ((((insert1625259895at_nat @ X1 @ bot_bo810816657at_nat)) = ((insert1625259895at_nat @ X0 @ X2))) | (X0 != X1) | (((ord_le1909159005at_nat @ X2 @ (insert1625259895at_nat @ X1 @ bot_bo810816657at_nat))) != $true)) )),
% 1.41/0.52 inference(cnf_transformation,[],[f1390])).
% 1.41/0.52 thf(f1961,plain,(
% 1.41/0.52 (((unival2092813468um_a_b @ f)) = $true)),
% 1.41/0.52 inference(cnf_transformation,[],[f740])).
% 1.41/0.52 thf(f1968,plain,(
% 1.41/0.52 ( ! [X2 : nat,X0 : nat,X1 : set_nat] : ((((insert_nat @ X0 @ bot_bot_set_nat)) = ((insert_nat @ X2 @ X1))) | ($true != ((ord_less_eq_set_nat @ X1 @ (insert_nat @ X0 @ bot_bot_set_nat)))) | (X0 != X2)) )),
% 1.41/0.52 inference(cnf_transformation,[],[f1453])).
% 1.41/0.52 thf(f1989,plain,(
% 1.41/0.52 ( ! [X0 : nat,X1 : set_nat] : ((((insert_nat @ X0 @ X1)) = ((insert_nat @ X0 @ (insert_nat @ X0 @ X1))))) )),
% 1.41/0.52 inference(cnf_transformation,[],[f253])).
% 1.41/0.52 thf(f2005,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1647387645at_nat] : ((((ord_le1909159005at_nat @ bot_bo810816657at_nat @ X0)) = $true)) )),
% 1.41/0.52 inference(cnf_transformation,[],[f823])).
% 1.41/0.52 thf(f2010,plain,(
% 1.41/0.52 (g = ((restri1162247455um_a_b @ g)))),
% 1.41/0.52 inference(cnf_transformation,[],[f1])).
% 1.41/0.52 thf(f2169,plain,(
% 1.41/0.52 ( ! [X2 : set_Pr1647387645at_nat,X1 : produc1032616263at_nat] : ((((insert1625259895at_nat @ X1 @ X2)) = ((insert1625259895at_nat @ X1 @ bot_bo810816657at_nat))) | (((ord_le1909159005at_nat @ X2 @ (insert1625259895at_nat @ X1 @ bot_bo810816657at_nat))) != $true)) )),
% 1.41/0.52 inference(equality_resolution,[],[f1885])).
% 1.41/0.52 thf(f2186,plain,(
% 1.41/0.52 ( ! [X2 : nat,X1 : set_nat] : ((((insert_nat @ X2 @ bot_bot_set_nat)) = ((insert_nat @ X2 @ X1))) | (((ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat))) != $true)) )),
% 1.41/0.52 inference(equality_resolution,[],[f1968])).
% 1.41/0.52 thf(f2266,definition,(
% 1.41/0.52 spl106_6 <=> (((insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) = f)),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_6])],[avatar_definition])).
% 1.41/0.52 thf(f2269,plain,(
% 1.41/0.52 spl106_6),
% 1.41/0.52 inference(avatar_split_clause,[],[f1747,f2266])).
% 1.41/0.52 thf(f2281,definition,(
% 1.41/0.52 spl106_9 <=> (g = ((restri1162247455um_a_b @ g)))),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_9])],[avatar_definition])).
% 1.41/0.52 thf(f2284,plain,(
% 1.41/0.52 spl106_9),
% 1.41/0.52 inference(avatar_split_clause,[],[f2010,f2281])).
% 1.41/0.52 thf(f2321,definition,(
% 1.41/0.52 spl106_17 <=> (((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) = $true)),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_17])],[avatar_definition])).
% 1.41/0.52 thf(f2325,definition,(
% 1.41/0.52 spl106_18 <=> (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) = ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))))),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_18])],[avatar_definition])).
% 1.41/0.52 thf(f2327,plain,(
% 1.41/0.52 (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) != ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) | spl106_18),
% 1.41/0.52 inference(avatar_component_clause,[],[f2325])).
% 1.41/0.52 thf(f2329,definition,(
% 1.41/0.52 spl106_19 <=> (((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g))) = $true)),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_19])],[avatar_definition])).
% 1.41/0.52 thf(f2333,definition,(
% 1.41/0.52 spl106_20 <=> (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g))) = $true)),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_20])],[avatar_definition])).
% 1.41/0.52 thf(f2335,plain,(
% 1.41/0.52 (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g))) != $true) | spl106_20),
% 1.41/0.52 inference(avatar_component_clause,[],[f2333])).
