%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL042-4 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:37:42 AM UTC 2026
% Result : Unsatisfiable 6.29s 2.02s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 45 unt; 8 def)
% Number of atoms : 49 ( 43 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)),
file('/export/starexec/sandbox2/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(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(sF3,b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
apply(sF3,b) = sF4,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF5 = apply(sF1,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
apply(sF1,sF4) = 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(f23,plain,
! [X0,X1] : apply(w1,apply(X0,X1)) = apply(apply(sF2,X0),X1),
inference(superposition,[],[f1,f10]) ).
fof(f25,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(f34,plain,
! [X0] : apply(apply(X0,w1),w1) = apply(sF0,X0),
inference(superposition,[],[f2,f6]) ).
fof(f35,plain,
! [X0,X1] : apply(sF2,apply(X0,X1)) = apply(apply(sF3,X0),X1),
inference(superposition,[],[f1,f12]) ).
fof(f36,plain,
! [X0,X1] : apply(sF5,apply(X0,X1)) = apply(apply(sF6,X0),X1),
inference(superposition,[],[f1,f18]) ).
fof(f37,plain,
! [X0,X1] : apply(sF0,apply(X0,X1)) = apply(apply(sF1,X0),X1),
inference(superposition,[],[f1,f8]) ).
fof(f38,plain,
! [X0] : apply(sF0,apply(sF4,X0)) = apply(sF5,X0),
inference(superposition,[],[f37,f16]) ).
fof(f44,plain,
! [X0] : apply(sF4,X0) = apply(sF2,apply(b,X0)),
inference(superposition,[],[f35,f14]) ).
fof(f55,plain,
! [X0] : apply(sF5,apply(b,X0)) = apply(sF7,X0),
inference(superposition,[],[f36,f20]) ).
fof(f65,plain,
! [X0,X1] : apply(w1,apply(apply(b,X0),X1)) = apply(apply(sF4,X0),X1),
inference(superposition,[],[f23,f44]) ).
fof(f69,plain,
! [X0,X1] : apply(apply(w1,X1),apply(sF2,X0)) = apply(apply(w1,apply(X0,X1)),X1),
inference(superposition,[],[f2,f23]) ).
fof(f125,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,f25]) ).
fof(f172,plain,
! [X2,X0,X1] : apply(X2,apply(apply(w1,X0),X1)) = apply(apply(w1,X0),apply(apply(b,apply(b,X2)),X1)),
inference(superposition,[],[f125,f2]) ).
fof(f282,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),X1)),
inference(superposition,[],[f2,f172]) ).
fof(f294,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(w1,X1),apply(sF2,apply(b,apply(b,X0))))),
inference(forward_demodulation,[],[f282,f69]) ).
fof(f307,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(w1,X1),apply(sF4,apply(b,X0)))),
inference(forward_demodulation,[],[f294,f44]) ).
fof(f313,plain,
! [X0,X1] : apply(X0,apply(apply(w1,X1),apply(sF4,apply(b,X0)))) = apply(apply(apply(sF4,apply(b,X0)),X1),w1),
inference(forward_demodulation,[],[f307,f65]) ).
fof(f317,plain,
! [X0] : apply(apply(apply(sF4,apply(b,X0)),w1),w1) = apply(X0,apply(sF0,apply(sF4,apply(b,X0)))),
inference(superposition,[],[f313,f6]) ).
fof(f375,plain,
! [X0] : apply(apply(apply(sF4,apply(b,X0)),w1),w1) = apply(X0,apply(sF5,apply(b,X0))),
inference(forward_demodulation,[],[f317,f38]) ).
fof(f380,plain,
! [X0] : apply(apply(apply(sF4,apply(b,X0)),w1),w1) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f375,f55]) ).
fof(f383,plain,
! [X0] : apply(sF0,apply(sF4,apply(b,X0))) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f380,f34]) ).
fof(f384,plain,
! [X0] : apply(sF5,apply(b,X0)) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f383,f38]) ).
