%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV482^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:38:43 AM UTC 2026
% Result : Theorem 0.19s 0.35s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV482^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:54:19 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.19/0.32 % (1214120)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.32 % (1214129)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=993476354:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.32 % (1214125)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3009060980:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.32 % (1214126)lrs+10_16_si=on:nwc=1.5:random_seed=274241412:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.32 % (1214127)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=317290114:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.32 % (1214128)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=2341402062: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)
% 0.19/0.32 % (1214129)Instruction limit reached!
% 0.19/0.32 % (1214129)------------------------------
% 0.19/0.32 % (1214129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1214129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1214129)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1214129)Termination reason: Instruction limit
% 0.19/0.32 % (1214129)Termination phase: Saturation
% 0.19/0.32 % (1214129)Time elapsed: 0.008 s
% 0.19/0.32 % (1214129)Peak memory usage: 12 MB
% 0.19/0.32 % (1214129)Instructions burned: 26 (million)
% 0.19/0.32 % (1214127)Refutation not found, incomplete strategy
% 0.19/0.32 % (1214127)------------------------------
% 0.19/0.32 % (1214127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1214127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1214127)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1214127)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.32 % (1214127)Time elapsed: 0.002 s
% 0.19/0.32 % (1214127)Peak memory usage: 12 MB
% 0.19/0.32 % (1214127)Instructions burned: 2 (million)
% 0.19/0.32 % (1214131)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.32 % (1214131)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
% 0.19/0.32 % (1214127)------------------------------
% 0.19/0.32 % (1214127)------------------------------
% 0.19/0.32 % (1214130)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3090397989:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.32 % (1214131)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=2200548552:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.32 % (1214137)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2223003977:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.32 % (1214126)Instruction limit reached!
% 0.19/0.32 % (1214126)------------------------------
% 0.19/0.32 % (1214126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1214126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1214126)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1214126)Termination reason: Instruction limit
% 0.19/0.32 % (1214126)Termination phase: Saturation
% 0.19/0.32 % (1214126)Time elapsed: 0.011 s
% 0.19/0.32 % (1214126)Peak memory usage: 12 MB
% 0.19/0.32 % (1214126)Instructions burned: 18 (million)
% 0.19/0.32 % (1214137)Instruction limit reached!
% 0.19/0.32 % (1214137)------------------------------
% 0.19/0.32 % (1214137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1214137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1214137)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1214137)Termination reason: Instruction limit
% 0.19/0.32 % (1214137)Termination phase: Saturation
% 0.19/0.32 % (1214137)Time elapsed: 0.001 s
% 0.19/0.32 % (1214137)Peak memory usage: 12 MB
% 0.19/0.32 % (1214137)Instructions burned: 4 (million)
% 0.19/0.32 % (1214128)Refutation not found, incomplete strategy
% 0.19/0.32 % (1214128)------------------------------
% 0.19/0.35 % (1214128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214128)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214128)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.35 % (1214128)Time elapsed: 0.016 s
% 0.19/0.35 % (1214128)Peak memory usage: 12 MB
% 0.19/0.35 % (1214128)Instructions burned: 24 (million)
% 0.19/0.35 % (1214128)------------------------------
% 0.19/0.35 % (1214128)------------------------------
% 0.19/0.35 % (1214138)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=767259508:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.19/0.35 % (1214131)Refutation not found, incomplete strategy
% 0.19/0.35 % (1214131)------------------------------
% 0.19/0.35 % (1214131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214131)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214131)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.35 % (1214131)Time elapsed: 0.016 s
% 0.19/0.35 % (1214131)Peak memory usage: 12 MB
% 0.19/0.35 % (1214131)Instructions burned: 25 (million)
% 0.19/0.35 % (1214131)------------------------------
% 0.19/0.35 % (1214131)------------------------------
% 0.19/0.35 % (1214143)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3809389603:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/0.35 % (1214138)Instruction limit reached!
% 0.19/0.35 % (1214138)------------------------------
% 0.19/0.35 % (1214138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214142)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.35 % (1214138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214138)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214138)Termination reason: Instruction limit
% 0.19/0.35 % (1214138)Termination phase: Saturation
% 0.19/0.35 % (1214138)Time elapsed: 0.004 s
% 0.19/0.35 % (1214138)Peak memory usage: 12 MB
% 0.19/0.35 % (1214138)Instructions burned: 6 (million)
% 0.19/0.35 % (1214143)Instruction limit reached!
% 0.19/0.35 % (1214143)------------------------------
% 0.19/0.35 % (1214143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214143)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214143)Termination reason: Instruction limit
% 0.19/0.35 % (1214143)Termination phase: Saturation
% 0.19/0.35 % (1214143)Time elapsed: 0.004 s
% 0.19/0.35 % (1214143)Peak memory usage: 12 MB
% 0.19/0.35 % (1214143)Instructions burned: 13 (million)
% 0.19/0.35 % (1214142)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1733481101:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/0.35 % (1214144)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
% 0.19/0.35 % (1214144)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.35 % (1214142)Instruction limit reached!
% 0.19/0.35 % (1214142)------------------------------
% 0.19/0.35 % (1214142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214142)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214142)Termination reason: Instruction limit
% 0.19/0.35 % (1214142)Termination phase: Saturation
% 0.19/0.35 % (1214142)Time elapsed: 0.005 s
% 0.19/0.35 % (1214142)Peak memory usage: 12 MB
% 0.19/0.35 % (1214142)Instructions burned: 8 (million)
% 0.19/0.35 % (1214149)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.19/0.35 % (1214144)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3843981582:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.19/0.35 % (1214149)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=686397885:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.35 % (1214149)Refutation not found, incomplete strategy
% 0.19/0.35 % (1214149)------------------------------
% 0.19/0.35 % (1214149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214149)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214149)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.35 % (1214149)Time elapsed: 0.001 s
% 0.19/0.35 % (1214149)Peak memory usage: 12 MB
% 0.19/0.35 % (1214149)Instructions burned: 4 (million)
% 0.19/0.35 % (1214149)------------------------------
% 0.19/0.35 % (1214149)------------------------------
% 0.19/0.35 % (1214147)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=832650190:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.19/0.35 % (1214148)lrs+10_1_si=on:cs=on:random_seed=2562074829:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.19/0.35 % (1214130)Instruction limit reached!