% 1.41/0.52 thf(f2337,definition,(
% 1.41/0.52 spl106_21 <=> (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))))),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_21])],[avatar_definition])).
% 1.41/0.52 thf(f2339,plain,(
% 1.41/0.52 (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) != ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) | spl106_21),
% 1.41/0.52 inference(avatar_component_clause,[],[f2337])).
% 1.41/0.52 thf(f2340,plain,(
% 1.41/0.52 ~spl106_9 | ~spl106_17 | ~spl106_18 | ~spl106_19 | ~spl106_20 | ~spl106_21),
% 1.41/0.52 inference(avatar_split_clause,[],[f1850,f2337,f2333,f2329,f2325,f2321,f2281])).
% 1.41/0.52 thf(f2382,definition,(
% 1.41/0.52 spl106_30 <=> (((unival2092813468um_a_b @ f)) = $true)),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_30])],[avatar_definition])).
% 1.41/0.52 thf(f2385,plain,(
% 1.41/0.52 spl106_30),
% 1.41/0.52 inference(avatar_split_clause,[],[f1961,f2382])).
% 1.41/0.52 thf(f2387,definition,(
% 1.41/0.52 spl106_31 <=> (((insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = ((domain1368163076um_a_b @ f)))),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_31])],[avatar_definition])).
% 1.41/0.52 thf(f2390,plain,(
% 1.41/0.52 spl106_31),
% 1.41/0.52 inference(avatar_split_clause,[],[f1726,f2387])).
% 1.41/0.52 thf(f2397,definition,(
% 1.41/0.52 spl106_33 <=> (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g))) = $true)),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_33])],[avatar_definition])).
% 1.41/0.52 thf(f2400,plain,(
% 1.41/0.52 spl106_33),
% 1.41/0.52 inference(avatar_split_clause,[],[f1866,f2397])).
% 1.41/0.52 thf(f2432,definition,(
% 1.41/0.52 spl106_40 <=> (((ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g))) = $true)),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_40])],[avatar_definition])).
% 1.41/0.52 thf(f2435,plain,(
% 1.41/0.52 spl106_40),
% 1.41/0.52 inference(avatar_split_clause,[],[f1776,f2432])).
% 1.41/0.52 thf(f2451,definition,(
% 1.41/0.52 (((insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != f) | (((unival2092813468um_a_b @ f)) != $true) | (((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) = $true)),
% 1.41/0.52 introduced(theory,[theory_tautology_sat_conflict])).
% 1.41/0.52 thf(f2455,plain,(
% 1.41/0.52 (((insert_nat @ zero_zero_nat @ bot_bot_set_nat)) != ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) | spl106_18),
% 1.41/0.52 inference(superposition,[],[f2327,f1746])).
% 1.41/0.52 thf(f2457,definition,(
% 1.41/0.52 spl106_44 <=> (((insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))))),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_44])],[avatar_definition])).
% 1.41/0.52 thf(f2458,plain,(
% 1.41/0.52 (((insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) | ~spl106_44),
% 1.41/0.52 inference(avatar_component_clause,[],[f2457])).
% 1.41/0.52 thf(f2460,plain,(
% 1.41/0.52 ~spl106_44 | spl106_18),
% 1.41/0.52 inference(avatar_split_clause,[],[f2455,f2325,f2457])).
% 1.41/0.52 thf(f2461,definition,(
% 1.41/0.52 (((insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != f) | (((insert_nat @ zero_zero_nat @ bot_bot_set_nat)) != ((domain1368163076um_a_b @ f))) | (((insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))))),
% 1.41/0.52 introduced(theory,[theory_tautology_sat_conflict])).
% 1.41/0.52 thf(f2462,definition,(
% 1.41/0.52 (((insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != f) | (((insert_nat @ zero_zero_nat @ bot_bot_set_nat)) != ((domain1368163076um_a_b @ f))) | (((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) != ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) | (((ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g))) != $true) | (((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g))) = $true)),
% 1.41/0.52 introduced(theory,[theory_tautology_sat_conflict])).
% 1.41/0.52 thf(f2471,plain,(
% 1.41/0.52 (((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g))) != $true) | spl106_20),
% 1.41/0.52 inference(forward_demodulation,[],[f2335,f1847])).
% 1.41/0.52 thf(f2472,plain,(
% 1.41/0.52 ~spl106_33 | spl106_20),
% 1.41/0.52 inference(avatar_split_clause,[],[f2471,f2333,f2397])).
