%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP176^1 : 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 : n002.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 0.93s 0.48s
% Output : Refutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP176^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n002.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 20:09:08 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 Running higher-order theorem proving
% 0.24/0.33 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
% 0.93/0.47 % (1789418)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.93/0.47 % (1789427)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2543363268:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.93/0.47 % (1789429)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.93/0.47 % (1789429)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
% 0.93/0.47 % (1789427)Instruction limit reached!
% 0.93/0.47 % (1789427)------------------------------
% 0.93/0.47 % (1789427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.47 % (1789427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.47 % (1789427)CaDiCaL version: 2.1.3
% 0.93/0.47 % (1789427)Termination reason: Instruction limit
% 0.93/0.47 % (1789427)Termination phase: Property scanning
% 0.93/0.47 % (1789427)Time elapsed: 0.007 s
% 0.93/0.47 % (1789427)Peak memory usage: 10 MB
% 0.93/0.47 % (1789427)Instructions burned: 27 (million)
% 0.93/0.47 % (1789424)lrs+10_16_si=on:nwc=1.5:random_seed=3515514637:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.93/0.47 % (1789423)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2457877793:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.93/0.47 % (1789425)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4094005239:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.93/0.47 % (1789426)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=908621842: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)
% 0.93/0.47 % (1789428)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2107291802:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.93/0.47 % (1789429)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=3491880740:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.93/0.47 % (1789425)Instruction limit reached!
% 0.93/0.47 % (1789425)------------------------------
% 0.93/0.47 % (1789425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.47 % (1789425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.47 % (1789425)CaDiCaL version: 2.1.3
% 0.93/0.47 % (1789425)Termination reason: Instruction limit
% 0.93/0.47 % (1789425)Termination phase: shuffling
% 0.93/0.47 % (1789425)Time elapsed: 0.004 s
% 0.93/0.47 % (1789425)Peak memory usage: 10 MB
% 0.93/0.47 % (1789425)Instructions burned: 7 (million)
% 0.93/0.47 % (1789424)Instruction limit reached!
% 0.93/0.47 % (1789424)------------------------------
% 0.93/0.47 % (1789424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.47 % (1789424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.47 % (1789424)CaDiCaL version: 2.1.3
% 0.93/0.47 % (1789424)Termination reason: Instruction limit
% 0.93/0.47 % (1789424)Termination phase: shuffling
% 0.93/0.47 % (1789424)Time elapsed: 0.009 s
% 0.93/0.47 % (1789424)Peak memory usage: 10 MB
% 0.93/0.47 % (1789424)Instructions burned: 18 (million)
% 0.93/0.47 % (1789435)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3694814146:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.93/0.47 % (1789435)Instruction limit reached!
% 0.93/0.47 % (1789435)------------------------------
% 0.93/0.47 % (1789435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.47 % (1789435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.47 % (1789435)CaDiCaL version: 2.1.3
% 0.93/0.47 % (1789435)Termination reason: Instruction limit
% 0.93/0.47 % (1789435)Termination phase: shuffling
% 0.93/0.47 % (1789435)Time elapsed: 0.001 s
% 0.93/0.47 % (1789435)Peak memory usage: 10 MB
% 0.93/0.47 % (1789435)Instructions burned: 3 (million)
% 0.93/0.47 % (1789441)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2710408479:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.93/0.48 % (1789438)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=830453162:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.93/0.48 % (1789439)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.93/0.48 % (1789441)Instruction limit reached!
% 0.93/0.48 % (1789441)------------------------------
% 0.93/0.48 % (1789441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789441)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789441)Termination reason: Instruction limit
% 0.93/0.48 % (1789441)Termination phase: shuffling
% 0.93/0.48 % (1789441)Time elapsed: 0.003 s
% 0.93/0.48 % (1789441)Peak memory usage: 10 MB
% 0.93/0.48 % (1789441)Instructions burned: 14 (million)
% 0.93/0.48 % (1789438)Instruction limit reached!
% 0.93/0.48 % (1789438)------------------------------
% 0.93/0.48 % (1789438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789438)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789438)Termination reason: Instruction limit
% 0.93/0.48 % (1789438)Termination phase: shuffling
% 0.93/0.48 % (1789438)Time elapsed: 0.003 s
% 0.93/0.48 % (1789438)Peak memory usage: 10 MB
% 0.93/0.48 % (1789438)Instructions burned: 7 (million)
% 0.93/0.48 % (1789439)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=553651421:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.93/0.48 % (1789439)Instruction limit reached!
% 0.93/0.48 % (1789439)------------------------------
% 0.93/0.48 % (1789439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789439)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789439)Termination reason: Instruction limit
% 0.93/0.48 % (1789439)Termination phase: shuffling
% 0.93/0.48 % (1789439)Time elapsed: 0.004 s
% 0.93/0.48 % (1789439)Peak memory usage: 10 MB
% 0.93/0.48 % (1789439)Instructions burned: 9 (million)
% 0.93/0.48 % (1789444)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
% 0.93/0.48 % (1789444)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.93/0.48 % (1789444)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=872590113:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.93/0.48 % (1789423)Instruction limit reached!