% 0.19/0.35 % (1214130)------------------------------
% 0.19/0.35 % (1214130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214130)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214130)Termination reason: Instruction limit
% 0.19/0.35 % (1214130)Termination phase: Saturation
% 0.19/0.35 % (1214130)Time elapsed: 0.041 s
% 0.19/0.35 % (1214130)Peak memory usage: 13 MB
% 0.19/0.35 % (1214130)Instructions burned: 76 (million)
% 0.19/0.35 % (1214125)Instruction limit reached!
% 0.19/0.35 % (1214125)------------------------------
% 0.19/0.35 % (1214125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214125)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214125)Termination reason: Instruction limit
% 0.19/0.35 % (1214125)Termination phase: Saturation
% 0.19/0.35 % (1214125)Time elapsed: 0.049 s
% 0.19/0.35 % (1214125)Peak memory usage: 15 MB
% 0.19/0.35 % (1214125)Instructions burned: 87 (million)
% 0.19/0.35 % (1214148)Instruction limit reached!
% 0.19/0.35 % (1214148)------------------------------
% 0.19/0.35 % (1214148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214148)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214148)Termination reason: Instruction limit
% 0.19/0.35 % (1214148)Termination phase: Saturation
% 0.19/0.35 % (1214148)Time elapsed: 0.004 s
% 0.19/0.35 % (1214148)Peak memory usage: 11 MB
% 0.19/0.35 % (1214148)Instructions burned: 8 (million)
% 0.19/0.35 % (1214154)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=32998993:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.19/0.35 % (1214144)Instruction limit reached!
% 0.19/0.35 % (1214144)------------------------------
% 0.19/0.35 % (1214144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214144)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214144)Termination reason: Instruction limit
% 0.19/0.35 % (1214144)Termination phase: Saturation
% 0.19/0.35 % (1214144)Time elapsed: 0.016 s
% 0.19/0.35 % (1214144)Peak memory usage: 12 MB
% 0.19/0.35 % (1214144)Instructions burned: 28 (million)
% 0.19/0.35 % (1214154)Refutation not found, incomplete strategy
% 0.19/0.35 % (1214154)------------------------------
% 0.19/0.35 % (1214154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214154)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214154)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.35 % (1214154)Time elapsed: 0.002 s
% 0.19/0.35 % (1214154)Peak memory usage: 12 MB
% 0.19/0.35 % (1214154)Instructions burned: 6 (million)
% 0.19/0.35 % (1214154)------------------------------
% 0.19/0.35 % (1214154)------------------------------
% 0.19/0.35 % (1214152)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=536472129:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.19/0.35 % (1214160)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2280162217:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.19/0.35 % (1214157)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1743679439:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.19/0.35 % (1214147) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1214120-1214147"...
% 0.19/0.35 % (1214158)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2861448758:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.19/0.35 % (1214157)Refutation not found, incomplete strategy
% 0.19/0.35 % (1214157)------------------------------
% 0.19/0.35 % (1214157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214157)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214157)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.35 % (1214157)Time elapsed: 0.005 s
% 0.19/0.35 % (1214157)Peak memory usage: 12 MB
% 0.19/0.35 % (1214157)Instructions burned: 6 (million)
% 0.19/0.35 % (1214161)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1415225347:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.19/0.35 % (1214157)------------------------------
% 0.19/0.35 % (1214157)------------------------------
% 0.19/0.35 % (1214162)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3384342213:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.35 % (1214147)...printing done.
% 0.19/0.35 % (1214162)Instruction limit reached!
% 0.19/0.35 % (1214162)------------------------------
% 0.19/0.35 % (1214162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214162)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214162)Termination reason: Instruction limit
% 0.19/0.35 % (1214162)Termination phase: Saturation
% 0.19/0.35 % (1214162)Time elapsed: 0.002 s
% 0.19/0.35 % (1214162)Peak memory usage: 11 MB
% 0.19/0.35 % (1214162)Instructions burned: 3 (million)
% 0.19/0.35 % (1214147)Refutation found. Thanks to Tanya!
% 0.19/0.35 % SZS status Theorem for theBenchmark
% 0.19/0.35 % SZS output start Proof for theBenchmark
% 0.19/0.35 thf(type_def_5, type, 'type/pair/prod': ($tType * $tType) > $tType).
% 0.19/0.35 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.35 thf(type_def_7, type, sK0: $tType).
% 0.19/0.35 thf(type_def_8, type, sK1: $tType).
% 0.19/0.35 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.19/0.35 thf(func_def_1, type, 'const/sets/CROSS': !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > $o) > 'type/pair/prod' @ X0 @ X1 > $o))).
% 0.19/0.35 thf(func_def_2, type, 'const/pair/,': !>[X0: $tType, X1: $tType]:((X0 > X1 > 'type/pair/prod' @ X0 @ X1))).
% 0.19/0.35 thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.35 thf(func_def_5, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.35 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.35 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.35 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.35 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.35 thf(func_def_12, type, vAND: ($o > $o > $o)).
% 0.19/0.35 thf(func_def_13, type, db3: !>[X0: $tType]:(X0)).
% 0.19/0.35 thf(func_def_14, type, vIMP: ($o > $o > $o)).
% 0.19/0.35 thf(func_def_15, type, sK2: (sK1 > $o)).
% 0.19/0.35 thf(func_def_16, type, sK3: ('type/pair/prod' @ sK1 @ sK0 > $o)).
