%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL042-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 : Tue Sep 29 09:38:14 AM UTC 2026
% Result : Unsatisfiable 3.98s 0.93s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 37 unt; 8 def)
% Number of atoms : 41 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,axiom,
! [X0] :
( apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt))
| fixed_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
sF0 = apply(w1,w1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(w1,w1) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = apply(b,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
apply(b,sF0) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
sF2 = apply(b,w1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
apply(b,w1) = sF2,
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
sF3 = apply(sF1,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
apply(sF1,sF2) = sF3,
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
sF4 = apply(b,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
apply(b,sF3) = sF4,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF5 = apply(sF4,b),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
apply(sF4,b) = sF5,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF6 = apply(b,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
apply(b,sF5) = sF6,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF7 = apply(sF6,b),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f20,plain,
apply(sF6,b) = sF7,
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
~ fixed_point(sF7),
inference(definition_folding,[],[f4,f20,f18,f16,f14,f12,f10,f8,f6]) ).
fof(f42,plain,
! [X0,X1] : apply(sF0,apply(X0,X1)) = apply(apply(sF1,X0),X1),
inference(superposition,[],[f1,f8]) ).
fof(f43,plain,
! [X0,X1] : apply(sF3,apply(X0,X1)) = apply(apply(sF4,X0),X1),
inference(superposition,[],[f1,f14]) ).
fof(f44,plain,
! [X0,X1] : apply(sF5,apply(X0,X1)) = apply(apply(sF6,X0),X1),
inference(superposition,[],[f1,f18]) ).
fof(f50,plain,
! [X2,X0,X1] : apply(apply(w1,X2),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f2,f1]) ).
fof(f111,plain,
! [X0] : apply(sF0,apply(sF2,X0)) = apply(sF3,X0),
inference(superposition,[],[f42,f12]) ).
fof(f124,plain,
! [X0] : apply(sF3,apply(b,X0)) = apply(sF5,X0),
inference(superposition,[],[f43,f16]) ).
fof(f141,plain,
! [X0] : apply(sF5,X0) = apply(sF0,apply(sF2,apply(b,X0))),
inference(forward_demodulation,[],[f124,f111]) ).
fof(f162,plain,
! [X0] : apply(sF5,apply(b,X0)) = apply(sF7,X0),
inference(superposition,[],[f44,f20]) ).
fof(f232,plain,
( apply(sF5,apply(b,fixed_pt)) != apply(fixed_pt,apply(sF5,apply(b,fixed_pt)))
| fixed_point(sF7) ),
inference(superposition,[],[f3,f162]) ).
fof(f235,plain,
apply(sF5,apply(b,fixed_pt)) != apply(fixed_pt,apply(sF5,apply(b,fixed_pt))),
inference(forward_subsumption_resolution,[],[f232,f21]) ).
fof(f564,plain,
! [X0,X1] : apply(apply(w1,X0),apply(apply(b,w1),X1)) = apply(apply(X0,apply(X1,X0)),apply(X1,X0)),
inference(superposition,[],[f2,f50]) ).
fof(f569,plain,
! [X2,X0,X1] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),X2)) = apply(X1,apply(apply(X2,X0),X0)),
inference(superposition,[],[f1,f50]) ).
fof(f586,plain,
! [X0,X1] : apply(apply(X0,apply(X1,X0)),apply(X1,X0)) = apply(apply(w1,X0),apply(sF2,X1)),
inference(forward_demodulation,[],[f564,f10]) ).
fof(f13631,plain,
! [X0] : apply(apply(w1,w1),apply(sF2,apply(b,apply(b,X0)))) = apply(X0,apply(apply(w1,w1),apply(sF2,apply(b,apply(b,X0))))),
inference(superposition,[],[f569,f586]) ).
fof(f14231,plain,
! [X0] : apply(sF0,apply(sF2,apply(b,apply(b,X0)))) = apply(X0,apply(sF0,apply(sF2,apply(b,apply(b,X0))))),
inference(forward_demodulation,[],[f13631,f6]) ).
fof(f14379,plain,
! [X0] : apply(sF5,apply(b,X0)) = apply(X0,apply(sF5,apply(b,X0))),
inference(forward_demodulation,[],[f14231,f141]) ).
fof(f14598,plain,
apply(sF5,apply(b,fixed_pt)) != apply(sF5,apply(b,fixed_pt)),
inference(superposition,[],[f235,f14379]) ).
fof(f14624,plain,
$false,
inference(trivial_inequality_removal,[],[f14598]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL042-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n011.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 21:30:31 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.98/0.92 % (3804162)Will run a generic schedule for satisfiability detection.