% 0.93/0.48 % (1789423)------------------------------
% 0.93/0.48 % (1789423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789423)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789423)Termination reason: Instruction limit
% 0.93/0.48 % (1789423)Termination phase: Function definition elimination
% 0.93/0.48 % (1789423)Time elapsed: 0.040 s
% 0.93/0.48 % (1789423)Peak memory usage: 12 MB
% 0.93/0.48 % (1789423)Instructions burned: 88 (million)
% 0.93/0.48 % (1789428)Instruction limit reached!
% 0.93/0.48 % (1789428)------------------------------
% 0.93/0.48 % (1789428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789428)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789428)Termination reason: Instruction limit
% 0.93/0.48 % (1789428)Termination phase: Property scanning
% 0.93/0.48 % (1789428)Time elapsed: 0.041 s
% 0.93/0.48 % (1789428)Peak memory usage: 12 MB
% 0.93/0.48 % (1789428)Instructions burned: 79 (million)
% 0.93/0.48 % (1789444)Instruction limit reached!
% 0.93/0.48 % (1789444)------------------------------
% 0.93/0.48 % (1789444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789444)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789444)Termination reason: Instruction limit
% 0.93/0.48 % (1789444)Termination phase: shuffling
% 0.93/0.48 % (1789444)Time elapsed: 0.008 s
% 0.93/0.48 % (1789444)Peak memory usage: 10 MB
% 0.93/0.48 % (1789444)Instructions burned: 33 (million)
% 0.93/0.48 % (1789446)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=1140537487:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.93/0.48 % (1789449)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.93/0.48 % (1789451)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3222746336:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.93/0.48 % (1789449)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=3392212696:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.93/0.48 % (1789447)lrs+10_1_si=on:cs=on:random_seed=599465862:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.93/0.48 % (1789450)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3025436888:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.93/0.48 % (1789449)Instruction limit reached!
% 0.93/0.48 % (1789449)------------------------------
% 0.93/0.48 % (1789449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789449)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789449)Termination reason: Instruction limit
% 0.93/0.48 % (1789449)Termination phase: shuffling
% 0.93/0.48 % (1789449)Time elapsed: 0.001 s
% 0.93/0.48 % (1789449)Peak memory usage: 10 MB
% 0.93/0.48 % (1789449)Instructions burned: 2 (million)
% 0.93/0.48 % (1789447)Instruction limit reached!
% 0.93/0.48 % (1789447)------------------------------
% 0.93/0.48 % (1789447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789447)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789447)Termination reason: Instruction limit
% 0.93/0.48 % (1789447)Termination phase: shuffling
% 0.93/0.48 % (1789447)Time elapsed: 0.009 s
% 0.93/0.48 % (1789447)Peak memory usage: 10 MB
% 0.93/0.48 % (1789447)Instructions burned: 9 (million)
% 0.93/0.48 % (1789429)Instruction limit reached!
% 0.93/0.48 % (1789429)------------------------------
% 0.93/0.48 % (1789429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789429)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789429)Termination reason: Instruction limit
% 0.93/0.48 % (1789429)Termination phase: Saturation
% 0.93/0.48 % (1789429)Time elapsed: 0.069 s
% 0.93/0.48 % (1789429)Peak memory usage: 14 MB
% 0.93/0.48 % (1789429)Instructions burned: 157 (million)
% 0.93/0.48 % (1789451)Refutation not found, incomplete strategy
% 0.93/0.48 % (1789451)------------------------------
% 0.93/0.48 % (1789451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789451)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789451)Termination reason: Refutation not found, incomplete strategy
% 0.93/0.48 % (1789451)Time elapsed: 0.019 s
% 0.93/0.48 % (1789451)Peak memory usage: 13 MB
% 0.93/0.48 % (1789451)Instructions burned: 72 (million)
% 0.93/0.48 % (1789451)------------------------------
% 0.93/0.48 % (1789451)------------------------------
% 0.93/0.48 % (1789450)Instruction limit reached!
% 0.93/0.48 % (1789450)------------------------------
% 0.93/0.48 % (1789450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789450)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789450)Termination reason: Instruction limit
% 0.93/0.48 % (1789450)Termination phase: SInE selection
% 0.93/0.48 % (1789450)Time elapsed: 0.018 s
% 0.93/0.48 % (1789450)Peak memory usage: 11 MB
% 0.93/0.48 % (1789450)Instructions burned: 39 (million)
% 0.93/0.48 % (1789457)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4176630658:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.93/0.48 % (1789426) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1789418-1789426"...
% 0.93/0.48 % (1789446)Instruction limit reached!
% 0.93/0.48 % (1789446)------------------------------
% 0.93/0.48 % (1789446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789446)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789446)Termination reason: Instruction limit
% 0.93/0.48 % (1789446)Termination phase: Property scanning
% 0.93/0.48 % (1789446)Time elapsed: 0.037 s
% 0.93/0.48 % (1789446)Peak memory usage: 11 MB
% 0.93/0.48 % (1789446)Instructions burned: 86 (million)
% 0.93/0.48 % (1789426)...printing done.
% 0.93/0.48 % (1789460)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3860642703:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.93/0.48 % (1789459)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1177332640:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.93/0.48 % (1789426)Refutation found. Thanks to Tanya!
