%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL003-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 09:38:07 AM UTC 2026
% Result : Unsatisfiable 4.25s 0.94s
% Output : Refutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 34 unt; 7 def)
% Number of atoms : 38 ( 33 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 : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 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(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_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(w,w)),w)),apply(apply(b,b),b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
sF0 = apply(w,w),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(w,w) = 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(sF1,w),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
apply(sF1,w) = sF2,
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
sF3 = apply(b,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
apply(b,sF2) = sF3,
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
sF4 = apply(b,b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
apply(b,b) = 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(sF3,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
apply(sF3,sF5) = sF6,
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
~ fixed_point(sF6),
inference(definition_folding,[],[f4,f18,f16,f14,f12,f10,f8,f6]) ).
fof(f24,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f25,plain,
! [X0] : apply(sF0,X0) = apply(apply(X0,X0),X0),
inference(forward_demodulation,[],[f24,f6]) ).
fof(f46,plain,
! [X0,X1] : apply(sF0,apply(X0,X1)) = apply(apply(sF1,X0),X1),
inference(superposition,[],[f1,f8]) ).
fof(f47,plain,
! [X0,X1] : apply(sF2,apply(X0,X1)) = apply(apply(sF3,X0),X1),
inference(superposition,[],[f1,f12]) ).
fof(f48,plain,
! [X0,X1] : apply(b,apply(X0,X1)) = apply(apply(sF4,X0),X1),
inference(superposition,[],[f1,f14]) ).
fof(f51,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f64,plain,
! [X0] : apply(sF0,apply(w,X0)) = apply(sF2,X0),
inference(superposition,[],[f46,f10]) ).
fof(f72,plain,
! [X0] : apply(sF2,apply(sF5,X0)) = apply(sF6,X0),
inference(superposition,[],[f47,f18]) ).
fof(f80,plain,
! [X0] : apply(b,apply(b,X0)) = apply(sF5,X0),
inference(superposition,[],[f48,f16]) ).
fof(f126,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2),
inference(superposition,[],[f1,f51]) ).
fof(f139,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(sF5,X0)),X1),X2),
inference(forward_demodulation,[],[f126,f80]) ).
fof(f186,plain,
( apply(sF2,apply(sF5,fixed_pt)) != apply(fixed_pt,apply(sF2,apply(sF5,fixed_pt)))
| fixed_point(sF6) ),
inference(superposition,[],[f3,f72]) ).
fof(f187,plain,
apply(sF2,apply(sF5,fixed_pt)) != apply(fixed_pt,apply(sF2,apply(sF5,fixed_pt))),
inference(forward_subsumption_resolution,[],[f186,f19]) ).
fof(f4232,plain,
! [X0] : apply(sF0,apply(w,apply(sF5,X0))) = apply(X0,apply(sF0,apply(w,apply(sF5,X0)))),
inference(superposition,[],[f139,f25]) ).
fof(f4441,plain,
! [X0] : apply(sF2,apply(sF5,X0)) = apply(X0,apply(sF2,apply(sF5,X0))),
inference(forward_demodulation,[],[f4232,f64]) ).
fof(f4533,plain,
apply(sF2,apply(sF5,fixed_pt)) != apply(sF2,apply(sF5,fixed_pt)),
inference(superposition,[],[f187,f4441]) ).
fof(f4550,plain,
$false,
inference(trivial_inequality_removal,[],[f4533]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:35:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 4.25/0.94 % (773860)Will run a generic schedule for satisfiability detection.
% 4.25/0.94 % (773867)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1294305479:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.25/0.94 % (773866)% WARNING: option uhcvi not known.
% 4.25/0.94 % (773865)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4192539102_2999 on theBenchmark for (2999ds/0Mi)
% 4.25/0.94 % (773866)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1153351179:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.25/0.94 % (773868)dis+10_1_sil=32000:sp=arity:random_seed=936853751:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.25/0.94 % (773870)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4036278862:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.25/0.94 % (773869)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4053904079:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.25/0.94 % (773871)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2527539870:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.25/0.94 % TRYING [1]
% 4.25/0.94 % TRYING [2]
% 4.25/0.94 % TRYING [3]
% 4.25/0.94 % TRYING [4]
% 4.25/0.94 % (773868)Instruction limit reached!
% 4.25/0.94 % (773868)------------------------------
% 4.25/0.94 % (773868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773868)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773868)Termination reason: Instruction limit
% 4.25/0.94 % (773868)Termination phase: Saturation
% 4.25/0.94 % (773868)Time elapsed: 0.057 s
% 4.25/0.94 % (773868)Peak memory usage: 12 MB
% 4.25/0.94 % (773868)Instructions burned: 103 (million)
% 4.25/0.94 % (773869)Instruction limit reached!
% 4.25/0.94 % (773869)------------------------------
% 4.25/0.94 % (773869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773869)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773869)Termination reason: Instruction limit
% 4.25/0.94 % (773869)Termination phase: Saturation
% 4.25/0.94 % (773869)Time elapsed: 0.071 s
% 4.25/0.94 % (773869)Peak memory usage: 12 MB
% 4.25/0.94 % (773869)Instructions burned: 117 (million)
% 4.25/0.94 % TRYING [5]
% 4.25/0.94 % (773879)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3126127247:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.25/0.94 % TRYING [1]
% 4.25/0.94 % TRYING [2]
% 4.25/0.94 % TRYING [3]
% 4.25/0.94 % (773870)Instruction limit reached!
