%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL042-8 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 3.10s 0.73s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 20 unt; 2 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 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,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
sF0 = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(strong_fixed_point,fixed_pt) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = apply(fixed_pt,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
apply(fixed_pt,sF0) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
sF0 != sF1,
inference(definition_folding,[],[f4,f8,f6,f6]) ).
fof(f19,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(f21,plain,
! [X0] : apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f23,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X0))),
inference(forward_demodulation,[],[f21,f1]) ).
fof(f24,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f23,f1]) ).
fof(f212,plain,
! [X0,X1] : apply(apply(X0,apply(X1,X0)),apply(X1,X0)) = apply(apply(w1,X0),apply(apply(b,w1),X1)),
inference(superposition,[],[f2,f19]) ).
fof(f214,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,f19]) ).
fof(f1978,plain,
! [X0] : apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0)))) = apply(X0,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0))))),
inference(superposition,[],[f214,f212]) ).
fof(f2208,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f1978,f24]) ).
fof(f2253,plain,
sF0 = apply(fixed_pt,sF0),
inference(superposition,[],[f2208,f6]) ).
fof(f2383,plain,
sF0 = sF1,
inference(superposition,[],[f8,f2253]) ).
fof(f2397,plain,
$false,
inference(forward_subsumption_resolution,[],[f2383,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL042-8 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:30:16 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 3.10/0.73 % (1206261)Will run a generic schedule for satisfiability detection.
% 3.10/0.73 % (1206267)% WARNING: option uhcvi not known.
% 3.10/0.73 % (1206272)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3597331878:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.10/0.73 % (1206270)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4192575166:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.10/0.73 % (1206269)dis+10_1_sil=32000:sp=arity:random_seed=3462877470:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.10/0.73 % (1206268)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=531008822:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.10/0.73 % (1206267)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=666188355:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.10/0.73 % (1206266)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3044059879_2999 on theBenchmark for (2999ds/0Mi)
% 3.10/0.73 % TRYING [1]
% 3.10/0.73 % TRYING [2]
% 3.10/0.73 % TRYING [3]
% 3.10/0.73 % (1206271)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=906787118:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.10/0.73 % TRYING [4]
% 3.10/0.73 % (1206272)Instruction limit reached!
% 3.10/0.73 % (1206272)------------------------------
% 3.10/0.73 % (1206272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206272)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206272)Termination reason: Instruction limit
% 3.10/0.73 % (1206272)Termination phase: Saturation
% 3.10/0.73 % (1206272)Time elapsed: 0.055 s
% 3.10/0.73 % (1206272)Peak memory usage: 13 MB
% 3.10/0.73 % (1206272)Instructions burned: 161 (million)
% 3.10/0.73 % (1206269)Instruction limit reached!
% 3.10/0.73 % (1206269)------------------------------
% 3.10/0.73 % (1206269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206269)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206269)Termination reason: Instruction limit
% 3.10/0.73 % (1206269)Termination phase: Saturation
% 3.10/0.73 % (1206269)Time elapsed: 0.058 s
% 3.10/0.73 % (1206269)Peak memory usage: 12 MB
% 3.10/0.73 % (1206269)Instructions burned: 104 (million)
% 3.10/0.73 % (1206280)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=864274408:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.10/0.73 % TRYING [1]
% 3.10/0.73 % TRYING [2]
% 3.10/0.73 % TRYING [3]
% 3.10/0.73 % TRYING [4]
% 3.10/0.73 % (1206270)Instruction limit reached!
% 3.10/0.73 % (1206270)------------------------------
% 3.10/0.73 % (1206270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206270)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206270)Termination reason: Instruction limit
% 3.10/0.73 % (1206270)Termination phase: Saturation
% 3.10/0.73 % (1206270)Time elapsed: 0.075 s
% 3.10/0.73 % (1206270)Peak memory usage: 12 MB
% 3.10/0.73 % (1206270)Instructions burned: 117 (million)
% 3.10/0.73 % (1206281)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1514082686:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.10/0.73 % TRYING [5]
% 3.10/0.73 % TRYING [5]
% 3.10/0.73 % (1206283)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=175422924:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.10/0.73 % (1206271)Instruction limit reached!
% 3.10/0.73 % (1206271)------------------------------
% 3.10/0.73 % (1206271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206271)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206271)Termination reason: Instruction limit
% 3.10/0.73 % (1206271)Termination phase: Saturation
% 3.10/0.73 % (1206271)Time elapsed: 0.138 s
% 3.10/0.73 % (1206271)Peak memory usage: 13 MB
% 3.10/0.73 % (1206271)Instructions burned: 132 (million)
% 3.10/0.73 % (1206281)Instruction limit reached!