% 0.93/0.48 % SZS status Theorem for theBenchmark
% 0.93/0.48 % SZS output start Proof for theBenchmark
% 0.93/0.48 thf(type_def_5, type, set_Pr2109276827od_b_b: $tType).
% 0.93/0.48 thf(type_def_6, type, produc970027067od_b_b: $tType).
% 0.93/0.48 thf(type_def_7, type, set_Pr1071216121od_b_b: $tType).
% 0.93/0.48 thf(type_def_8, type, set_Pr2134561957od_b_b: $tType).
% 0.93/0.48 thf(type_def_9, type, set_Pr1021918435od_b_b: $tType).
% 0.93/0.48 thf(type_def_10, type, produc1052326083od_b_b: $tType).
% 0.93/0.48 thf(type_def_11, type, produc1990339951od_b_b: $tType).
% 0.93/0.48 thf(type_def_12, type, set_Pr2060523537od_b_b: $tType).
% 0.93/0.48 thf(type_def_13, type, set_Pr1906739389_b_b_b: $tType).
% 0.93/0.48 thf(type_def_14, type, produc1605346267od_b_b: $tType).
% 0.93/0.48 thf(type_def_15, type, produc276146823_b_b_b: $tType).
% 0.93/0.48 thf(type_def_16, type, set_Pr306736955tant_a: $tType).
% 0.93/0.48 thf(type_def_17, type, set_Pr1324126435od_b_b: $tType).
% 0.93/0.48 thf(type_def_18, type, labele1835558936od_b_b: $tType).
% 0.93/0.48 thf(type_def_19, type, set_Pr2007082183od_b_b: $tType).
% 0.93/0.48 thf(type_def_20, type, produc1367125253tant_a: $tType).
% 0.93/0.48 thf(type_def_21, type, produc1213276845od_b_b: $tType).
% 0.93/0.48 thf(type_def_22, type, produc1168037607od_b_b: $tType).
% 0.93/0.48 thf(type_def_23, type, labele1159362096nt_a_b: $tType).
% 0.93/0.48 thf(type_def_24, type, set_Pr621705391od_b_b: $tType).
% 0.93/0.48 thf(type_def_25, type, set_Pr357419743_b_b_b: $tType).
% 0.93/0.48 thf(type_def_26, type, produc255402447od_b_b: $tType).
% 0.93/0.48 thf(type_def_27, type, produc2112523263_b_b_b: $tType).
% 0.93/0.48 thf(type_def_28, type, set_St761939237tant_a: $tType).
% 0.93/0.48 thf(type_def_29, type, set_Product_prod_b_b: $tType).
% 0.93/0.48 thf(type_def_30, type, standard_Constant_a: $tType).
% 0.93/0.48 thf(type_def_31, type, product_prod_b_b: $tType).
% 0.93/0.48 thf(type_def_32, type, set_b: $tType).
% 0.93/0.48 thf(type_def_33, type, b: $tType).
% 0.93/0.48 thf(type_def_34, type, sTfun: ($tType * $tType) > $tType).
% 0.93/0.48 thf(func_def_0, type, equiv_1629197578_set_b: (set_Pr2109276827od_b_b > set_Product_prod_b_b > (produc1213276845od_b_b > b > set_b) > $o)).
% 0.93/0.48 thf(func_def_1, type, equiv_1036235914_set_b: (set_Pr2007082183od_b_b > set_Product_prod_b_b > (product_prod_b_b > b > set_b) > $o)).
% 0.93/0.48 thf(func_def_2, type, equiv_167626658_set_b: (set_Product_prod_b_b > set_Product_prod_b_b > (b > b > set_b) > $o)).
% 0.93/0.48 thf(func_def_3, type, equiv_1821124534_set_b: (set_Product_prod_b_b > (b > set_b) > $o)).
% 0.93/0.48 thf(func_def_4, type, equiv_2048442231od_b_b: (set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o)).
% 0.93/0.48 thf(func_def_5, type, equiv_1125628061od_b_b: (set_Product_prod_b_b > set_Pr2007082183od_b_b > $o)).
% 0.93/0.48 thf(func_def_6, type, equiv_equiv_b: (set_b > set_Product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_7, type, equiv_proj_b_b: (set_Product_prod_b_b > b > set_b)).
% 0.93/0.48 thf(func_def_8, type, hilber46179633od_b_b: ((produc1213276845od_b_b > $o) > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_9, type, hilber620807523od_b_b: ((product_prod_b_b > $o) > product_prod_b_b)).
% 0.93/0.48 thf(func_def_10, type, hilbert_Eps_b: ((b > $o) > b)).
% 0.93/0.48 thf(func_def_11, type, if_b: ($o > b > b > b)).
% 0.93/0.48 thf(func_def_12, type, standard_S_Idt_a: standard_Constant_a).
% 0.93/0.48 thf(func_def_13, type, getRel904497637nt_a_b: (standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_14, type, graph_792023598_b_b_b: (labele1835558936od_b_b > labele1159362096nt_a_b > set_Pr357419743_b_b_b > $o)).
