%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP183^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:08:43 AM UTC 2026
% Result : Theorem 0.59s 0.47s
% Output : Refutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP183^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n014.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 20:08:00 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.23/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.47 % (3153949)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.59/0.47 % (3153955)lrs+10_16_si=on:nwc=1.5:random_seed=3037838630:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.59/0.47 % (3153955)Instruction limit reached!
% 0.59/0.47 % (3153955)------------------------------
% 0.59/0.47 % (3153955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153955)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153955)Termination reason: Instruction limit
% 0.59/0.47 % (3153955)Termination phase: shuffling
% 0.59/0.47 % (3153955)Time elapsed: 0.007 s
% 0.59/0.47 % (3153955)Peak memory usage: 10 MB
% 0.59/0.47 % (3153955)Instructions burned: 20 (million)
% 0.59/0.47 % (3153954)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4008027030:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.59/0.47 % (3153958)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2111640580:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.59/0.47 % (3153960)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.59/0.47 % (3153960)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.59/0.47 % (3153960)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=269821727:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.59/0.47 % (3153959)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4162578482:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.59/0.47 % (3153956)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1848323364:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.59/0.47 % (3153957)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=509802725:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.59/0.47 % (3153958)Instruction limit reached!
% 0.59/0.47 % (3153958)------------------------------
% 0.59/0.47 % (3153958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153958)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153958)Termination reason: Instruction limit
% 0.59/0.47 % (3153958)Termination phase: shuffling
% 0.59/0.47 % (3153958)Time elapsed: 0.021 s
% 0.59/0.47 % (3153958)Peak memory usage: 10 MB
% 0.59/0.47 % (3153958)Instructions burned: 24 (million)
% 0.59/0.47 % (3153954)Instruction limit reached!
% 0.59/0.47 % (3153954)------------------------------
% 0.59/0.47 % (3153954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153954)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153954)Termination reason: Instruction limit
% 0.59/0.47 % (3153954)Termination phase: Property scanning
% 0.59/0.47 % (3153954)Time elapsed: 0.041 s
% 0.59/0.47 % (3153954)Peak memory usage: 12 MB
% 0.59/0.47 % (3153954)Instructions burned: 88 (million)
% 0.59/0.47 % (3153956)Instruction limit reached!
% 0.59/0.47 % (3153956)------------------------------
% 0.59/0.47 % (3153956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153956)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153956)Termination reason: Instruction limit
% 0.59/0.47 % (3153956)Termination phase: shuffling
% 0.59/0.47 % (3153956)Time elapsed: 0.009 s
% 0.59/0.47 % (3153956)Peak memory usage: 10 MB
% 0.59/0.47 % (3153956)Instructions burned: 4 (million)
% 0.59/0.47 % (3153969)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3391503001:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.59/0.47 % (3153969)Instruction limit reached!
% 0.59/0.47 % (3153969)------------------------------
% 0.59/0.47 % (3153969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153969)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153969)Termination reason: Instruction limit
% 0.59/0.47 % (3153969)Termination phase: shuffling
% 0.59/0.47 % (3153969)Time elapsed: 0.003 s
% 0.59/0.47 % (3153969)Peak memory usage: 10 MB
% 0.59/0.47 % (3153969)Instructions burned: 12 (million)
% 0.59/0.47 % (3153963)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3936307987:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.59/0.47 % (3153963)Instruction limit reached!
% 0.59/0.47 % (3153963)------------------------------
% 0.59/0.47 % (3153963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153963)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153963)Termination reason: Instruction limit
% 0.59/0.47 % (3153963)Termination phase: shuffling
% 0.59/0.47 % (3153963)Time elapsed: 0.005 s
% 0.59/0.47 % (3153963)Peak memory usage: 10 MB
% 0.59/0.47 % (3153963)Instructions burned: 3 (million)
% 0.59/0.47 % (3153973)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.59/0.47 % (3153973)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.47 % (3153973)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=879316121:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 0.59/0.47 % (3153970)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.47 % (3153971)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=459965754:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.59/0.47 % (3153973)Instruction limit reached!