% 1.41/0.52 thf(f2663,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1174980151um_a_b] : (($true != ((ord_le823954903um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ X0))) | ($true = ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (domain1368163076um_a_b @ X0))))) ) | ~spl106_44),
% 1.41/0.52 inference(superposition,[],[f1737,f2458])).
% 1.41/0.52 thf(f3050,plain,(
% 1.41/0.52 ( ! [X0 : set_nat] : ((((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ X0))) != ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ X0))))) | ($true != ((ord_less_eq_set_nat @ X0 @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) ) | spl106_21),
% 1.41/0.52 inference(superposition,[],[f2339,f2186])).
% 1.41/0.52 thf(f3119,plain,(
% 1.41/0.52 ( ! [X0 : set_nat] : ((((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ X0))) != ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ X0))))) | ($true != ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ X0) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) ) | spl106_21),
% 1.41/0.52 inference(superposition,[],[f3050,f1989])).
% 1.41/0.52 thf(f3163,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1174980151um_a_b] : ((((ord_le823954903um_a_b @ bot_bo575978147um_a_b @ X0)) != $true) | ($true = ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (domain1368163076um_a_b @ X0)))) | ($true != ((member1294585472um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ X0))) | ($true != $true)) ) | ~spl106_44),
% 1.41/0.52 inference(superposition,[],[f2663,f1711])).
% 1.41/0.52 thf(f3170,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1174980151um_a_b] : (($true != ((member1294585472um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ X0))) | (((ord_le823954903um_a_b @ bot_bo575978147um_a_b @ X0)) != $true) | ($true = ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (domain1368163076um_a_b @ X0))))) ) | ~spl106_44),
% 1.41/0.52 inference(trivial_inequality_removal,[],[f3163])).
% 1.41/0.52 thf(f3173,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1174980151um_a_b] : (($true = ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (domain1368163076um_a_b @ X0)))) | ($true != ((member1294585472um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ X0)))) ) | ~spl106_44),
% 1.41/0.52 inference(forward_subsumption_resolution,[],[f3170,f1878])).
% 1.41/0.52 thf(f3214,plain,(
% 1.41/0.52 ( ! [X0 : set_Pr1647387645at_nat,X1 : set_nat] : ((((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ X0) @ (insert_nat @ zero_zero_nat @ X1))) != ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ X0) @ (insert_nat @ zero_zero_nat @ X1))))) | ($true != ((ord_le1909159005at_nat @ X0 @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat)))) | ($true != ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ X1) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) ) | spl106_21),
% 1.41/0.52 inference(superposition,[],[f3119,f2169])).
% 1.41/0.52 thf(f3251,plain,(
% 1.41/0.52 ($true = ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | ($true != ((member1294585472um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)))) | ~spl106_44),
% 1.41/0.52 inference(superposition,[],[f3173,f2458])).
% 1.41/0.52 thf(f3259,plain,(
% 1.41/0.52 ($true = ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | ~spl106_44),
% 1.41/0.52 inference(forward_subsumption_resolution,[],[f3251,f1663])).
% 1.41/0.52 thf(f3262,definition,(
% 1.41/0.52 spl106_60 <=> ($true = ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))),
% 1.41/0.52 introduced(definition,[new_symbols(definition,[spl106_60])],[avatar_definition])).
% 1.41/0.52 thf(f3264,plain,(
% 1.41/0.52 ($true = ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | ~spl106_60),
% 1.41/0.52 inference(avatar_component_clause,[],[f3262])).
% 1.41/0.52 thf(f3265,plain,(
% 1.41/0.52 spl106_60 | ~spl106_44),
% 1.41/0.52 inference(avatar_split_clause,[],[f3259,f2457,f3262])).
% 1.41/0.52 thf(f3650,plain,(
% 1.41/0.52 ($true != ((ord_le1909159005at_nat @ bot_bo810816657at_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat)))) | (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) != ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))) | ($true != ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | spl106_21),
% 1.41/0.52 inference(superposition,[],[f3214,f1879])).
% 1.41/0.52 thf(f3654,plain,(
% 1.41/0.52 ($true != ((ord_le1909159005at_nat @ bot_bo810816657at_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat)))) | ($true != ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | spl106_21),
% 1.41/0.52 inference(trivial_inequality_removal,[],[f3650])).
% 1.41/0.52 thf(f3658,plain,(
% 1.41/0.52 ($true != ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | spl106_21),
% 1.41/0.52 inference(forward_subsumption_resolution,[],[f3654,f2005])).