% 4.25/0.94 % (773870)------------------------------
% 4.25/0.94 % (773870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773870)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773870)Termination reason: Instruction limit
% 4.25/0.94 % (773870)Termination phase: Saturation
% 4.25/0.94 % (773870)Time elapsed: 0.080 s
% 4.25/0.94 % (773870)Peak memory usage: 13 MB
% 4.25/0.94 % (773870)Instructions burned: 131 (million)
% 4.25/0.94 % TRYING [4]
% 4.25/0.94 % (773880)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1749245923:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 4.25/0.94 % (773871)Instruction limit reached!
% 4.25/0.94 % (773871)------------------------------
% 4.25/0.94 % (773871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773871)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773871)Termination reason: Instruction limit
% 4.25/0.94 % (773871)Termination phase: Saturation
% 4.25/0.94 % (773871)Time elapsed: 0.095 s
% 4.25/0.94 % (773871)Peak memory usage: 13 MB
% 4.25/0.94 % (773871)Instructions burned: 159 (million)
% 4.25/0.94 % (773882)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=3221844281:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 4.25/0.94 % (773884)ott-21_1_sil=16000:fs=off:random_seed=1497119658:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.25/0.94 % TRYING [5]
% 4.25/0.94 % (773880)Instruction limit reached!
% 4.25/0.94 % (773880)------------------------------
% 4.25/0.94 % (773880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773880)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773880)Termination reason: Instruction limit
% 4.25/0.94 % (773880)Termination phase: Saturation
% 4.25/0.94 % (773880)Time elapsed: 0.084 s
% 4.25/0.94 % (773880)Peak memory usage: 13 MB
% 4.25/0.94 % (773880)Instructions burned: 131 (million)
% 4.25/0.94 % (773887)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=222342273:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 4.25/0.94 % (773884)Instruction limit reached!
% 4.25/0.94 % (773884)------------------------------
% 4.25/0.94 % (773884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773884)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773884)Termination reason: Instruction limit
% 4.25/0.94 % (773884)Termination phase: Saturation
% 4.25/0.94 % (773884)Time elapsed: 0.083 s
% 4.25/0.94 % (773884)Peak memory usage: 11 MB
% 4.25/0.94 % (773884)Instructions burned: 180 (million)
% 4.25/0.94 % (773889)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=543061031:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 4.25/0.94 % TRYING [1]
% 4.25/0.94 % TRYING [2]
% 4.25/0.94 % TRYING [3]
% 4.25/0.94 % TRYING [4]
% 4.25/0.94 % TRYING [5]
% 4.25/0.94 % TRYING [6]
% 4.25/0.94 % TRYING [6]
% 4.25/0.94 % TRYING [6]
% 4.25/0.94 % (773887)Instruction limit reached!
% 4.25/0.94 % (773887)------------------------------
% 4.25/0.94 % (773887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773887)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773887)Termination reason: Instruction limit
% 4.25/0.94 % (773887)Termination phase: Saturation
% 4.25/0.94 % (773887)Time elapsed: 0.255 s
% 4.25/0.94 % (773887)Peak memory usage: 15 MB
% 4.25/0.94 % (773887)Instructions burned: 478 (million)
% 4.25/0.94 % (773882)Instruction limit reached!
% 4.25/0.94 % (773882)------------------------------
% 4.25/0.94 % (773882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773882)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773882)Termination reason: Instruction limit
% 4.25/0.94 % (773882)Termination phase: Saturation
% 4.25/0.94 % (773882)Time elapsed: 0.352 s
% 4.25/0.94 % (773882)Peak memory usage: 17 MB
% 4.25/0.94 % (773882)Instructions burned: 686 (million)
% 4.25/0.94 % (773891)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2909664894:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 4.25/0.94 % (773892)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1829921710:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 4.25/0.94 % (773879)Instruction limit reached!
% 4.25/0.94 % (773879)------------------------------
% 4.25/0.94 % (773879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773879)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773879)Termination reason: Instruction limit
% 4.25/0.94 % (773879)Termination phase: Finite model building SAT solving
% 4.25/0.94 % (773879)Time elapsed: 0.415 s
% 4.25/0.94 % (773879)Peak memory usage: 16 MB
% 4.25/0.94 % (773879)Instructions burned: 715 (million)
% 4.25/0.94 % TRYING [14]
% 4.25/0.94 % (773895)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=2376138990: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)
% 4.25/0.94 % (773889)Instruction limit reached!
% 4.25/0.94 % (773889)------------------------------
% 4.25/0.94 % (773889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773889)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773889)Termination reason: Instruction limit
% 4.25/0.94 % (773889)Termination phase: Finite model building SAT solving
% 4.25/0.94 % (773889)Time elapsed: 0.434 s
% 4.25/0.94 % (773889)Peak memory usage: 15 MB
% 4.25/0.94 % (773889)Instructions burned: 865 (million)
% 4.25/0.94 % (773891) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-773860-773891"...
% 4.25/0.94 % (773891)...printing done.
% 4.25/0.94 % (773891)Refutation found. Thanks to Tanya!
% 4.25/0.94 % SZS status Unsatisfiable for theBenchmark
% 4.25/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 4.25/0.94 % (773891)------------------------------
% 4.25/0.94 % (773891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.94 % (773891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.94 % (773891)CaDiCaL version: 2.1.3
% 4.25/0.94 % (773891)Termination reason: Refutation
% 4.25/0.94 % (773891)Time elapsed: 0.189 s
% 4.25/0.94 % (773891)Peak memory usage: 16 MB
% 4.25/0.94 % (773891)Instructions burned: 307 (million)
% 4.25/0.94 % (773860)Success in time 0.701 s
% 4.25/0.94 % Vampire exiting
%------------------------------------------------------------------------------