% 0.59/0.47 % (3153973)------------------------------
% 0.59/0.47 % (3153973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153973)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153973)Termination reason: Instruction limit
% 0.59/0.47 % (3153973)Termination phase: shuffling
% 0.59/0.47 % (3153973)Time elapsed: 0.007 s
% 0.59/0.47 % (3153973)Peak memory usage: 10 MB
% 0.59/0.47 % (3153973)Instructions burned: 29 (million)
% 0.59/0.47 % (3153970)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=684117609:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.59/0.47 % (3153975)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=3720769205:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.59/0.47 % (3153970)Instruction limit reached!
% 0.59/0.47 % (3153970)------------------------------
% 0.59/0.47 % (3153970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153970)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153970)Termination reason: Instruction limit
% 0.59/0.47 % (3153970)Termination phase: shuffling
% 0.59/0.47 % (3153970)Time elapsed: 0.006 s
% 0.59/0.47 % (3153970)Peak memory usage: 9 MB
% 0.59/0.47 % (3153970)Instructions burned: 7 (million)
% 0.59/0.47 % (3153978)lrs+10_1_si=on:cs=on:random_seed=2402318167:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.59/0.47 % (3153971)Instruction limit reached!
% 0.59/0.47 % (3153971)------------------------------
% 0.59/0.47 % (3153971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153971)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153971)Termination reason: Instruction limit
% 0.59/0.47 % (3153971)Termination phase: shuffling
% 0.59/0.47 % (3153971)Time elapsed: 0.011 s
% 0.59/0.47 % (3153971)Peak memory usage: 10 MB
% 0.59/0.47 % (3153971)Instructions burned: 13 (million)
% 0.59/0.47 % (3153978)Instruction limit reached!
% 0.59/0.47 % (3153978)------------------------------
% 0.59/0.47 % (3153978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153978)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153978)Termination reason: Instruction limit
% 0.59/0.47 % (3153978)Termination phase: shuffling
% 0.59/0.47 % (3153978)Time elapsed: 0.003 s
% 0.59/0.47 % (3153978)Peak memory usage: 10 MB
% 0.59/0.47 % (3153978)Instructions burned: 13 (million)
% 0.59/0.47 % (3153959)Instruction limit reached!
% 0.59/0.47 % (3153959)------------------------------
% 0.59/0.47 % (3153959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153959)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153959)Termination reason: Instruction limit
% 0.59/0.47 % (3153959)Termination phase: Property scanning
% 0.59/0.47 % (3153959)Time elapsed: 0.064 s
% 0.59/0.47 % (3153959)Peak memory usage: 12 MB
% 0.59/0.47 % (3153959)Instructions burned: 75 (million)
% 0.59/0.47 % (3153984)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=719915764:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.59/0.47 % (3153981)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.59/0.47 % (3153981)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=3179312711:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.59/0.47 % (3153981)Instruction limit reached!
% 0.59/0.47 % (3153981)------------------------------
% 0.59/0.47 % (3153981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153981)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153981)Termination reason: Instruction limit
% 0.59/0.47 % (3153981)Termination phase: shuffling
% 0.59/0.47 % (3153981)Time elapsed: 0.003 s
% 0.59/0.47 % (3153981)Peak memory usage: 10 MB
% 0.59/0.47 % (3153981)Instructions burned: 6 (million)
% 0.59/0.47 % (3153960)Instruction limit reached!
% 0.59/0.47 % (3153960)------------------------------
% 0.59/0.47 % (3153960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153960)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153960)Termination reason: Instruction limit
% 0.59/0.47 % (3153960)Termination phase: Saturation
% 0.59/0.47 % (3153960)Time elapsed: 0.086 s
% 0.59/0.47 % (3153960)Peak memory usage: 14 MB
% 0.59/0.47 % (3153960)Instructions burned: 157 (million)
% 0.59/0.47 % (3153984) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3153949-3153984"...
% 0.59/0.47 % (3153984)...printing done.
% 0.59/0.47 % (3153984)Refutation found. Thanks to Tanya!
% 0.59/0.47 % SZS status Theorem for theBenchmark
% 0.59/0.47 % SZS output start Proof for theBenchmark
% 0.59/0.47 thf(type_def_5, type, late_residual: $tType).