fof(f385,plain,
! [X0] : apply(sF7,X0) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f384,f55]) ).
fof(f419,plain,
( apply(sF7,fixed_pt) != apply(sF7,fixed_pt)
| fixed_point(sF7) ),
inference(superposition,[],[f3,f385]) ).
fof(f425,plain,
fixed_point(sF7),
inference(trivial_inequality_removal,[],[f419]) ).
fof(f427,plain,
$false,
inference(forward_subsumption_resolution,[],[f425,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-4 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.27 % Computer : n008.cluster.edu
% 0.13/0.27 % Model : x86_64 x86_64
% 0.13/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.27 % Memory : 8046.5625MB
% 0.13/0.27 % OS : Linux 6.8.0-71-generic
% 0.13/0.27 % CPULimit : 300
% 0.13/0.27 % WCLimit : 300
% 0.13/0.27 % DateTime : Mon Sep 28 21:31:09 UTC 2026
% 0.13/0.27 % CPUTime :
% 0.13/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.33 Running first-order theorem proving
% 0.28/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.55/1.82 % (2673870)Input is clausal, will run a generic CNF schedule.
% 3.55/1.82 % (2673875)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3168949460:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.55/1.82 % (2673877)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4451361:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.55/1.82 % (2673878)lrs+10_1_sil=8000:sp=occurrence:random_seed=1378457629:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.55/1.82 % (2673880)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1872164877:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.55/1.82 % (2673876)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2118177543:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.55/1.82 % (2673881)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3409947579:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.55/1.82 % (2673883)dis-21_1_sil=8000:lcm=predicate:random_seed=3230958525:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.55/1.82 % (2673883)Refutation not found, incomplete strategy
% 3.55/1.82 % (2673883)------------------------------
% 3.55/1.82 % (2673883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.82 % (2673883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.82 % (2673883)CaDiCaL version: 2.1.3
% 3.55/1.82 % (2673883)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.82 % (2673883)Time elapsed: 0.001 s
% 3.55/1.82 % (2673883)Peak memory usage: 88 MB
% 3.55/1.82 % (2673880)Instruction limit reached!
% 3.55/1.82 % (2673880)------------------------------
% 3.55/1.82 % (2673880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.82 % (2673880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.82 % (2673880)CaDiCaL version: 2.1.3
% 3.55/1.82 % (2673880)Termination reason: Instruction limit
% 3.55/1.82 % (2673880)Termination phase: Saturation
% 3.55/1.82 % (2673880)Time elapsed: 0.070 s
% 3.55/1.82 % (2673880)Peak memory usage: 88 MB
% 3.55/1.82 % (2673880)Instructions burned: 114 (million)
% 3.55/1.82 % (2673878)Instruction limit reached!
% 3.55/1.82 % (2673878)------------------------------
% 3.55/1.82 % (2673878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.82 % (2673878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.82 % (2673878)CaDiCaL version: 2.1.3
% 3.55/1.82 % (2673878)Termination reason: Instruction limit
% 3.55/1.82 % (2673878)Termination phase: Saturation
% 3.55/1.82 % (2673878)Time elapsed: 0.073 s
% 3.55/1.82 % (2673878)Peak memory usage: 89 MB
% 3.55/1.82 % (2673878)Instructions burned: 108 (million)
% 3.55/1.82 % (2673881)Instruction limit reached!