% 0.19/0.35 thf(func_def_17, type, sK4: (sK0 > $o)).
% 0.19/0.35 thf(func_def_19, type, sK6: sK1).
% 0.19/0.35 thf(func_def_20, type, sK7: sK0).
% 0.19/0.35 thf(func_def_21, type, vNOT: ($o > $o)).
% 0.19/0.35 thf(func_def_22, type, db4: !>[X0: $tType]:(X0)).
% 0.19/0.35 thf(func_def_23, type, db5: !>[X0: $tType]:(X0)).
% 0.19/0.35 thf(func_def_24, type, db6: !>[X0: $tType]:(X0)).
% 0.19/0.35 thf(func_def_25, type, sK8: 'type/pair/prod' @ sK1 @ sK0).
% 0.19/0.35 thf(func_def_26, type, sK9: sK1).
% 0.19/0.35 thf(func_def_27, type, sK10: sK0).
% 0.19/0.35 thf(f1,axiom,(
% 0.19/0.35 ! [X0 : $tType,X1 : $tType,X4 : X1,X5 : (X0 > $o),X3 : X0,X6 : (X1 > $o)] : (('const/sets/IN' @ X1 @ X4 @ X6) & ('const/sets/IN' @ X0 @ X3 @ X5) = (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X3 @ X4) @ ('const/sets/CROSS' @ X0 @ X1 @ X5 @ X6))))),
% 0.19/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_CROSS_')).
% 0.19/0.35 thf(f2,axiom,(
% 0.19/0.35 ! [X1 : $tType,X0 : $tType,X2 : ('type/pair/prod' @ X0 @ X1 > $o)] : (! [X3 : 'type/pair/prod' @ X0 @ X1] : (X2 @ X3) = ! [X4 : X1,X3 : X0] : (X2 @ ('const/pair/,' @ X0 @ X1 @ X3 @ X4)))),
% 0.19/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/pair/FORALL_PAIR_THM_')).
% 0.19/0.35 thf(f3,conjecture,(
% 0.19/0.35 ! [X0 : $tType,X1 : $tType,X2 : ('type/pair/prod' @ X0 @ X1 > $o),X3 : (X0 > $o),X4 : (X1 > $o)] : (! [X5 : 'type/pair/prod' @ X0 @ X1] : (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ X5 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ X5)) = ! [X6 : X1,X5 : X0] : ((('const/sets/IN' @ X1 @ X6 @ X4) & ('const/sets/IN' @ X0 @ X5 @ X3)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6))))),
% 0.19/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FORALL_IN_CROSS_')).
% 0.19/0.35 thf(f4,negated_conjecture,(
% 0.19/0.35 ~ ! [X0 : $tType,X1 : $tType,X2 : ('type/pair/prod' @ X0 @ X1 > $o),X3 : (X0 > $o),X4 : (X1 > $o)] : (! [X5 : 'type/pair/prod' @ X0 @ X1] : (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ X5 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ X5)) = ! [X6 : X1,X5 : X0] : ((('const/sets/IN' @ X1 @ X6 @ X4) & ('const/sets/IN' @ X0 @ X5 @ X3)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6))))),
% 0.19/0.35 inference(negated_conjecture,[status(cth)],[f3])).
% 0.19/0.35 thf(f5,plain,(
% 0.19/0.35 ! [X0 : $tType,X1 : $tType,X2 : ('type/pair/prod' @ X1 @ X0 > $o)] : (! [X3 : 'type/pair/prod' @ X1 @ X0] : (X2 @ X3) = ! [X4 : X0,X5 : X1] : (X2 @ ('const/pair/,' @ X1 @ X0 @ X5 @ X4)))),
% 0.19/0.35 inference(rectify,[],[f2])).
% 0.19/0.35 thf(f6,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType] : ((((!! @ ('type/pair/prod' @ X1 @ X0 > $o) @ (^[Y0 : 'type/pair/prod' @ X1 @ X0 > $o]: ((!! @ 'type/pair/prod' @ X1 @ X0 @ (^[Y1 : 'type/pair/prod' @ X1 @ X0]: (Y0 @ Y1))) = (!! @ X1 @ (^[Y1 : X1]: (!! @ X0 @ (^[Y2 : X0]: (Y0 @ ('const/pair/,' @ X1 @ X0 @ Y1 @ Y2)))))))))) = $true)) )),
% 0.19/0.35 inference(fool_elimination,[],[f5])).
% 0.19/0.35 thf(f7,plain,(
% 0.19/0.35 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : (X0 > $o),X4 : X0,X5 : (X1 > $o)] : (('const/sets/IN' @ X1 @ X2 @ X5) & ('const/sets/IN' @ X0 @ X4 @ X3) = (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X4 @ X2) @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X5))))),
% 0.19/0.35 inference(rectify,[],[f1])).
% 0.19/0.35 thf(f8,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType] : ((((!! @ (X1 > $o) @ (^[Y0 : X1 > $o]: (!! @ X0 @ (^[Y1 : X0]: (!! @ (X0 > $o) @ (^[Y2 : X0 > $o]: (!! @ X1 @ (^[Y3 : X1]: ((('const/sets/IN' @ X0 @ Y1 @ Y2) & ('const/sets/IN' @ X1 @ Y3 @ Y0)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y3) @ ('const/sets/CROSS' @ X0 @ X1 @ Y2 @ Y0)))))))))))) = $true)) )),
% 0.19/0.35 inference(fool_elimination,[],[f7])).
% 0.19/0.35 thf(f9,plain,(
% 0.19/0.35 ~ ! [X0 : $tType,X1 : $tType,X2 : ('type/pair/prod' @ X0 @ X1 > $o),X3 : (X0 > $o),X4 : (X1 > $o)] : (! [X5 : 'type/pair/prod' @ X0 @ X1] : (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ X5 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ X5)) = ! [X6 : X1,X7 : X0] : ((('const/sets/IN' @ X1 @ X6 @ X4) & ('const/sets/IN' @ X0 @ X7 @ X3)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ X7 @ X6))))),
% 0.19/0.35 inference(rectify,[],[f4])).