% 0.59/0.47 thf(type_def_6, type, late_subject: $tType).
% 0.59/0.47 thf(type_def_7, type, late_freeRes: $tType).
% 0.59/0.47 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 0.59/0.47 thf(type_def_9, type, noption: $tType > $tType).
% 0.59/0.47 thf(type_def_10, type, name: $tType).
% 0.59/0.47 thf(type_def_11, type, pi: $tType).
% 0.59/0.47 thf(type_def_12, type, set: $tType > $tType).
% 0.59/0.47 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 0.59/0.47 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.59/0.47 thf(func_def_1, type, fs_name: !>[X0: $tType]:($o)).
% 0.59/0.47 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.59/0.47 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.59/0.47 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 0.59/0.47 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 0.59/0.47 thf(func_def_6, type, input: (name > name > pi > pi)).
% 0.59/0.47 thf(func_def_7, type, mismatch: (name > name > pi > pi)).
% 0.59/0.47 thf(func_def_8, type, output: (name > name > pi > pi)).
% 0.59/0.47 thf(func_def_9, type, par: (pi > pi > pi)).
% 0.59/0.47 thf(func_def_10, type, piNil: pi).
% 0.59/0.47 thf(func_def_11, type, res: (name > pi > pi)).
% 0.59/0.47 thf(func_def_12, type, sum: (pi > pi > pi)).
% 0.59/0.47 thf(func_def_13, type, tau: (pi > pi)).
% 0.59/0.47 thf(func_def_14, type, subs: (pi > name > name > pi)).
% 0.59/0.47 thf(func_def_15, type, late_OutputR: (name > name > late_freeRes)).
% 0.59/0.47 thf(func_def_16, type, late_TauR: late_freeRes).
% 0.59/0.47 thf(func_def_17, type, late_freeRes_rec: !>[X0: $tType]:(((name > name > X0) > X0 > late_freeRes > X0))).
% 0.59/0.47 thf(func_def_18, type, late_BoundR: (late_subject > name > pi > late_residual)).
% 0.59/0.47 thf(func_def_19, type, late_FreeR: (late_freeRes > pi > late_residual)).
% 0.59/0.47 thf(func_def_20, type, late_BoundOutputS: (name > late_subject)).
% 0.59/0.47 thf(func_def_21, type, late_InputS: (name > late_subject)).
% 0.59/0.47 thf(func_def_22, type, late_subject_rec: !>[X0: $tType]:(((name > X0) > (name > X0) > late_subject > X0))).
% 0.59/0.47 thf(func_def_23, type, late_transitions: (pi > late_residual > $o)).
% 0.59/0.47 thf(func_def_24, type, abs_fun: !>[X0: $tType, X1: $tType]:((X0 > X1 > X0 > noption @ X1))).
% 0.59/0.47 thf(func_def_25, type, fresh: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o))).
% 0.59/0.47 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.59/0.47 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.59/0.47 thf(func_def_28, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.59/0.47 thf(func_def_29, type, eqvt: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.59/0.47 thf(func_def_30, type, id: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 0.59/0.47 thf(func_def_31, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.59/0.47 thf(func_def_32, type, strong2129052853vative: (pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o)).
% 0.59/0.47 thf(func_def_33, type, strong743114133lation: (pi > set @ product_prod @ pi @ pi > pi > $o)).
% 0.59/0.47 thf(func_def_34, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.59/0.47 thf(func_def_35, type, p: pi).
% 0.59/0.47 thf(func_def_36, type, pq: pi).
% 0.59/0.47 thf(func_def_37, type, q: pi).
% 0.59/0.47 thf(func_def_38, type, q2: pi).
% 0.59/0.47 thf(func_def_39, type, rel: set @ product_prod @ pi @ pi).
% 0.59/0.47 thf(func_def_40, type, alpha: late_freeRes).
% 0.59/0.47 thf(func_def_41, type, x: name).
% 0.59/0.47 thf(func_def_43, type, vAND: ($o > $o > $o)).
% 0.59/0.47 thf(func_def_44, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.59/0.47 thf(func_def_47, type, db1: !>[X0: $tType]:(X0)).
