%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL044-9 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:37:44 AM UTC 2026
% Result : Unsatisfiable 20.38s 3.65s
% Output : Refutation 20.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 27 unt; 2 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 12 ( 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 : 41 ( 41 !; 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,
! [X2,X0,X1] : apply(apply(apply(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),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(f11,plain,
! [X2,X3,X0,X1] : apply(apply(apply(n,apply(apply(b,X0),X1)),X3),X2) = apply(apply(apply(X0,apply(X1,X2)),X3),X2),
inference(superposition,[],[f2,f1]) ).
fof(f16,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(b,X0)),X2),X1) = apply(apply(X0,apply(X1,X2)),X1),
inference(superposition,[],[f2,f1]) ).
fof(f18,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(X0,X2)),X2),X1) = apply(apply(apply(apply(n,X0),X1),X2),X1),
inference(superposition,[],[f2,f2]) ).
fof(f22,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(X0,X2)),X2),X1) = apply(apply(apply(n,apply(n,X0)),X2),X1),
inference(forward_demodulation,[],[f18,f2]) ).
fof(f26,plain,
! [X0] : apply(apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f30,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n),apply(b,apply(b,X0))),
inference(forward_demodulation,[],[f26,f1]) ).
fof(f54,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X2,X1),X2)),
inference(superposition,[],[f1,f16]) ).
fof(f128,plain,
! [X2,X3,X0,X1] : apply(apply(apply(n,apply(apply(b,apply(b,X0)),X1)),X3),X2) = apply(apply(X0,apply(apply(X1,X2),X3)),X2),
inference(superposition,[],[f11,f1]) ).
fof(f152,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(superposition,[],[f1,f11]) ).
fof(f297,plain,
! [X0,X1] : apply(apply(apply(n,apply(n,apply(b,b))),X0),X1) = apply(apply(X0,X1),apply(X0,X1)),
inference(superposition,[],[f22,f152]) ).
fof(f615,plain,
! [X2,X3,X0,X1] : apply(apply(apply(n,apply(n,apply(apply(b,apply(b,X0)),X1))),X2),X3) = apply(apply(apply(X0,apply(apply(X1,X2),X3)),X2),X3),
inference(superposition,[],[f2,f128]) ).
fof(f786,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(b,apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X0)))),n),apply(b,apply(b,X0))),
inference(superposition,[],[f30,f615]) ).
fof(f850,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f786,f1]) ).
fof(f1087,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),apply(n,apply(b,apply(b,X0)))),
inference(superposition,[],[f850,f297]) ).
fof(f1196,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(superposition,[],[f54,f1087]) ).
fof(f1239,plain,
sF0 = apply(fixed_pt,sF0),
inference(superposition,[],[f1196,f6]) ).
fof(f1329,plain,
sF0 = sF1,
inference(superposition,[],[f8,f1239]) ).
fof(f1334,plain,
$false,
inference(forward_subsumption_resolution,[],[f1329,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:36:49 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.38/3.65 % (776294)Detected a unit-equality problem, will run specialized UEQ schedule.
% 20.38/3.65 % (776386)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1982777920:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 20.38/3.65 % (776383)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=456201425:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 20.38/3.65 % (776382)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1125239405:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 20.38/3.65 % (776385)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1148705679:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 20.38/3.65 % (776381)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2665125301:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 20.38/3.65 % (776388)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=878355571:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 20.38/3.65 % (776387)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3500789248:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 20.38/3.65 % (776386)Instruction limit reached!
% 20.38/3.65 % (776386)------------------------------
% 20.38/3.65 % (776386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.38/3.65 % (776386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.38/3.65 % (776386)CaDiCaL version: 2.1.3
% 20.38/3.65 % (776386)Termination reason: Instruction limit
% 20.38/3.65 % (776386)Termination phase: Saturation
% 20.38/3.65 % (776386)Time elapsed: 0.059 s
% 20.38/3.65 % (776386)Peak memory usage: 90 MB
% 20.38/3.65 % (776386)Instructions burned: 182 (million)
% 20.38/3.65 % (776385)Instruction limit reached!
% 20.38/3.65 % (776385)------------------------------
% 20.38/3.65 % (776385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.38/3.65 % (776385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.38/3.65 % (776385)CaDiCaL version: 2.1.3
% 20.38/3.65 % (776385)Termination reason: Instruction limit
% 20.38/3.65 % (776385)Termination phase: Saturation
% 20.38/3.65 % (776385)Time elapsed: 0.085 s
% 20.38/3.65 % (776385)Peak memory usage: 89 MB
% 20.38/3.65 % (776385)Instructions burned: 137 (million)
% 20.38/3.65 % (776387)Instruction limit reached!