% 1.41/0.52 thf(f3664,plain,(
% 1.41/0.52 ($true != ((ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | spl106_21),
% 1.41/0.52 inference(forward_demodulation,[],[f3658,f1989])).
% 1.41/0.52 thf(f3667,plain,(
% 1.41/0.52 $false | (spl106_21 | ~spl106_60)),
% 1.41/0.52 inference(forward_subsumption_resolution,[],[f3664,f3264])).
% 1.41/0.52 thf(f3668,plain,(
% 1.41/0.52 spl106_21 | ~spl106_60),
% 1.41/0.52 inference(avatar_contradiction_clause,[],[f3667])).
% 1.41/0.52 cnf(s7, plain, spl106_6, inference(sat_conversion,[],[f2269])).
% 1.41/0.52 cnf(s10, plain, spl106_9, inference(sat_conversion,[],[f2284])).
% 1.41/0.52 cnf(s18, plain, ~spl106_9 | ~spl106_17 | ~spl106_18 | ~spl106_19 | ~spl106_20 | ~spl106_21, inference(sat_conversion,[],[f2340])).
% 1.41/0.52 cnf(s30, plain, spl106_30, inference(sat_conversion,[],[f2385])).
% 1.41/0.52 cnf(s33, plain, spl106_31, inference(sat_conversion,[],[f2390])).
% 1.41/0.52 cnf(s35, plain, spl106_33, inference(sat_conversion,[],[f2400])).
% 1.41/0.52 cnf(s44, plain, spl106_40, inference(sat_conversion,[],[f2435])).
% 1.41/0.52 cnf(s50, plain, ~spl106_6 | spl106_17 | ~spl106_30, inference(sat_conversion,[],[f2451])).
% 1.41/0.52 cnf(s51, plain, spl106_18 | ~spl106_44, inference(sat_conversion,[],[f2460])).
% 1.41/0.52 cnf(s52, plain, ~spl106_6 | ~spl106_31 | spl106_44, inference(sat_conversion,[],[f2461])).
% 1.41/0.52 cnf(s53, plain, ~spl106_6 | ~spl106_18 | spl106_19 | ~spl106_31 | ~spl106_40, inference(sat_conversion,[],[f2462])).
% 1.41/0.52 cnf(s56, plain, spl106_20 | ~spl106_33, inference(sat_conversion,[],[f2472])).
% 1.41/0.52 cnf(s74, plain, ~spl106_44 | spl106_60, inference(sat_conversion,[],[f3265])).
% 1.41/0.52 cnf(s81, plain, spl106_21 | ~spl106_60, inference(sat_conversion,[],[f3668])).
% 1.41/0.52 cnf(s86, plain, spl106_20, inference(rat,[],[s56,s35])).
% 1.41/0.52 cnf(s88, plain, ~spl106_9 | ~spl106_17 | ~spl106_18 | ~spl106_19 | ~spl106_21, inference(rat,[],[s18,s86])).
% 1.41/0.52 cnf(s90, plain, spl106_44, inference(rat,[],[s52,s33,s7])).
% 1.41/0.52 cnf(s91, plain, spl106_17, inference(rat,[],[s50,s30,s7])).
% 1.41/0.52 cnf(s92, plain, spl106_60, inference(rat,[],[s74,s90])).
% 1.41/0.52 cnf(s93, plain, spl106_18, inference(rat,[],[s51,s90])).
% 1.41/0.52 cnf(s94, plain, spl106_21, inference(rat,[],[s81,s92])).
% 1.41/0.52 cnf(s95, plain, spl106_19, inference(rat,[],[s53,s44,s33,s7,s93])).
% 1.41/0.52 cnf(s96, plain, $false, inference(rat,[],[s88,s94,s91,s10,s95,s93])).
% 1.41/0.52 thf(f3669,plain,(
% 1.41/0.52 $false),
% 1.41/0.52 inference(avatar_sat_refutation,[],[s96])).
% 1.41/0.52 % SZS output end Proof for theBenchmark
% 1.41/0.52 % (1755623)------------------------------
% 1.41/0.52 % (1755623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.52 % (1755623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.52 % (1755623)CaDiCaL version: 2.1.3
% 1.41/0.52 % (1755623)Termination reason: Refutation
% 1.41/0.52 % (1755623)Time elapsed: 0.173 s
% 1.41/0.52 % (1755623)Peak memory usage: 16 MB
% 1.41/0.52 % (1755623)Instructions burned: 313 (million)
% 1.41/0.52 % (1755615)Success in time 0.228 s
% 1.41/0.52 % Vampire exiting
%------------------------------------------------------------------------------