% 0.93/0.48 thf(func_def_15, type, graph_222606102_a_b_b: (labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_16, type, labele170595300od_b_b: (set_Pr1021918435od_b_b > set_Product_prod_b_b > labele1835558936od_b_b)).
% 0.93/0.48 thf(func_def_17, type, labele1230159100nt_a_b: (set_Pr1324126435od_b_b > set_b > labele1159362096nt_a_b)).
% 0.93/0.48 thf(func_def_18, type, labele377702064od_b_b: ((set_Pr1324126435od_b_b > set_b > set_Pr1324126435od_b_b) > labele1159362096nt_a_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_19, type, labele1287464530_set_b: ((set_Pr1324126435od_b_b > set_b > set_b) > labele1159362096nt_a_b > set_b)).
% 0.93/0.48 thf(func_def_20, type, labele1741081071nt_a_b: (labele1159362096nt_a_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_21, type, labele1424214014nt_a_b: (labele1159362096nt_a_b > set_b)).
% 0.93/0.48 thf(func_def_22, type, restri446606278nt_a_b: (labele1159362096nt_a_b > labele1159362096nt_a_b)).
% 0.93/0.48 thf(func_def_23, type, order_609163036od_b_b: (set_Product_prod_b_b > set_Pr2007082183od_b_b > $o)).
% 0.93/0.48 thf(func_def_24, type, order_653178932r_on_b: (set_b > set_Product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_25, type, bot_bo1734638456_b_b_o: (standard_Constant_a > product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_26, type, bot_bo1167600078_b_b_o: (produc1213276845od_b_b > $o)).
% 0.93/0.48 thf(func_def_27, type, bot_bo1302443370_b_b_o: (product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_28, type, bot_bot_b_b_o: (b > b > $o)).
% 0.93/0.48 thf(func_def_29, type, bot_bot_b_o: (b > $o)).
% 0.93/0.48 thf(func_def_30, type, bot_bo1160111033tant_a: set_St761939237tant_a).
% 0.93/0.48 thf(func_def_31, type, bot_bo1964903287od_b_b: set_Pr1021918435od_b_b).
% 0.93/0.48 thf(func_def_32, type, bot_bo1664927607od_b_b: set_Pr1324126435od_b_b).
% 0.93/0.48 thf(func_def_33, type, bot_bo1174586163od_b_b: set_Pr2007082183od_b_b).
% 0.93/0.48 thf(func_def_34, type, bot_bo1124087115_b_b_b: set_Pr357419743_b_b_b).
% 0.93/0.48 thf(func_def_35, type, bot_bo1343651123od_b_b: set_Product_prod_b_b).
% 0.93/0.48 thf(func_def_36, type, bot_bot_set_b: set_b).
% 0.93/0.48 thf(func_def_37, type, ord_le123089219od_b_b: (set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o)).
% 0.93/0.48 thf(func_def_38, type, ord_le1036320359od_b_b: (set_Product_prod_b_b > set_Product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_39, type, ord_less_eq_set_b: (set_b > set_b > $o)).
% 0.93/0.48 thf(func_def_40, type, produc1432590431od_b_b: (standard_Constant_a > product_prod_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_41, type, produc449289715od_b_b: (produc1213276845od_b_b > produc1213276845od_b_b > produc970027067od_b_b)).
% 0.93/0.48 thf(func_def_42, type, produc1597690145od_b_b: (produc1213276845od_b_b > product_prod_b_b > produc1990339951od_b_b)).
% 0.93/0.48 thf(func_def_43, type, produc1580777273_b_b_b: (produc1213276845od_b_b > b > produc276146823_b_b_b)).
% 0.93/0.48 thf(func_def_44, type, produc1977323903tant_a: (product_prod_b_b > standard_Constant_a > produc1367125253tant_a)).
% 0.93/0.48 thf(func_def_45, type, produc732676669od_b_b: (product_prod_b_b > produc1213276845od_b_b > produc1052326083od_b_b)).
% 0.93/0.48 thf(func_def_46, type, produc546497367od_b_b: (product_prod_b_b > product_prod_b_b > produc1168037607od_b_b)).
% 0.93/0.48 thf(func_def_47, type, produc1001682799_b_b_b: (product_prod_b_b > b > produc2112523263_b_b_b)).
% 0.93/0.48 thf(func_def_48, type, produc800495189od_b_b: (b > produc1213276845od_b_b > produc1605346267od_b_b)).
% 0.93/0.48 thf(func_def_49, type, produc1257047359od_b_b: (b > product_prod_b_b > produc255402447od_b_b)).
% 0.93/0.48 thf(func_def_50, type, product_Pair_b_b: (b > b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_51, type, image_1916422435od_b_b: (set_Pr1324126435od_b_b > set_St761939237tant_a > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_52, type, image_763305007od_b_b: (set_Pr2109276827od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_53, type, image_1397930469od_b_b: (set_Pr2134561957od_b_b > set_Pr1324126435od_b_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_54, type, image_1764625405_b_b_b: (set_Pr1906739389_b_b_b > set_Pr1324126435od_b_b > set_b)).