% 3.98/0.92 % (3804172)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=559963013:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.98/0.92 % (3804168)% WARNING: option uhcvi not known.
% 3.98/0.92 % (3804169)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1443160428:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.98/0.92 % (3804167)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1991359227_2999 on theBenchmark for (2999ds/0Mi)
% 3.98/0.92 % (3804168)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=708149852:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.98/0.92 % (3804170)dis+10_1_sil=32000:sp=arity:random_seed=657158066:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.98/0.92 % (3804171)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3314896495:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.98/0.92 % (3804173)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2940001719:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.98/0.92 % TRYING [1]
% 3.98/0.92 % TRYING [2]
% 3.98/0.92 % TRYING [3]
% 3.98/0.92 % TRYING [4]
% 3.98/0.92 % (3804172)Instruction limit reached!
% 3.98/0.92 % (3804172)------------------------------
% 3.98/0.92 % (3804172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.92 % (3804172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.92 % (3804172)CaDiCaL version: 2.1.3
% 3.98/0.92 % (3804172)Termination reason: Instruction limit
% 3.98/0.92 % (3804172)Termination phase: Saturation
% 3.98/0.92 % (3804172)Time elapsed: 0.046 s
% 3.98/0.92 % (3804172)Peak memory usage: 13 MB
% 3.98/0.92 % (3804172)Instructions burned: 134 (million)
% 3.98/0.92 % TRYING [5]
% 3.98/0.92 % (3804181)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3662908865:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.98/0.92 % TRYING [1]
% 3.98/0.92 % TRYING [2]
% 3.98/0.92 % TRYING [3]
% 3.98/0.92 % TRYING [4]
% 3.98/0.92 % (3804170)Instruction limit reached!
% 3.98/0.92 % (3804170)------------------------------
% 3.98/0.92 % (3804170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.92 % (3804170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.92 % (3804170)CaDiCaL version: 2.1.3
% 3.98/0.92 % (3804170)Termination reason: Instruction limit
% 3.98/0.92 % (3804170)Termination phase: Saturation
% 3.98/0.92 % (3804170)Time elapsed: 0.059 s
% 3.98/0.92 % (3804170)Peak memory usage: 12 MB
% 3.98/0.92 % (3804170)Instructions burned: 104 (million)
% 3.98/0.92 % (3804171)Instruction limit reached!
% 3.98/0.92 % (3804171)------------------------------
% 3.98/0.92 % (3804171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.92 % (3804171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.92 % (3804171)CaDiCaL version: 2.1.3
% 3.98/0.92 % (3804171)Termination reason: Instruction limit
% 3.98/0.92 % (3804171)Termination phase: Saturation
% 3.98/0.92 % (3804171)Time elapsed: 0.074 s
% 3.98/0.92 % (3804171)Peak memory usage: 12 MB
% 3.98/0.92 % (3804171)Instructions burned: 116 (million)
% 3.98/0.92 % TRYING [5]
% 3.98/0.92 % (3804183)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2073698248:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.98/0.92 % (3804184)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=586705443:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.98/0.92 % (3804173)Instruction limit reached!
% 3.98/0.92 % (3804173)------------------------------
% 3.98/0.92 % (3804173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.92 % (3804173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.92 % (3804173)CaDiCaL version: 2.1.3
% 3.98/0.92 % (3804173)Termination reason: Instruction limit
% 3.98/0.92 % (3804173)Termination phase: Saturation
% 3.98/0.92 % (3804173)Time elapsed: 0.100 s
% 3.98/0.92 % (3804173)Peak memory usage: 13 MB
% 3.98/0.92 % (3804173)Instructions burned: 159 (million)
% 3.98/0.92 % (3804187)ott-21_1_sil=16000:fs=off:random_seed=4279071349:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.98/0.92 % (3804183)Instruction limit reached!