% 0.19/0.35 thf(f10,plain,(
% 0.19/0.35 ~ ! [X0 : $tType,X1 : $tType,X3 : (X0 > $o),X4 : (X1 > $o),X2 : ('type/pair/prod' @ X0 @ X1 > $o)] : (((!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ Y0 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ Y0))))) = ((!! @ X0 @ (^[Y0 : X0]: (!! @ X1 @ (^[Y1 : X1]: ((('const/sets/IN' @ X0 @ Y0 @ X3) & ('const/sets/IN' @ X1 @ Y1 @ X4)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ Y0 @ Y1)))))))))),
% 0.19/0.35 inference(fool_elimination,[],[f9])).
% 0.19/0.35 thf(f11,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType] : ((((!! @ ('type/pair/prod' @ X0 @ X1 > $o) @ (^[Y0 : 'type/pair/prod' @ X0 @ X1 > $o]: ((!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y1 : 'type/pair/prod' @ X0 @ X1]: (Y0 @ Y1))) = (!! @ X0 @ (^[Y1 : X0]: (!! @ X1 @ (^[Y2 : X1]: (Y0 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y2)))))))))) = $true)) )),
% 0.19/0.35 inference(rectify,[],[f6])).
% 0.19/0.35 thf(f12,plain,(
% 0.19/0.35 ! [X0 : $tType,X1 : $tType] : (((!! @ ('type/pair/prod' @ X0 @ X1 > $o) @ (^[Y0 : 'type/pair/prod' @ X0 @ X1 > $o]: ((!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y1 : 'type/pair/prod' @ X0 @ X1]: (Y0 @ Y1))) = (!! @ X0 @ (^[Y1 : X0]: (!! @ X1 @ (^[Y2 : X1]: (Y0 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y2)))))))))) = $true)),
% 0.19/0.35 inference(closure,[],[f11])).
% 0.19/0.35 thf(f13,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType] : ((((!! @ (X0 > $o) @ (^[Y0 : X0 > $o]: (!! @ X1 @ (^[Y1 : X1]: (!! @ (X1 > $o) @ (^[Y2 : X1 > $o]: (!! @ X0 @ (^[Y3 : X0]: ((('const/sets/IN' @ X1 @ Y1 @ Y2) & ('const/sets/IN' @ X0 @ Y3 @ Y0)) = ('const/sets/IN' @ 'type/pair/prod' @ X1 @ X0 @ ('const/pair/,' @ X1 @ X0 @ Y1 @ Y3) @ ('const/sets/CROSS' @ X1 @ X0 @ Y2 @ Y0)))))))))))) = $true)) )),
% 0.19/0.35 inference(rectify,[],[f8])).
% 0.19/0.35 thf(f14,plain,(
% 0.19/0.35 ! [X1 : $tType,X0 : $tType] : (((!! @ (X0 > $o) @ (^[Y0 : X0 > $o]: (!! @ X1 @ (^[Y1 : X1]: (!! @ (X1 > $o) @ (^[Y2 : X1 > $o]: (!! @ X0 @ (^[Y3 : X0]: ((('const/sets/IN' @ X1 @ Y1 @ Y2) & ('const/sets/IN' @ X0 @ Y3 @ Y0)) = ('const/sets/IN' @ 'type/pair/prod' @ X1 @ X0 @ ('const/pair/,' @ X1 @ X0 @ Y1 @ Y3) @ ('const/sets/CROSS' @ X1 @ X0 @ Y2 @ Y0)))))))))))) = $true)),
% 0.19/0.35 inference(closure,[],[f13])).
% 0.19/0.35 thf(f15,plain,(
% 0.19/0.35 ? [X1 : $tType,X0 : $tType,X3 : (X0 > $o),X2 : ('type/pair/prod' @ X0 @ X1 > $o),X4 : (X1 > $o)] : (((!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ Y0 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ Y0))))) != ((!! @ X0 @ (^[Y0 : X0]: (!! @ X1 @ (^[Y1 : X1]: ((('const/sets/IN' @ X0 @ Y0 @ X3) & ('const/sets/IN' @ X1 @ Y1 @ X4)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ Y0 @ Y1)))))))))),
% 0.19/0.35 inference(ennf_transformation,[],[f10])).
% 0.19/0.35 thf(f16,plain,(
% 0.19/0.35 ! [X0 : $tType,X1 : $tType] : (((!! @ (X1 > $o) @ (^[Y0 : X1 > $o]: (!! @ X0 @ (^[Y1 : X0]: (!! @ (X0 > $o) @ (^[Y2 : X0 > $o]: (!! @ X1 @ (^[Y3 : X1]: ((('const/sets/IN' @ X0 @ Y1 @ Y2) & ('const/sets/IN' @ X1 @ Y3 @ Y0)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y3) @ ('const/sets/CROSS' @ X0 @ X1 @ Y2 @ Y0)))))))))))) = $true)),
% 0.19/0.35 inference(rectify,[],[f14])).
% 0.19/0.35 thf(f17,plain,(
% 0.19/0.35 ? [X0 : $tType,X1 : $tType,X2 : (X1 > $o),X3 : ('type/pair/prod' @ X1 @ X0 > $o),X4 : (X0 > $o)] : (((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: ((('const/sets/IN' @ X1 @ Y0 @ X2) & ('const/sets/IN' @ X0 @ Y1 @ X4)) => (X3 @ ('const/pair/,' @ X1 @ X0 @ Y0 @ Y1)))))))) != ((!! @ 'type/pair/prod' @ X1 @ X0 @ (^[Y0 : 'type/pair/prod' @ X1 @ X0]: (('const/sets/IN' @ 'type/pair/prod' @ X1 @ X0 @ Y0 @ ('const/sets/CROSS' @ X1 @ X0 @ X2 @ X4)) => (X3 @ Y0))))))),
% 0.19/0.35 inference(rectify,[],[f15])).