% 0.93/0.48 thf(func_def_55, type, image_532916993od_b_b: (set_Pr1071216121od_b_b > set_Product_prod_b_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_56, type, image_1928024979od_b_b: (set_Pr2007082183od_b_b > set_Product_prod_b_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_57, type, image_921732011_b_b_b: (set_Pr357419743_b_b_b > set_Product_prod_b_b > set_b)).
% 0.93/0.48 thf(func_def_58, type, image_984343321od_b_b: (set_Pr2060523537od_b_b > set_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_59, type, image_1177096571od_b_b: (set_Pr621705391od_b_b > set_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_60, type, image_b_b: (set_Product_prod_b_b > set_b > set_b)).
% 0.93/0.48 thf(func_def_61, type, conver1398856763od_b_b: (set_Pr1324126435od_b_b > set_Pr306736955tant_a)).
% 0.93/0.48 thf(func_def_62, type, conver1943590235tant_a: (set_Pr306736955tant_a > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_63, type, converse_b_b: (set_Product_prod_b_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_64, type, refl_o1921098222od_b_b: (set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o)).
% 0.93/0.48 thf(func_def_65, type, refl_o2134473190od_b_b: (set_Product_prod_b_b > set_Pr2007082183od_b_b > $o)).
% 0.93/0.48 thf(func_def_66, type, refl_on_b: (set_b > set_Product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_67, type, total_771970601od_b_b: (set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o)).
% 0.93/0.48 thf(func_def_68, type, total_178717291od_b_b: (set_Product_prod_b_b > set_Pr2007082183od_b_b > $o)).
% 0.93/0.48 thf(func_def_69, type, total_on_b: (set_b > set_Product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_70, type, collec279084418od_b_b: ((produc1213276845od_b_b > $o) > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_71, type, collec1481886546od_b_b: ((product_prod_b_b > $o) > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_72, type, collect_b: ((b > $o) > set_b)).
% 0.93/0.48 thf(func_def_73, type, insert1909710879tant_a: (standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a)).
% 0.93/0.48 thf(func_def_74, type, insert2037698781od_b_b: (produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_75, type, insert1098249399od_b_b: (produc1168037607od_b_b > set_Pr2007082183od_b_b > set_Pr2007082183od_b_b)).
% 0.93/0.48 thf(func_def_76, type, insert1952693431od_b_b: (product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_77, type, insert_b: (b > set_b > set_b)).
% 0.93/0.48 thf(func_def_78, type, is_sin1465183929od_b_b: (set_Pr1324126435od_b_b > $o)).
% 0.93/0.48 thf(func_def_79, type, is_sin1713057243od_b_b: (set_Product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_80, type, is_singleton_b: (set_b > $o)).
% 0.93/0.48 thf(func_def_81, type, the_el329196508od_b_b: (set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_82, type, the_elem_b: (set_b > b)).
% 0.93/0.48 thf(func_def_83, type, member1632892294tant_a: (standard_Constant_a > set_St761939237tant_a > $o)).
% 0.93/0.48 thf(func_def_84, type, member1516365892od_b_b: (produc1213276845od_b_b > set_Pr1324126435od_b_b > $o)).
% 0.93/0.48 thf(func_def_85, type, member1086024932od_b_b: (produc970027067od_b_b > set_Pr2109276827od_b_b > $o)).
% 0.93/0.48 thf(func_def_86, type, member942707974od_b_b: (produc1990339951od_b_b > set_Pr2134561957od_b_b > $o)).
% 0.93/0.48 thf(func_def_87, type, member1417789726_b_b_b: (produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o)).
% 0.93/0.48 thf(func_def_88, type, member1670214300tant_a: (produc1367125253tant_a > set_Pr306736955tant_a > $o)).
% 0.93/0.48 thf(func_def_89, type, member4694106od_b_b: (produc1052326083od_b_b > set_Pr1071216121od_b_b > $o)).
% 0.93/0.48 thf(func_def_90, type, member1652792080od_b_b: (produc1168037607od_b_b > set_Pr2007082183od_b_b > $o)).
% 0.93/0.48 thf(func_def_91, type, member351494440_b_b_b: (produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o)).
% 0.93/0.48 thf(func_def_92, type, member599505522od_b_b: (produc1605346267od_b_b > set_Pr2060523537od_b_b > $o)).
% 0.93/0.48 thf(func_def_93, type, member641857272od_b_b: (produc255402447od_b_b > set_Pr621705391od_b_b > $o)).
% 0.93/0.48 thf(func_def_94, type, member1285940496od_b_b: (product_prod_b_b > set_Product_prod_b_b > $o)).
% 0.93/0.48 thf(func_def_95, type, member_b: (b > set_b > $o)).
% 0.93/0.48 thf(func_def_96, type, g: labele1159362096nt_a_b).
% 0.93/0.48 thf(func_def_97, type, p: (b > b > $o)).
% 0.93/0.48 thf(func_def_98, type, f: (b > b)).
% 0.93/0.48 thf(func_def_99, type, x: b).
% 0.93/0.48 thf(func_def_100, type, y: b).
% 0.93/0.48 thf(func_def_102, type, vAND: ($o > $o > $o)).
% 0.93/0.48 thf(func_def_103, type, db0: !>[X0: $tType]:(X0)).
% 0.93/0.48 thf(func_def_104, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.93/0.48 thf(func_def_107, type, db1: !>[X0: $tType]:(X0)).