% 0.59/0.47 thf(func_def_48, type, db0: !>[X0: $tType]:(X0)).
% 0.59/0.47 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.59/0.47 thf(func_def_50, type, vOR: ($o > $o > $o)).
% 0.59/0.47 thf(func_def_51, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.59/0.47 thf(func_def_52, type, vIMP: ($o > $o > $o)).
% 0.59/0.47 thf(func_def_53, type, db2: !>[X0: $tType]:(X0)).
% 0.59/0.47 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.59/0.47 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.59/0.47 thf(func_def_56, type, db5: !>[X0: $tType]:(X0)).
% 0.59/0.47 thf(func_def_57, type, db4: !>[X0: $tType]:(X0)).
% 0.59/0.47 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 0.59/0.47 thf(func_def_59, type, db6: !>[X0: $tType]:(X0)).
% 0.59/0.47 thf(func_def_60, type, sP0: (late_subject > name > pi > name > pi > $o)).
% 0.59/0.47 thf(func_def_61, type, sP1: (name > pi > late_residual > $o)).
% 0.59/0.47 thf(func_def_62, type, sP2: (name > pi > late_residual > $o)).
% 0.59/0.47 thf(func_def_63, type, sK3: ((late_residual > $o) > pi)).
% 0.59/0.47 thf(func_def_64, type, sK4: ((late_residual > $o) > name)).
% 0.59/0.47 thf(func_def_65, type, sK5: ((late_residual > $o) > late_subject)).
% 0.59/0.47 thf(func_def_66, type, sK6: ((late_residual > $o) > late_freeRes)).
% 0.59/0.47 thf(func_def_67, type, sK7: ((late_residual > $o) > pi)).
% 0.59/0.47 thf(func_def_68, type, sK8: (late_subject > name > pi > name > pi > name)).
% 0.59/0.47 thf(func_def_69, type, sK9: (late_subject > name > pi > name > pi > late_subject)).
% 0.59/0.47 thf(func_def_70, type, sK10: (late_subject > name > pi > name > pi > pi)).
% 0.59/0.47 thf(func_def_71, type, sK11: (late_subject > name > pi > name > pi > pi)).
% 0.59/0.47 thf(func_def_72, type, sK12: (late_subject > name > pi > name > pi > name)).
% 0.59/0.47 thf(func_def_73, type, sK13: (late_subject > name > name > pi > pi > pi)).
% 0.59/0.47 thf(func_def_74, type, sK14: (late_subject > name > name > pi > pi > name)).
% 0.59/0.47 thf(func_def_75, type, sK15: (late_subject > name > name > pi > pi > name)).
% 0.59/0.47 thf(func_def_76, type, sK16: (late_subject > name > name > pi > pi > pi)).
% 0.59/0.47 thf(func_def_77, type, sK17: (name > pi > late_residual > late_freeRes)).
% 0.59/0.47 thf(func_def_78, type, sK18: (name > pi > late_residual > pi)).
% 0.59/0.47 thf(func_def_79, type, sK19: (name > pi > late_residual > name)).
% 0.59/0.47 thf(func_def_80, type, sK20: (name > pi > late_residual > pi)).
% 0.59/0.47 thf(func_def_81, type, sK21: (name > pi > late_residual > name)).
% 0.59/0.47 thf(func_def_82, type, sK22: (name > pi > late_residual > late_subject)).
% 0.59/0.47 thf(func_def_83, type, sK23: (name > pi > late_residual > pi)).
% 0.59/0.47 thf(func_def_84, type, sK24: (name > pi > late_residual > name)).
% 0.59/0.47 thf(func_def_85, type, sK25: (name > pi > late_residual > pi)).
% 0.59/0.47 thf(func_def_86, type, sK26: (pi > late_residual > name > name)).
% 0.59/0.47 thf(func_def_87, type, sK27: (pi > late_residual > name > name)).
% 0.59/0.47 thf(func_def_88, type, sK28: (pi > late_residual > name > pi)).
% 0.59/0.47 thf(func_def_89, type, sK29: (pi > late_residual > name > pi)).