% 0.19/0.35 thf(f18,plain,(
% 0.19/0.35 (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) != ((!! @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0))))))),
% 0.19/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f17])).
% 0.19/0.35 thf(f19,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType] : ((((!! @ (X1 > $o) @ (^[Y0 : X1 > $o]: (!! @ X0 @ (^[Y1 : X0]: (!! @ (X0 > $o) @ (^[Y2 : X0 > $o]: (!! @ X1 @ (^[Y3 : X1]: ((('const/sets/IN' @ X0 @ Y1 @ Y2) & ('const/sets/IN' @ X1 @ Y3 @ Y0)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y3) @ ('const/sets/CROSS' @ X0 @ X1 @ Y2 @ Y0)))))))))))) = $true)) )),
% 0.19/0.35 inference(cnf_transformation,[],[f16])).
% 0.19/0.35 thf(f20,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType] : ((((!! @ ('type/pair/prod' @ X0 @ X1 > $o) @ (^[Y0 : 'type/pair/prod' @ X0 @ X1 > $o]: ((!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y1 : 'type/pair/prod' @ X0 @ X1]: (Y0 @ Y1))) = (!! @ X0 @ (^[Y1 : X0]: (!! @ X1 @ (^[Y2 : X1]: (Y0 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y2)))))))))) = $true)) )),
% 0.19/0.35 inference(cnf_transformation,[],[f12])).
% 0.19/0.35 thf(f21,plain,(
% 0.19/0.35 (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) != ((!! @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0))))))),
% 0.19/0.35 inference(cnf_transformation,[],[f18])).
% 0.19/0.35 thf(f24,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType] : ((((!! @ ('type/pair/prod' @ X0 @ X1 > $o) @ (^[Y0 : 'type/pair/prod' @ X0 @ X1 > $o]: ((!! @ 'type/pair/prod' @ X0 @ X1 @ Y0) = (!! @ X0 @ (^[Y1 : X0]: (!! @ X1 @ (^[Y2 : X1]: (Y0 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y2)))))))))) = $true)) )),
% 0.19/0.35 inference(beta-eta_normalization,[],[f20])).
% 0.19/0.35 thf(f25,plain,(
% 0.19/0.35 (((!! @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0))))) = $true) | (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) = $true)),
% 0.19/0.35 inference(xor_proxy_clausification,[],[f21])).
% 0.19/0.35 thf(f26,plain,(
% 0.19/0.35 (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) = $false) | ($false = ((!! @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0))))))),
% 0.19/0.35 inference(xor_proxy_clausification,[],[f21])).
% 0.19/0.35 thf(f28,definition,(
% 0.19/0.35 spl5_1 <=> (((!! @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0))))) = $true)),
% 0.19/0.35 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.19/0.35 thf(f30,plain,(
% 0.19/0.35 (((!! @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0))))) = $true) | ~spl5_1),
% 0.19/0.35 inference(avatar_component_clause,[],[f28])).
% 0.19/0.35 thf(f32,definition,(
% 0.19/0.35 spl5_2 <=> (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) = $true)),
% 0.19/0.35 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.19/0.35 thf(f34,plain,(
% 0.19/0.35 (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) = $true) | ~spl5_2),
% 0.19/0.35 inference(avatar_component_clause,[],[f32])).
% 0.19/0.35 thf(f35,plain,(
% 0.19/0.35 spl5_1 | spl5_2),
% 0.19/0.35 inference(avatar_split_clause,[],[f25,f32,f28])).
% 0.19/0.35 thf(f37,definition,(
% 0.19/0.35 spl5_3 <=> (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) = $false)),
% 0.19/0.35 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.19/0.35 thf(f39,plain,(
% 0.19/0.35 (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) = $false) | ~spl5_3),
% 0.19/0.35 inference(avatar_component_clause,[],[f37])).
% 0.19/0.35 thf(f41,definition,(
% 0.19/0.35 spl5_4 <=> ($false = ((!! @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0))))))),
% 0.19/0.35 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.19/0.35 thf(f43,plain,(
% 0.19/0.35 ($false = ((!! @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0)))))) | ~spl5_4),
% 0.19/0.35 inference(avatar_component_clause,[],[f41])).
% 0.19/0.35 thf(f44,plain,(
% 0.19/0.35 spl5_3 | spl5_4),
% 0.19/0.35 inference(avatar_split_clause,[],[f26,f41,f37])).
% 0.19/0.35 thf(f45,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : ('type/pair/prod' @ X0 @ X1 > $o)] : (((((^[Y0 : 'type/pair/prod' @ X0 @ X1 > $o]: ((!! @ 'type/pair/prod' @ X0 @ X1 @ Y0) = (!! @ X0 @ (^[Y1 : X0]: (!! @ X1 @ (^[Y2 : X1]: (Y0 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y2)))))))) @ X2)) = $true)) )),
% 0.19/0.35 inference(pi_proxy_clausification,[],[f24])).
% 0.19/0.35 thf(f46,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : ('type/pair/prod' @ X0 @ X1 > $o)] : (((((!! @ 'type/pair/prod' @ X0 @ X1 @ X2) = (!! @ X0 @ (^[Y0 : X0]: (!! @ X1 @ (^[Y1 : X1]: (X2 @ ('const/pair/,' @ X0 @ X1 @ Y0 @ Y1)))))))) = $true)) )),
% 0.19/0.35 inference(beta-eta_normalization,[],[f45])).