% 0.93/0.48 thf(func_def_108, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.93/0.48 thf(func_def_109, type, vIMP: ($o > $o > $o)).
% 0.93/0.48 thf(func_def_110, type, db2: !>[X0: $tType]:(X0)).
% 0.93/0.48 thf(func_def_111, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.93/0.48 thf(func_def_112, type, vOR: ($o > $o > $o)).
% 0.93/0.48 thf(func_def_113, type, db3: !>[X0: $tType]:(X0)).
% 0.93/0.48 thf(func_def_114, type, vNOT: ($o > $o)).
% 0.93/0.48 thf(func_def_115, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.93/0.48 thf(func_def_116, type, sK0: (set_b > b)).
% 0.93/0.48 thf(func_def_117, type, sK1: (standard_Constant_a > set_Pr306736955tant_a > product_prod_b_b > standard_Constant_a)).
% 0.93/0.48 thf(func_def_118, type, sK2: (standard_Constant_a > set_Pr306736955tant_a > product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_119, type, sK3: (set_Pr1324126435od_b_b > b > set_Pr1906739389_b_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_120, type, sK4: (b > set_b > set_b)).
% 0.93/0.48 thf(func_def_121, type, sK5: ((b > $o) > (b > $o) > b)).
% 0.93/0.48 thf(func_def_122, type, sK6: (product_prod_b_b > set_Pr1324126435od_b_b > set_Pr2134561957od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_123, type, sK7: (produc1213276845od_b_b > set_Pr306736955tant_a > product_prod_b_b)).
% 0.93/0.48 thf(func_def_124, type, sK8: (produc1213276845od_b_b > set_Pr306736955tant_a > standard_Constant_a)).
% 0.93/0.48 thf(func_def_125, type, sK9: (b > set_Product_prod_b_b > set_b > b)).
% 0.93/0.48 thf(func_def_126, type, sK10: (set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_127, type, sK11: (set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > standard_Constant_a)).
% 0.93/0.48 thf(func_def_128, type, sK12: (set_Pr1071216121od_b_b > produc1213276845od_b_b > set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_129, type, sK13: (product_prod_b_b > set_Pr2007082183od_b_b > set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_130, type, sK14: (set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_131, type, sK15: (product_prod_b_b > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_132, type, sK16: (product_prod_b_b > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_133, type, sK17: (set_b > b > set_b)).
% 0.93/0.48 thf(func_def_134, type, sK18: (set_Pr1324126435od_b_b > (produc1213276845od_b_b > $o) > (produc1213276845od_b_b > $o) > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_135, type, sK19: (set_Pr2109276827od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_136, type, sK20: ((b > $o) > set_b > (b > $o) > b)).
% 0.93/0.48 thf(func_def_137, type, sK21: ((product_prod_b_b > $o) > b)).
% 0.93/0.48 thf(func_def_138, type, sK22: ((product_prod_b_b > $o) > b)).
% 0.93/0.48 thf(func_def_139, type, sK23: (product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_140, type, sK24: (product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_141, type, sK25: ((b > $o) > (b > $o) > b)).
% 0.93/0.48 thf(func_def_142, type, sK26: (set_Pr1324126435od_b_b > (product_prod_b_b > standard_Constant_a > $o) > product_prod_b_b)).
% 0.93/0.48 thf(func_def_143, type, sK27: (set_Pr1324126435od_b_b > (product_prod_b_b > standard_Constant_a > $o) > standard_Constant_a)).
% 0.93/0.48 thf(func_def_144, type, sK28: (set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_145, type, sK29: (set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_146, type, sK30: (set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_147, type, sK31: (product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_148, type, sK32: (product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_149, type, sK33: (product_prod_b_b > set_b > set_Pr621705391od_b_b > b)).
% 0.93/0.48 thf(func_def_150, type, sK34: (set_b > b)).
% 0.93/0.48 thf(func_def_151, type, sK35: (set_Pr2007082183od_b_b > set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_152, type, sK36: (set_Pr2007082183od_b_b > set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_153, type, sK37: ((produc1213276845od_b_b > $o) > product_prod_b_b)).
% 0.93/0.48 thf(func_def_154, type, sK38: ((produc1213276845od_b_b > $o) > standard_Constant_a)).
% 0.93/0.48 thf(func_def_155, type, sK39: (set_Pr1324126435od_b_b > standard_Constant_a > product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_156, type, sK40: (set_Pr1324126435od_b_b > standard_Constant_a > product_prod_b_b > standard_Constant_a)).
% 0.93/0.48 thf(func_def_157, type, sK41: ((b > $o) > (b > $o) > b)).
% 0.93/0.48 thf(func_def_158, type, sK42: (b > b > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_159, type, sK43: (b > b > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_160, type, sK44: (set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_161, type, sK45: (set_Product_prod_b_b > (b > set_b) > b)).
% 0.93/0.48 thf(func_def_162, type, sK46: (set_Product_prod_b_b > (b > set_b) > b)).