% 3.98/0.92 % (3804183)------------------------------
% 3.98/0.92 % (3804183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.93 % (3804183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.93 % (3804183)CaDiCaL version: 2.1.3
% 3.98/0.93 % (3804183)Termination reason: Instruction limit
% 3.98/0.93 % (3804183)Termination phase: Saturation
% 3.98/0.93 % (3804183)Time elapsed: 0.089 s
% 3.98/0.93 % (3804183)Peak memory usage: 13 MB
% 3.98/0.93 % (3804183)Instructions burned: 131 (million)
% 3.98/0.93 % TRYING [6]
% 3.98/0.93 % (3804189)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2415239428:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 3.98/0.93 % (3804187)Instruction limit reached!
% 3.98/0.93 % (3804187)------------------------------
% 3.98/0.93 % (3804187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.93 % (3804187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.93 % (3804187)CaDiCaL version: 2.1.3
% 3.98/0.93 % (3804187)Termination reason: Instruction limit
% 3.98/0.93 % (3804187)Termination phase: Saturation
% 3.98/0.93 % (3804187)Time elapsed: 0.101 s
% 3.98/0.93 % (3804187)Peak memory usage: 12 MB
% 3.98/0.93 % (3804187)Instructions burned: 181 (million)
% 3.98/0.93 % (3804204)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3988268942:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 3.98/0.93 % TRYING [1]
% 3.98/0.93 % TRYING [2]
% 3.98/0.93 % TRYING [3]
% 3.98/0.93 % TRYING [4]
% 3.98/0.93 % (3804181)Instruction limit reached!
% 3.98/0.93 % (3804181)------------------------------
% 3.98/0.93 % (3804181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.93 % (3804181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.93 % (3804181)CaDiCaL version: 2.1.3
% 3.98/0.93 % (3804181)Termination reason: Instruction limit
% 3.98/0.93 % (3804181)Termination phase: Finite model building SAT solving
% 3.98/0.93 % (3804181)Time elapsed: 0.222 s
% 3.98/0.93 % (3804181)Peak memory usage: 16 MB
% 3.98/0.93 % (3804181)Instructions burned: 717 (million)
% 3.98/0.93 % (3804218)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2454025586:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 3.98/0.93 % TRYING [6]
% 3.98/0.93 % TRYING [5]
% 3.98/0.93 % TRYING [6]
% 3.98/0.93 % (3804189)Instruction limit reached!
% 3.98/0.93 % (3804189)------------------------------
% 3.98/0.93 % (3804189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.93 % (3804189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.93 % (3804189)CaDiCaL version: 2.1.3
% 3.98/0.93 % (3804189)Termination reason: Instruction limit
% 3.98/0.93 % (3804189)Termination phase: Saturation
% 3.98/0.93 % (3804189)Time elapsed: 0.265 s
% 3.98/0.93 % (3804189)Peak memory usage: 15 MB
% 3.98/0.93 % (3804189)Instructions burned: 478 (million)
% 3.98/0.93 % (3804184)Instruction limit reached!
% 3.98/0.93 % (3804184)------------------------------
% 3.98/0.93 % (3804184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.93 % (3804184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.93 % (3804184)CaDiCaL version: 2.1.3
% 3.98/0.93 % (3804184)Termination reason: Instruction limit
% 3.98/0.93 % (3804184)Termination phase: Saturation
% 3.98/0.93 % (3804184)Time elapsed: 0.370 s
% 3.98/0.93 % (3804184)Peak memory usage: 17 MB
% 3.98/0.93 % (3804184)Instructions burned: 685 (million)
% 3.98/0.93 % (3804274)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2067610582:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 3.98/0.93 % (3804278)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3418210930:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 3.98/0.93 % TRYING [14]
% 3.98/0.93 % (3804218) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3804162-3804218"...
% 3.98/0.93 % (3804218)...printing done.
% 3.98/0.93 % (3804218)Refutation found. Thanks to Tanya!
% 3.98/0.93 % SZS status Unsatisfiable for theBenchmark
% 3.98/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/0.93 % (3804218)------------------------------
% 3.98/0.93 % (3804218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.98/0.93 % (3804218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/0.93 % (3804218)CaDiCaL version: 2.1.3
% 3.98/0.93 % (3804218)Termination reason: Refutation
% 3.98/0.93 % (3804218)Time elapsed: 0.353 s
% 3.98/0.93 % (3804218)Peak memory usage: 25 MB
% 3.98/0.93 % (3804218)Instructions burned: 1044 (million)
% 3.98/0.93 % (3804162)Success in time 0.685 s
% 3.98/0.93 % Vampire exiting
%------------------------------------------------------------------------------