% 0.19/0.35 thf(f47,plain,(
% 0.19/0.35 ( ! [X1 : sK1] : (((((^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))) @ X1)) = $true)) ) | ~spl5_2),
% 0.19/0.35 inference(pi_proxy_clausification,[],[f34])).
% 0.19/0.35 thf(f48,plain,(
% 0.19/0.35 ( ! [X1 : sK1] : ((((!! @ sK0 @ (^[Y0 : sK0]: ((('const/sets/IN' @ sK1 @ X1 @ sK2) & ('const/sets/IN' @ sK0 @ Y0 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ X1 @ Y0)))))) = $true)) ) | ~spl5_2),
% 0.19/0.35 inference(beta-eta_normalization,[],[f47])).
% 0.19/0.35 thf(f49,plain,(
% 0.19/0.35 ( ! [X2 : sK0,X1 : sK1] : (((((^[Y0 : sK0]: ((('const/sets/IN' @ sK1 @ X1 @ sK2) & ('const/sets/IN' @ sK0 @ Y0 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ X1 @ Y0)))) @ X2)) = $true)) ) | ~spl5_2),
% 0.19/0.35 inference(pi_proxy_clausification,[],[f48])).
% 0.19/0.35 thf(f52,plain,(
% 0.19/0.35 ($false = (((^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK2) & ('const/sets/IN' @ sK0 @ Y1 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))) @ sK6))) | ~spl5_3),
% 0.19/0.35 inference(sigma_proxy_clausification,[],[f39])).
% 0.19/0.35 thf(f53,plain,(
% 0.19/0.35 ($false = ((!! @ sK0 @ (^[Y0 : sK0]: ((('const/sets/IN' @ sK1 @ sK6 @ sK2) & ('const/sets/IN' @ sK0 @ Y0 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ sK6 @ Y0))))))) | ~spl5_3),
% 0.19/0.35 inference(beta-eta_normalization,[],[f52])).
% 0.19/0.35 thf(f54,plain,(
% 0.19/0.35 ($false = $true) | (~spl5_2 | ~spl5_3)),
% 0.19/0.35 inference(forward_demodulation,[],[f53,f48])).
% 0.19/0.35 thf(f55,plain,(
% 0.19/0.35 $false | (~spl5_2 | ~spl5_3)),
% 0.19/0.35 inference(trivial_inequality_removal,[],[f54])).
% 0.19/0.35 thf(f56,plain,(
% 0.19/0.35 ~spl5_2 | ~spl5_3),
% 0.19/0.35 inference(avatar_contradiction_clause,[],[f55])).
% 0.19/0.35 thf(f58,plain,(
% 0.19/0.35 ((((^[Y0 : sK0]: ((('const/sets/IN' @ sK1 @ sK6 @ sK2) & ('const/sets/IN' @ sK0 @ Y0 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ sK6 @ Y0)))) @ sK7)) = $false) | ~spl5_3),
% 0.19/0.35 inference(sigma_proxy_clausification,[],[f53])).
% 0.19/0.35 thf(f59,plain,(
% 0.19/0.35 ($false = (((('const/sets/IN' @ sK1 @ sK6 @ sK2) & ('const/sets/IN' @ sK0 @ sK7 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ sK6 @ sK7))))) | ~spl5_3),
% 0.19/0.35 inference(beta-eta_normalization,[],[f58])).
% 0.19/0.35 thf(f60,plain,(
% 0.19/0.35 ($false = ((sK3 @ ('const/pair/,' @ sK1 @ sK0 @ sK6 @ sK7)))) | ~spl5_3),
% 0.19/0.35 inference(imp_proxy_clausification,[],[f59])).
% 0.19/0.35 thf(f61,plain,(
% 0.19/0.35 (((('const/sets/IN' @ sK1 @ sK6 @ sK2) & ('const/sets/IN' @ sK0 @ sK7 @ sK4))) = $true) | ~spl5_3),
% 0.19/0.35 inference(imp_proxy_clausification,[],[f59])).
% 0.19/0.35 thf(f82,plain,(
% 0.19/0.35 ( ! [X1 : 'type/pair/prod' @ sK1 @ sK0] : (((((^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y0))) @ X1)) = $true)) ) | ~spl5_1),
% 0.19/0.35 inference(pi_proxy_clausification,[],[f30])).
% 0.19/0.35 thf(f83,plain,(
% 0.19/0.35 ( ! [X1 : 'type/pair/prod' @ sK1 @ sK0] : ((((('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ X1 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ X1))) = $true)) ) | ~spl5_1),
% 0.19/0.35 inference(beta-eta_normalization,[],[f82])).
% 0.19/0.35 thf(f85,plain,(
% 0.19/0.35 (((('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ sK6 @ sK7) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => $false)) = $true) | (~spl5_1 | ~spl5_3)),
% 0.19/0.35 inference(constrained_superposition,[],[f83,f60])).
% 0.19/0.35 thf(f86,plain,(
% 0.19/0.35 (((~ ('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ sK6 @ sK7) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)))) = $true) | (~spl5_1 | ~spl5_3)),
% 0.19/0.35 inference(boolean_simplification,[],[f85])).
% 0.19/0.35 thf(f87,plain,(
% 0.19/0.35 ($false = (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ sK6 @ sK7) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)))) | (~spl5_1 | ~spl5_3)),
% 0.19/0.35 inference(not_proxy_clausification,[],[f86])).
% 0.19/0.35 thf(f132,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o)] : (((((^[Y0 : X1 > $o]: (!! @ X0 @ (^[Y1 : X0]: (!! @ (X0 > $o) @ (^[Y2 : X0 > $o]: (!! @ X1 @ (^[Y3 : X1]: ((('const/sets/IN' @ X0 @ Y1 @ Y2) & ('const/sets/IN' @ X1 @ Y3 @ Y0)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y3) @ ('const/sets/CROSS' @ X0 @ X1 @ Y2 @ Y0)))))))))) @ X2)) = $true)) )),
% 0.19/0.35 inference(pi_proxy_clausification,[],[f19])).