% 0.59/0.47 thf(func_def_90, type, sK30: (name > (pi > $o) > late_freeRes > pi > pi)).
% 0.59/0.47 thf(func_def_91, type, sK31: (late_freeRes > pi > name > pi > name)).
% 0.59/0.47 thf(func_def_92, type, sK32: (late_freeRes > pi > name > pi > late_freeRes)).
% 0.59/0.47 thf(func_def_93, type, sK33: (late_freeRes > pi > name > pi > pi)).
% 0.59/0.47 thf(func_def_94, type, sK34: (late_freeRes > pi > name > pi > pi)).
% 0.59/0.47 thf(f1,axiom,(
% 0.59/0.47 (fresh @ name @ late_freeRes @ x @ alpha)),
% 0.59/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_cRes_Ohyps_I2_J)).
% 0.59/0.47 thf(f3,axiom,(
% 0.59/0.47 (late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))),
% 0.59/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062)).
% 0.59/0.47 thf(f14,axiom,(
% 0.59/0.47 ! [X1 : late_freeRes,X3 : name,X2 : pi,X0 : pi] : ((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) => ((fresh @ name @ late_freeRes @ X3 @ X1) => (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))))),
% 0.59/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_ResF)).
% 0.59/0.47 thf(f274,conjecture,(
% 0.59/0.47 (late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 0.59/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.59/0.47 thf(f275,negated_conjecture,(
% 0.59/0.47 ~(late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 0.59/0.47 inference(negated_conjecture,[status(cth)],[f274])).
% 0.59/0.47 thf(f475,plain,(
% 0.59/0.47 (fresh @ name @ late_freeRes @ x @ alpha)),
% 0.59/0.47 inference(rectify,[],[f1])).
% 0.59/0.47 thf(f476,plain,(
% 0.59/0.47 (((fresh @ name @ late_freeRes @ x @ alpha)) = $true)),
% 0.59/0.47 inference(fool_elimination,[],[f475])).
% 0.59/0.47 thf(f492,plain,(
% 0.59/0.47 (late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))),
% 0.59/0.47 inference(rectify,[],[f3])).
% 0.59/0.47 thf(f493,plain,(
% 0.59/0.47 (((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))) = $true)),
% 0.59/0.47 inference(fool_elimination,[],[f492])).
% 0.59/0.47 thf(f596,plain,(
% 0.59/0.47 ! [X0 : late_freeRes,X1 : name,X2 : pi,X3 : pi] : ((late_transitions @ X3 @ (late_FreeR @ X0 @ X2)) => ((fresh @ name @ late_freeRes @ X1 @ X0) => (late_transitions @ (res @ X1 @ X3) @ (late_FreeR @ X0 @ (res @ X1 @ X2)))))),
% 0.59/0.47 inference(rectify,[],[f14])).
% 0.59/0.47 thf(f597,plain,(
% 0.59/0.47 ! [X1 : name,X3 : pi,X2 : pi,X0 : late_freeRes] : (($true = ((late_transitions @ X3 @ (late_FreeR @ X0 @ X2)))) => (($true = ((fresh @ name @ late_freeRes @ X1 @ X0))) => ($true = ((late_transitions @ (res @ X1 @ X3) @ (late_FreeR @ X0 @ (res @ X1 @ X2)))))))),
% 0.59/0.47 inference(fool_elimination,[],[f596])).
% 0.59/0.47 thf(f624,plain,(
% 0.59/0.47 ~(late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 0.59/0.47 inference(rectify,[],[f275])).
% 0.59/0.47 thf(f625,plain,(
% 0.59/0.47 ~ (((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))) = $true)),
% 0.59/0.47 inference(fool_elimination,[],[f624])).
% 0.59/0.47 thf(f716,plain,(
% 0.59/0.47 (((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))) != $true)),
% 0.59/0.47 inference(flattening,[],[f625])).
% 0.59/0.47 thf(f763,plain,(
% 0.59/0.47 ! [X1 : name,X3 : pi,X2 : pi,X0 : late_freeRes] : ((($true = ((late_transitions @ (res @ X1 @ X3) @ (late_FreeR @ X0 @ (res @ X1 @ X2))))) | ($true != ((fresh @ name @ late_freeRes @ X1 @ X0)))) | ($true != ((late_transitions @ X3 @ (late_FreeR @ X0 @ X2)))))),
% 0.59/0.47 inference(ennf_transformation,[],[f597])).