% 3.55/1.82 % (2673881)------------------------------
% 3.55/1.82 % (2673881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.82 % (2673881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.82 % (2673881)CaDiCaL version: 2.1.3
% 3.55/1.82 % (2673881)Termination reason: Instruction limit
% 3.55/1.82 % (2673881)Termination phase: Saturation
% 3.55/1.82 % (2673881)Time elapsed: 0.103 s
% 3.55/1.82 % (2673881)Peak memory usage: 89 MB
% 3.55/1.82 % (2673881)Instructions burned: 181 (million)
% 3.55/1.82 % (2673965)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3887814853:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.55/1.82 % (2673964)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2863674627:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.55/1.82 % (2673964)Refutation not found, incomplete strategy
% 3.55/1.82 % (2673964)------------------------------
% 3.55/1.82 % (2673964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.82 % (2673964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.82 % (2673964)CaDiCaL version: 2.1.3
% 3.55/1.82 % (2673964)Termination reason: Refutation not found, incomplete strategy
% 6.29/2.02 % (2673964)Time elapsed: 0.001 s
% 6.29/2.02 % (2673964)Peak memory usage: 87 MB
% 6.29/2.02 % (2673965)Refutation not found, incomplete strategy
% 6.29/2.02 % (2673965)------------------------------
% 6.29/2.02 % (2673965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.29/2.02 % (2673965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/2.02 % (2673965)CaDiCaL version: 2.1.3
% 6.29/2.02 % (2673965)Termination reason: Refutation not found, incomplete strategy
% 6.29/2.02 % (2673965)Time elapsed: 0.001 s
% 6.29/2.02 % (2673965)Peak memory usage: 88 MB
% 6.29/2.02 % (2673965)Instructions burned: 1 (million)
% 6.29/2.02 % (2673972)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2871714592:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.29/2.02 % (2673972)Refutation not found, incomplete strategy
% 6.29/2.02 % (2673972)------------------------------
% 6.29/2.02 % (2673972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.29/2.02 % (2673972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/2.02 % (2673972)CaDiCaL version: 2.1.3
% 6.29/2.02 % (2673972)Termination reason: Refutation not found, incomplete strategy
% 6.29/2.02 % (2673972)Time elapsed: 0.001 s
% 6.29/2.02 % (2673972)Peak memory usage: 88 MB
% 6.29/2.02 % (2673883)------------------------------
% 6.29/2.02 % (2673883)------------------------------
% 6.29/2.02 % (2673875)First to succeed.
% 6.29/2.02 % (2673875)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2673870"
% 6.29/2.02 % (2674023)lrs+10_64_to=lpo:sil=8000:random_seed=3925205980:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.29/2.02 % (2673964)------------------------------
% 6.29/2.02 % (2673964)------------------------------
% 6.29/2.02 % (2673965)------------------------------
% 6.29/2.02 % (2673965)------------------------------
% 6.29/2.02 % (2673972)------------------------------
% 6.29/2.02 % (2673972)------------------------------
% 6.29/2.02 % (2674023)Instruction limit reached!
% 6.29/2.02 % (2674023)------------------------------
% 6.29/2.02 % (2674023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.29/2.02 % (2674023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/2.02 % (2674023)CaDiCaL version: 2.1.3
% 6.29/2.02 % (2674023)Termination reason: Instruction limit
% 6.29/2.02 % (2674023)Termination phase: Saturation
% 6.29/2.02 % (2674023)Time elapsed: 0.085 s
% 6.29/2.02 % (2674023)Peak memory usage: 89 MB
% 6.29/2.02 % (2674023)Instructions burned: 127 (million)
% 6.29/2.02 % (2673875)Refutation found. Thanks to Tanya!
% 6.29/2.02 % SZS status Unsatisfiable for theBenchmark
% 6.29/2.02 % SZS output start Proof for theBenchmark
% See solution above
% 6.29/2.02 % (2673875)------------------------------
% 6.29/2.02 % (2673875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.29/2.02 % (2673875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/2.02 % (2673875)CaDiCaL version: 2.1.3
% 6.29/2.02 % (2673875)Termination reason: Refutation
% 6.29/2.02 % (2673875)Time elapsed: 0.453 s
% 6.29/2.02 % (2673875)Peak memory usage: 129 MB
% 6.29/2.02 % (2673875)Instructions burned: 1029 (million)
% 6.29/2.02 % (2673875)------------------------------
% 6.29/2.02 % (2673875)------------------------------
% 6.29/2.02 % (2673870)Success in time 0.758 s
% 6.29/2.02 % Vampire exiting
%------------------------------------------------------------------------------