% 0.93/0.48 thf(func_def_163, type, sK47: ((product_prod_b_b > $o) > (product_prod_b_b > $o) > set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_164, type, sK48: (product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_165, type, sK49: (product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_166, type, sK50: ((b > b > $o) > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_167, type, sK51: ((b > b > $o) > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_168, type, sK52: (set_Product_prod_b_b > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_169, type, sK53: (set_Product_prod_b_b > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_170, type, sK54: ((product_prod_b_b > $o) > b)).
% 0.93/0.48 thf(func_def_171, type, sK55: ((product_prod_b_b > $o) > b)).
% 0.93/0.48 thf(func_def_172, type, sK56: (b > (b > $o) > b)).
% 0.93/0.48 thf(func_def_173, type, sK57: ((b > $o) > b)).
% 0.93/0.48 thf(func_def_174, type, sK58: ((b > $o) > (b > $o) > b)).
% 0.93/0.48 thf(func_def_175, type, sK59: (set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_176, type, sK60: ((b > $o) > b > b)).
% 0.93/0.48 thf(func_def_177, type, sK61: (set_b > b)).
% 0.93/0.48 thf(func_def_178, type, sK62: (set_Pr1324126435od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_179, type, sK63: (set_St761939237tant_a > set_Pr1324126435od_b_b > product_prod_b_b > standard_Constant_a)).
% 0.93/0.48 thf(func_def_180, type, sK64: ((produc1213276845od_b_b > $o) > product_prod_b_b)).
% 0.93/0.48 thf(func_def_181, type, sK65: ((produc1213276845od_b_b > $o) > standard_Constant_a)).
% 0.93/0.48 thf(func_def_182, type, sK66: (set_b > set_b > b)).
% 0.93/0.48 thf(func_def_183, type, sK67: (set_b > b)).
% 0.93/0.48 thf(func_def_184, type, sK68: (set_b > b)).
% 0.93/0.48 thf(func_def_185, type, sK69: (set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b)).
% 0.93/0.48 thf(func_def_186, type, sK70: (set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_187, type, sK71: (set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_188, type, sK72: ((b > $o) > (b > $o) > b)).
% 0.93/0.48 thf(func_def_189, type, sK73: (set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_190, type, sK74: ((b > $o) > (b > $o) > b)).
% 0.93/0.48 thf(func_def_191, type, sK75: (set_Product_prod_b_b > set_b > b > b)).
% 0.93/0.48 thf(func_def_192, type, sK76: (b > set_Pr357419743_b_b_b > set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_193, type, sK77: ((standard_Constant_a > product_prod_b_b > $o) > set_Pr306736955tant_a > standard_Constant_a)).
% 0.93/0.48 thf(func_def_194, type, sK78: ((standard_Constant_a > product_prod_b_b > $o) > set_Pr306736955tant_a > product_prod_b_b)).
% 0.93/0.48 thf(func_def_195, type, sK79: (produc1213276845od_b_b > standard_Constant_a)).
% 0.93/0.48 thf(func_def_196, type, sK80: (produc1213276845od_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_197, type, sK81: (set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_198, type, sK82: ((product_prod_b_b > $o) > product_prod_b_b)).
% 0.93/0.48 thf(func_def_199, type, sK83: (product_prod_b_b > product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b)).
% 0.93/0.48 thf(func_def_200, type, sK84: (set_Pr1324126435od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_201, type, sK85: (set_Pr1324126435od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_202, type, sK86: (set_Product_prod_b_b > set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_203, type, sK87: (set_Pr1324126435od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_204, type, sK88: ((b > $o) > b)).
% 0.93/0.48 thf(func_def_205, type, sK89: (produc1213276845od_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_206, type, sK90: (produc1213276845od_b_b > standard_Constant_a)).
% 0.93/0.48 thf(func_def_207, type, sK91: (set_b > b)).
% 0.93/0.48 thf(func_def_208, type, sK92: ((b > $o) > b)).
% 0.93/0.48 thf(func_def_209, type, sK93: ((produc1213276845od_b_b > $o) > standard_Constant_a)).
% 0.93/0.48 thf(func_def_210, type, sK94: ((produc1213276845od_b_b > $o) > b)).
% 0.93/0.48 thf(func_def_211, type, sK95: ((produc1213276845od_b_b > $o) > b)).
% 0.93/0.48 thf(func_def_212, type, sK96: (produc1367125253tant_a > set_Pr1324126435od_b_b > product_prod_b_b)).
% 0.93/0.48 thf(func_def_213, type, sK97: (produc1367125253tant_a > set_Pr1324126435od_b_b > standard_Constant_a)).
% 0.93/0.48 thf(func_def_214, type, sK98: (b > set_b > b > set_b > set_b)).
% 0.93/0.48 thf(func_def_215, type, sK99: (set_Pr1324126435od_b_b > produc1213276845od_b_b)).
% 0.93/0.48 thf(func_def_216, type, sK100: (set_b > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_217, type, sK101: (set_b > set_Product_prod_b_b > b)).
% 0.93/0.48 thf(func_def_218, type, sK102: (produc1213276845od_b_b > b)).
% 0.93/0.48 thf(func_def_219, type, sK103: (produc1213276845od_b_b > standard_Constant_a)).
% 0.93/0.48 thf(func_def_220, type, sK104: (produc1213276845od_b_b > b)).