% 0.19/0.35 thf(f133,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o)] : ((((!! @ X0 @ (^[Y0 : X0]: (!! @ (X0 > $o) @ (^[Y1 : X0 > $o]: (!! @ X1 @ (^[Y2 : X1]: ((('const/sets/IN' @ X0 @ Y0 @ Y1) & ('const/sets/IN' @ X1 @ Y2 @ X2)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ Y0 @ Y2) @ ('const/sets/CROSS' @ X0 @ X1 @ Y1 @ X2)))))))))) = $true)) )),
% 0.19/0.35 inference(beta-eta_normalization,[],[f132])).
% 0.19/0.35 thf(f134,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o),X3 : X0] : (((((^[Y0 : X0]: (!! @ (X0 > $o) @ (^[Y1 : X0 > $o]: (!! @ X1 @ (^[Y2 : X1]: ((('const/sets/IN' @ X0 @ Y0 @ Y1) & ('const/sets/IN' @ X1 @ Y2 @ X2)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ Y0 @ Y2) @ ('const/sets/CROSS' @ X0 @ X1 @ Y1 @ X2)))))))) @ X3)) = $true)) )),
% 0.19/0.35 inference(pi_proxy_clausification,[],[f133])).
% 0.19/0.35 thf(f139,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o),X3 : X0] : ((((!! @ (X0 > $o) @ (^[Y0 : X0 > $o]: (!! @ X1 @ (^[Y1 : X1]: ((('const/sets/IN' @ X0 @ X3 @ Y0) & ('const/sets/IN' @ X1 @ Y1 @ X2)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X3 @ Y1) @ ('const/sets/CROSS' @ X0 @ X1 @ Y0 @ X2)))))))) = $true)) )),
% 0.19/0.35 inference(beta-eta_normalization,[],[f134])).
% 0.19/0.35 thf(f142,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o),X3 : X0,X4 : (X0 > $o)] : (((((^[Y0 : X0 > $o]: (!! @ X1 @ (^[Y1 : X1]: ((('const/sets/IN' @ X0 @ X3 @ Y0) & ('const/sets/IN' @ X1 @ Y1 @ X2)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X3 @ Y1) @ ('const/sets/CROSS' @ X0 @ X1 @ Y0 @ X2)))))) @ X4)) = $true)) )),
% 0.19/0.35 inference(pi_proxy_clausification,[],[f139])).
% 0.19/0.35 thf(f143,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o),X3 : X0,X4 : (X0 > $o)] : ((((!! @ X1 @ (^[Y0 : X1]: ((('const/sets/IN' @ X0 @ X3 @ X4) & ('const/sets/IN' @ X1 @ Y0 @ X2)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X3 @ Y0) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X2)))))) = $true)) )),
% 0.19/0.35 inference(beta-eta_normalization,[],[f142])).
% 0.19/0.35 thf(f144,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o),X3 : X0,X4 : (X0 > $o),X5 : X1] : (($true = (((^[Y0 : X1]: ((('const/sets/IN' @ X0 @ X3 @ X4) & ('const/sets/IN' @ X1 @ Y0 @ X2)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X3 @ Y0) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X2)))) @ X5)))) )),
% 0.19/0.35 inference(pi_proxy_clausification,[],[f143])).
% 0.19/0.35 thf(f148,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o),X3 : X0,X4 : (X0 > $o),X5 : X1] : (((((('const/sets/IN' @ X0 @ X3 @ X4) & ('const/sets/IN' @ X1 @ X5 @ X2)) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X3 @ X5) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X2)))) = $true)) )),
% 0.19/0.35 inference(beta-eta_normalization,[],[f144])).
% 0.19/0.35 thf(f152,plain,(
% 0.19/0.35 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o),X3 : X0,X4 : (X0 > $o),X5 : X1] : (((('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X3 @ X5) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X2))) = ((('const/sets/IN' @ X0 @ X3 @ X4) & ('const/sets/IN' @ X1 @ X5 @ X2))))) )),
% 0.19/0.35 inference(equality_proxy_clausification,[],[f148])).
% 0.19/0.35 thf(f153,plain,(
% 0.19/0.35 ((((('const/sets/IN' @ sK1 @ sK6 @ sK2) & ('const/sets/IN' @ sK0 @ sK7 @ sK4)) = $false)) = $true) | (~spl5_1 | ~spl5_3)),
% 0.19/0.35 inference(constrained_superposition,[],[f148,f87])).
% 0.19/0.35 thf(f171,plain,(
% 0.19/0.35 ((($true = $false)) = $true) | (~spl5_1 | ~spl5_3)),
% 0.19/0.35 inference(forward_demodulation,[],[f153,f61])).
% 0.19/0.35 thf(f193,plain,(
% 0.19/0.35 ($false = $true) | (~spl5_1 | ~spl5_3)),
% 0.19/0.35 inference(equality_proxy_clausification,[],[f171])).
% 0.19/0.35 thf(f194,plain,(
% 0.19/0.35 $false | (~spl5_1 | ~spl5_3)),
% 0.19/0.35 inference(trivial_inequality_removal,[],[f193])).
% 0.19/0.35 thf(f195,plain,(
% 0.19/0.35 ~spl5_1 | ~spl5_3),
% 0.19/0.35 inference(avatar_contradiction_clause,[],[f194])).
% 0.19/0.35 thf(f197,plain,(
% 0.19/0.35 ( ! [X2 : sK0,X1 : sK1] : (((((('const/sets/IN' @ sK1 @ X1 @ sK2) & ('const/sets/IN' @ sK0 @ X2 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ X1 @ X2)))) = $true)) ) | ~spl5_2),
% 0.19/0.35 inference(beta-eta_normalization,[],[f49])).