% 3.10/0.73 % (1206281)------------------------------
% 3.10/0.73 % (1206281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206281)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206281)Termination reason: Instruction limit
% 3.10/0.73 % (1206281)Termination phase: Saturation
% 3.10/0.73 % (1206281)Time elapsed: 0.087 s
% 3.10/0.73 % (1206281)Peak memory usage: 13 MB
% 3.10/0.73 % (1206281)Instructions burned: 131 (million)
% 3.10/0.73 % (1206286)ott-21_1_sil=16000:fs=off:random_seed=3379659929:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.10/0.73 % (1206287)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1956424718:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.10/0.73 % TRYING [6]
% 3.10/0.73 % (1206280)Instruction limit reached!
% 3.10/0.73 % (1206280)------------------------------
% 3.10/0.73 % (1206280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206280)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206280)Termination reason: Instruction limit
% 3.10/0.73 % (1206280)Termination phase: Finite model building SAT solving
% 3.10/0.73 % (1206280)Time elapsed: 0.228 s
% 3.10/0.73 % (1206280)Peak memory usage: 16 MB
% 3.10/0.73 % (1206280)Instructions burned: 716 (million)
% 3.10/0.73 % TRYING [6]
% 3.10/0.73 % (1206286)Instruction limit reached!
% 3.10/0.73 % (1206286)------------------------------
% 3.10/0.73 % (1206286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206286)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206286)Termination reason: Instruction limit
% 3.10/0.73 % (1206286)Termination phase: Saturation
% 3.10/0.73 % (1206286)Time elapsed: 0.114 s
% 3.10/0.73 % (1206286)Peak memory usage: 12 MB
% 3.10/0.73 % (1206286)Instructions burned: 182 (million)
% 3.10/0.73 % (1206304)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3352224493:fmbsr=1.3:i=865:ins=25_2996 on theBenchmark for (2996ds/865Mi)
% 3.10/0.73 % TRYING [1]
% 3.10/0.73 % TRYING [2]
% 3.10/0.73 % TRYING [3]
% 3.10/0.73 % TRYING [4]
% 3.10/0.73 % (1206305)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1549685180:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 3.10/0.73 % TRYING [5]
% 3.10/0.73 % TRYING [6]
% 3.10/0.73 % (1206287)Instruction limit reached!
% 3.10/0.73 % (1206287)------------------------------
% 3.10/0.73 % (1206287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206287)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206287)Termination reason: Instruction limit
% 3.10/0.73 % (1206287)Termination phase: Saturation
% 3.10/0.73 % (1206287)Time elapsed: 0.257 s
% 3.10/0.73 % (1206287)Peak memory usage: 14 MB
% 3.10/0.73 % (1206287)Instructions burned: 477 (million)
% 3.10/0.73 % (1206305) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1206261-1206305"...
% 3.10/0.73 % (1206305)...printing done.
% 3.10/0.73 % (1206283)Instruction limit reached!
% 3.10/0.73 % (1206283)------------------------------
% 3.10/0.73 % (1206283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206283)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206283)Termination reason: Instruction limit
% 3.10/0.73 % (1206283)Termination phase: Saturation
% 3.10/0.73 % (1206283)Time elapsed: 0.368 s
% 3.10/0.73 % (1206283)Peak memory usage: 16 MB
% 3.10/0.73 % (1206283)Instructions burned: 684 (million)
% 3.10/0.73 % (1206358)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2356796014:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 3.10/0.73 % (1206305)Refutation found. Thanks to Tanya!
% 3.10/0.73 % SZS status Unsatisfiable for theBenchmark
% 3.10/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 3.10/0.73 % (1206305)------------------------------
% 3.10/0.73 % (1206305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.10/0.73 % (1206305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/0.73 % (1206305)CaDiCaL version: 2.1.3
% 3.10/0.73 % (1206305)Termination reason: Refutation
% 3.10/0.73 % (1206305)Time elapsed: 0.141 s
% 3.10/0.73 % (1206305)Peak memory usage: 15 MB
% 3.10/0.73 % (1206305)Instructions burned: 212 (million)
% 3.10/0.73 % (1206261)Success in time 0.5 s
% 3.10/0.73 % Vampire exiting
%------------------------------------------------------------------------------