% 0.93/0.48 thf(func_def_221, type, sK105: (produc1213276845od_b_b > set_b > set_Pr2060523537od_b_b > b)).
% 0.93/0.48 thf(func_def_222, type, sK106: (product_prod_b_b > set_Pr1324126435od_b_b > set_St761939237tant_a > standard_Constant_a)).
% 0.93/0.48 thf(func_def_223, type, sK107: ((product_prod_b_b > $o) > product_prod_b_b)).
% 0.93/0.48 thf(func_def_224, type, sK108: (set_Product_prod_b_b > product_prod_b_b)).
% 0.93/0.48 thf(f1,axiom,(
% 0.93/0.48 (((image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b))) = ((image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b))))),
% 0.93/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062)).
% 0.93/0.48 thf(f359,conjecture,(
% 0.93/0.48 (((hilbert_Eps_b @ (^[X0 : b] : ((member_b @ X0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b))))))) = ((hilbert_Eps_b @ (^[X0 : b] : ((member_b @ X0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b))))))))),
% 0.93/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.93/0.48 thf(f360,negated_conjecture,(
% 0.93/0.48 ~ (((hilbert_Eps_b @ (^[X0 : b] : ((member_b @ X0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b))))))) = ((hilbert_Eps_b @ (^[X0 : b] : ((member_b @ X0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b))))))))),
% 0.93/0.48 inference(negated_conjecture,[status(cth)],[f359])).
% 0.93/0.48 thf(f739,plain,(
% 0.93/0.48 ~ (((hilbert_Eps_b @ (^[X0 : b] : ((member_b @ X0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b))))))) = ((hilbert_Eps_b @ (^[X1 : b] : ((member_b @ X1 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b))))))))),
% 0.93/0.48 inference(rectify,[],[f360])).
% 0.93/0.48 thf(f740,plain,(
% 0.93/0.48 ~ (((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b)))))) = ((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b)))))))),
% 0.93/0.48 inference(fool_elimination,[],[f739])).
% 0.93/0.48 thf(f989,plain,(
% 0.93/0.48 (((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b)))))) != ((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b)))))))),
% 0.93/0.48 inference(flattening,[],[f740])).
% 0.93/0.48 thf(f1645,plain,(
% 0.93/0.48 (((image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b))) = ((image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b))))),
% 0.93/0.48 inference(cnf_transformation,[],[f1])).
% 0.93/0.48 thf(f1704,plain,(
% 0.93/0.48 (((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b)))))) != ((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b)))))))),
% 0.93/0.48 inference(cnf_transformation,[],[f989])).
% 0.93/0.48 thf(f2345,definition,(
% 0.93/0.48 spl109_1 <=> (((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b)))))) = ((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b)))))))),
% 0.93/0.48 introduced(definition,[new_symbols(definition,[spl109_1])],[avatar_definition])).
% 0.93/0.48 thf(f2348,plain,(
% 0.93/0.48 ~spl109_1),
% 0.93/0.48 inference(avatar_split_clause,[],[f1704,f2345])).
% 0.93/0.48 thf(f2470,definition,(
% 0.93/0.48 spl109_26 <=> (((image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b))) = ((image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b))))),
% 0.93/0.48 introduced(definition,[new_symbols(definition,[spl109_26])],[avatar_definition])).
% 0.93/0.48 thf(f2473,plain,(
% 0.93/0.48 spl109_26),
% 0.93/0.48 inference(avatar_split_clause,[],[f1645,f2470])).
% 0.93/0.48 thf(f2554,definition,(
% 0.93/0.48 (((image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b))) != ((image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b)))) | (((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b)))))) = ((hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ y @ bot_bot_set_b)))))))),
% 0.93/0.48 introduced(theory,[theory_tautology_sat_conflict])).
% 0.93/0.48 cnf(s1, plain, ~spl109_1, inference(sat_conversion,[],[f2348])).
% 0.93/0.48 cnf(s31, plain, spl109_26, inference(sat_conversion,[],[f2473])).
% 0.93/0.48 cnf(s51, plain, spl109_1 | ~spl109_26, inference(sat_conversion,[],[f2554])).
% 0.93/0.48 cnf(s52, plain, spl109_1, inference(rat,[],[s51,s31])).
% 0.93/0.48 cnf(s53, plain, $false, inference(rat,[],[s1,s52])).
% 0.93/0.48 thf(f2555,plain,(
% 0.93/0.48 $false),
% 0.93/0.48 inference(avatar_sat_refutation,[],[s53])).
% 0.93/0.48 % SZS output end Proof for theBenchmark
% 0.93/0.48 % (1789426)------------------------------
% 0.93/0.48 % (1789426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.48 % (1789426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.48 % (1789426)CaDiCaL version: 2.1.3
% 0.93/0.48 % (1789426)Termination reason: Refutation
% 0.93/0.48 % (1789426)Time elapsed: 0.084 s
% 0.93/0.48 % (1789426)Peak memory usage: 14 MB
% 0.93/0.48 % (1789426)Instructions burned: 149 (million)
% 0.93/0.48 % (1789418)Success in time 0.141 s
% 0.93/0.48 % Vampire exiting
%------------------------------------------------------------------------------