% 0.19/0.35 thf(f202,plain,(
% 0.19/0.35 ((($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((^[Y2 : 'type/pair/prod' @ sK1 @ sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ Y2 @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ Y2))) @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))))) = $true) | ~spl5_4),
% 0.19/0.35 inference(constrained_superposition,[],[f46,f43])).
% 0.19/0.35 thf(f203,plain,(
% 0.19/0.35 ((($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1))))))))) = $true) | ~spl5_4),
% 0.19/0.35 inference(beta-eta_normalization,[],[f202])).
% 0.19/0.35 thf(f234,plain,(
% 0.19/0.35 ($false = ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1))))))))) | ~spl5_4),
% 0.19/0.35 inference(equality_proxy_clausification,[],[f203])).
% 0.19/0.35 thf(f235,plain,(
% 0.19/0.35 ($false = (((^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ Y0 @ Y1)))))) @ sK9))) | ~spl5_4),
% 0.19/0.35 inference(sigma_proxy_clausification,[],[f234])).
% 0.19/0.35 thf(f236,plain,(
% 0.19/0.35 ($false = ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ sK9 @ Y0) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ sK9 @ Y0))))))) | ~spl5_4),
% 0.19/0.35 inference(beta-eta_normalization,[],[f235])).
% 0.19/0.35 thf(f237,plain,(
% 0.19/0.35 ($false = (((^[Y0 : sK0]: (('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ sK9 @ Y0) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ sK9 @ Y0)))) @ sK10))) | ~spl5_4),
% 0.19/0.35 inference(sigma_proxy_clausification,[],[f236])).
% 0.19/0.35 thf(f238,plain,(
% 0.19/0.35 ($false = ((('const/sets/IN' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/pair/,' @ sK1 @ sK0 @ sK9 @ sK10) @ ('const/sets/CROSS' @ sK1 @ sK0 @ sK2 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ sK9 @ sK10))))) | ~spl5_4),
% 0.19/0.35 inference(beta-eta_normalization,[],[f237])).
% 0.19/0.35 thf(f239,plain,(
% 0.19/0.35 ($false = (((('const/sets/IN' @ sK1 @ sK9 @ sK2) & ('const/sets/IN' @ sK0 @ sK10 @ sK4)) => (sK3 @ ('const/pair/,' @ sK1 @ sK0 @ sK9 @ sK10))))) | ~spl5_4),
% 0.19/0.35 inference(forward_demodulation,[],[f238,f152])).
% 0.19/0.35 thf(f240,plain,(
% 0.19/0.35 ($false = $true) | (~spl5_2 | ~spl5_4)),
% 0.19/0.35 inference(forward_demodulation,[],[f239,f197])).
% 0.19/0.35 thf(f241,plain,(
% 0.19/0.35 $false | (~spl5_2 | ~spl5_4)),
% 0.19/0.35 inference(trivial_inequality_removal,[],[f240])).
% 0.19/0.35 thf(f242,plain,(
% 0.19/0.35 ~spl5_2 | ~spl5_4),
% 0.19/0.35 inference(avatar_contradiction_clause,[],[f241])).
% 0.19/0.35 thf(f244,plain,(
% 0.19/0.35 ($false = $true) | (~spl5_1 | ~spl5_4)),
% 0.19/0.35 inference(forward_demodulation,[],[f30,f43])).
% 0.19/0.35 thf(f245,plain,(
% 0.19/0.35 $false | (~spl5_1 | ~spl5_4)),
% 0.19/0.35 inference(trivial_inequality_removal,[],[f244])).
% 0.19/0.35 thf(f246,plain,(
% 0.19/0.35 ~spl5_1 | ~spl5_4),
% 0.19/0.35 inference(avatar_contradiction_clause,[],[f245])).
% 0.19/0.35 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f35])).
% 0.19/0.35 cnf(s2, plain, spl5_3 | spl5_4, inference(sat_conversion,[],[f44])).
% 0.19/0.35 cnf(s3, plain, ~spl5_2 | ~spl5_3, inference(sat_conversion,[],[f56])).
% 0.19/0.35 cnf(s4, plain, ~spl5_1 | ~spl5_3, inference(sat_conversion,[],[f195])).
% 0.19/0.35 cnf(s5, plain, ~spl5_2 | ~spl5_4, inference(sat_conversion,[],[f242])).
% 0.19/0.35 cnf(s6, plain, ~spl5_1 | ~spl5_4, inference(sat_conversion,[],[f246])).
% 0.19/0.35 cnf(s7, plain, ~spl5_2, inference(rat,[],[s2,s3,s5])).
% 0.19/0.35 cnf(s8, plain, spl5_1, inference(rat,[],[s1,s7])).
% 0.19/0.35 cnf(s9, plain, ~spl5_4, inference(rat,[],[s6,s8])).
% 0.19/0.35 cnf(s10, plain, ~spl5_3, inference(rat,[],[s4,s8])).
% 0.19/0.35 cnf(s11, plain, $false, inference(rat,[],[s2,s9,s10])).
% 0.19/0.35 thf(f247,plain,(
% 0.19/0.35 $false),
% 0.19/0.35 inference(avatar_sat_refutation,[],[s11])).
% 0.19/0.35 % SZS output end Proof for theBenchmark
% 0.19/0.35 % (1214147)------------------------------
% 0.19/0.35 % (1214147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (1214147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (1214147)CaDiCaL version: 2.1.3
% 0.19/0.35 % (1214147)Termination reason: Refutation
% 0.19/0.35 % (1214147)Time elapsed: 0.030 s
% 0.19/0.35 % (1214147)Peak memory usage: 13 MB
% 0.19/0.35 % (1214147)Instructions burned: 41 (million)
% 0.19/0.35 % (1214120)Success in time 0.11 s
% 0.19/0.35 % Vampire exiting
%------------------------------------------------------------------------------