% 0.59/0.47 thf(f764,plain,(
% 0.59/0.47 ! [X2 : pi,X1 : name,X0 : late_freeRes,X3 : pi] : (($true != ((late_transitions @ X3 @ (late_FreeR @ X0 @ X2)))) | ($true != ((fresh @ name @ late_freeRes @ X1 @ X0))) | ($true = ((late_transitions @ (res @ X1 @ X3) @ (late_FreeR @ X0 @ (res @ X1 @ X2))))))),
% 0.59/0.47 inference(flattening,[],[f763])).
% 0.59/0.47 thf(f811,plain,(
% 0.59/0.47 ! [X0 : pi,X1 : name,X2 : late_freeRes,X3 : pi] : ((((late_transitions @ X3 @ (late_FreeR @ X2 @ X0))) != $true) | (((fresh @ name @ late_freeRes @ X1 @ X2)) != $true) | (((late_transitions @ (res @ X1 @ X3) @ (late_FreeR @ X2 @ (res @ X1 @ X0)))) = $true))),
% 0.59/0.47 inference(rectify,[],[f764])).
% 0.59/0.47 thf(f860,plain,(
% 0.59/0.47 (((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))) != $true)),
% 0.59/0.47 inference(cnf_transformation,[],[f716])).
% 0.59/0.47 thf(f878,plain,(
% 0.59/0.47 ( ! [X2 : late_freeRes,X3 : pi,X0 : pi,X1 : name] : ((((late_transitions @ (res @ X1 @ X3) @ (late_FreeR @ X2 @ (res @ X1 @ X0)))) = $true) | (((late_transitions @ X3 @ (late_FreeR @ X2 @ X0))) != $true) | (((fresh @ name @ late_freeRes @ X1 @ X2)) != $true)) )),
% 0.59/0.47 inference(cnf_transformation,[],[f811])).
% 0.59/0.47 thf(f882,plain,(
% 0.59/0.47 (((fresh @ name @ late_freeRes @ x @ alpha)) = $true)),
% 0.59/0.47 inference(cnf_transformation,[],[f476])).
% 0.59/0.47 thf(f928,plain,(
% 0.59/0.47 (((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))) = $true)),
% 0.59/0.47 inference(cnf_transformation,[],[f493])).
% 0.59/0.47 thf(f941,plain,(
% 0.59/0.47 (((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))) != $true) | (((fresh @ name @ late_freeRes @ x @ alpha)) != $true) | ($true != $true)),
% 0.59/0.47 inference(superposition,[],[f860,f878])).
% 0.59/0.47 thf(f944,plain,(
% 0.59/0.47 (((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))) != $true) | (((fresh @ name @ late_freeRes @ x @ alpha)) != $true)),
% 0.59/0.47 inference(trivial_inequality_removal,[],[f941])).
% 0.59/0.47 thf(f945,plain,(
% 0.59/0.47 (((fresh @ name @ late_freeRes @ x @ alpha)) != $true)),
% 0.59/0.47 inference(forward_subsumption_resolution,[],[f944,f928])).
% 0.59/0.47 thf(f946,plain,(
% 0.59/0.47 $false),
% 0.59/0.47 inference(forward_subsumption_resolution,[],[f945,f882])).
% 0.59/0.47 % SZS output end Proof for theBenchmark
% 0.59/0.47 % (3153984)------------------------------
% 0.59/0.47 % (3153984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.47 % (3153984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.47 % (3153984)CaDiCaL version: 2.1.3
% 0.59/0.47 % (3153984)Termination reason: Refutation
% 0.59/0.47 % (3153984)Time elapsed: 0.019 s
% 0.59/0.47 % (3153984)Peak memory usage: 13 MB
% 0.59/0.47 % (3153984)Instructions burned: 73 (million)
% 0.59/0.47 % (3153949)Success in time 0.175 s
% 0.59/0.47 % Vampire exiting
%------------------------------------------------------------------------------