% 20.38/3.65 % (776387)------------------------------
% 20.38/3.65 % (776387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.38/3.65 % (776387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.38/3.65 % (776387)CaDiCaL version: 2.1.3
% 20.38/3.65 % (776387)Termination reason: Instruction limit
% 20.38/3.65 % (776387)Termination phase: Saturation
% 20.38/3.65 % (776387)Time elapsed: 0.164 s
% 20.38/3.65 % (776387)Peak memory usage: 91 MB
% 20.38/3.65 % (776387)Instructions burned: 261 (million)
% 20.38/3.65 % (776434)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1171355206:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 20.38/3.65 % (776444)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3354378422:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 20.38/3.65 % (776446)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2574624329:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 20.38/3.65 % (776446)Refutation not found, incomplete strategy
% 20.38/3.65 % (776446)------------------------------
% 20.38/3.65 % (776446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.38/3.65 % (776446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.38/3.65 % (776446)CaDiCaL version: 2.1.3
% 20.38/3.65 % (776446)Termination reason: Refutation not found, incomplete strategy
% 20.38/3.65 % (776446)Time elapsed: 0.002 s
% 20.38/3.65 % (776446)Peak memory usage: 88 MB
% 20.38/3.65 % (776446)Instructions burned: 1 (million)
% 20.38/3.65 % (776446)------------------------------
% 20.38/3.65 % (776446)------------------------------
% 20.38/3.65 % (776388)Instruction limit reached!
% 20.38/3.65 % (776388)------------------------------
% 20.38/3.65 % (776388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.38/3.65 % (776388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.38/3.65 % (776388)CaDiCaL version: 2.1.3
% 20.38/3.65 % (776388)Termination reason: Instruction limit
% 20.38/3.65 % (776388)Termination phase: Saturation
% 20.38/3.65 % (776388)Time elapsed: 0.778 s
% 20.38/3.65 % (776388)Peak memory usage: 99 MB
% 20.38/3.65 % (776388)Instructions burned: 1187 (million)
% 20.38/3.65 % (776464)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=813313318:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 20.38/3.65 % (776464)Instruction limit reached!
% 20.38/3.65 % (776464)------------------------------
% 20.38/3.65 % (776464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.38/3.65 % (776464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.38/3.65 % (776464)CaDiCaL version: 2.1.3
% 20.38/3.65 % (776464)Termination reason: Instruction limit
% 20.38/3.65 % (776464)Termination phase: Saturation
% 20.38/3.65 % (776464)Time elapsed: 0.138 s
% 20.38/3.65 % (776464)Peak memory usage: 90 MB
% 20.38/3.65 % (776464)Instructions burned: 317 (million)
% 20.38/3.65 % (776466)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2530794779:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 20.38/3.65 % (776471)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=795410691:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2988 on theBenchmark for (2988ds/2836Mi)
% 20.38/3.65 % (776434)Instruction limit reached!
% 20.38/3.65 % (776434)------------------------------
% 20.38/3.65 % (776434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.38/3.65 % (776434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.38/3.65 % (776434)CaDiCaL version: 2.1.3
% 20.38/3.65 % (776434)Termination reason: Instruction limit
% 20.38/3.65 % (776434)Termination phase: Saturation
% 20.38/3.65 % (776434)Time elapsed: 1.916 s
% 20.38/3.65 % (776434)Peak memory usage: 138 MB
% 20.38/3.65 % (776434)Instructions burned: 2052 (million)
% 20.38/3.65 % (776481)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=3815120510:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2977 on theBenchmark for (2977ds/14534Mi)
% 20.38/3.65 % (776466)First to succeed.
% 20.38/3.65 % (776466)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-776294"
% 20.38/3.65 % (776466)Refutation found. Thanks to Tanya!
% 20.38/3.65 % SZS status Unsatisfiable for theBenchmark
% 20.38/3.65 % SZS output start Proof for theBenchmark
% See solution above
% 20.38/3.65 % (776466)------------------------------
% 20.38/3.65 % (776466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.38/3.65 % (776466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.38/3.65 % (776466)CaDiCaL version: 2.1.3
% 20.38/3.65 % (776466)Termination reason: Refutation
% 20.38/3.65 % (776466)Time elapsed: 1.289 s
% 20.38/3.65 % (776466)Peak memory usage: 135 MB
% 20.38/3.65 % (776466)Instructions burned: 1506 (million)
% 20.38/3.65 % (776466)------------------------------
% 20.38/3.65 % (776466)------------------------------
% 20.38/3.65 % (776294)Success in time 2.803 s
% 20.38/3.65 % Vampire exiting
%------------------------------------------------------------------------------