%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:37:32 AM UTC 2026
% Result : Unsatisfiable 5.38s 1.54s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f3,negated_conjecture,
! [X0] : X0 != apply(combinator,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f4,plain,
! [X0] : apply(combinator,X0) != X0,
inference(reorient_equations,[],[f3]) ).
fof(f6,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(apply(s,apply(k,X0)),X1),X2),
inference(superposition,[],[f1,f2]) ).
fof(f12,plain,
! [X0,X1] : apply(apply(apply(s,k),X1),X0) = X0,
inference(superposition,[],[f1,f2]) ).
fof(f29,plain,
! [X2,X0,X1] : apply(apply(apply(s,apply(s,apply(k,X0))),X1),X2) = apply(X0,apply(X2,apply(X1,X2))),
inference(superposition,[],[f6,f1]) ).
fof(f2214,plain,
! [X0,X1] : apply(X1,apply(X0,X1)) != apply(apply(apply(s,apply(s,apply(k,combinator))),X0),X1),
inference(superposition,[],[f4,f29]) ).
fof(f2302,plain,
! [X0,X1] : apply(X0,X0) != apply(apply(apply(s,apply(s,apply(k,combinator))),apply(apply(s,k),X1)),X0),
inference(superposition,[],[f2214,f12]) ).
fof(f2494,plain,
$false,
inference(equality_resolution,[],[f2302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n006.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 21:28:10 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 5.38/1.54 % (220925)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.38/1.54 % (220943)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=3552679423:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 5.38/1.54 % (220944)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=532662125:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 5.38/1.54 % (220950)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4281191343:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 5.38/1.54 % (220945)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=620712273:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 5.38/1.54 % (220949)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1014943886:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 5.38/1.54 % (220952)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1961362034:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 5.38/1.54 % (220951)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1428354434:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 5.38/1.54 % (220949)Instruction limit reached!
% 5.38/1.54 % (220949)------------------------------
% 5.38/1.54 % (220949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.54 % (220949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.54 % (220949)CaDiCaL version: 2.1.3
% 5.38/1.54 % (220949)Termination reason: Instruction limit
% 5.38/1.54 % (220949)Termination phase: Saturation
% 5.38/1.54 % (220949)Time elapsed: 0.134 s
% 5.38/1.54 % (220949)Peak memory usage: 89 MB
% 5.38/1.54 % (220949)Instructions burned: 136 (million)
% 5.38/1.54 % (220950)Instruction limit reached!
% 5.38/1.54 % (220950)------------------------------
% 5.38/1.54 % (220950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.54 % (220950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.54 % (220950)CaDiCaL version: 2.1.3
% 5.38/1.54 % (220950)Termination reason: Instruction limit
% 5.38/1.54 % (220950)Termination phase: Saturation
% 5.38/1.54 % (220950)Time elapsed: 0.166 s
% 5.38/1.54 % (220950)Peak memory usage: 88 MB
% 5.38/1.54 % (220950)Instructions burned: 181 (million)
% 5.38/1.54 % (220952)First to succeed.
% 5.38/1.54 % (220952)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-220925"
% 5.38/1.54 % (220951)Instruction limit reached!
% 5.38/1.54 % (220951)------------------------------
% 5.38/1.54 % (220951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.54 % (220951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.54 % (220951)CaDiCaL version: 2.1.3
% 5.38/1.54 % (220951)Termination reason: Instruction limit
% 5.38/1.54 % (220951)Termination phase: Saturation
% 5.38/1.54 % (220951)Time elapsed: 0.234 s
% 5.38/1.54 % (220951)Peak memory usage: 90 MB
% 5.38/1.54 % (220951)Instructions burned: 258 (million)
% 5.38/1.54 % (220961)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3044361570:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 5.38/1.54 % (220962)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1478416484:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 5.38/1.54 % (220943)Also succeeded, but the first one will report.
% 5.38/1.54 % (220963)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3824151599:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 5.38/1.54 % (220952)Refutation found. Thanks to Tanya!
% 5.38/1.54 % SZS status Unsatisfiable for theBenchmark
% 5.38/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.38/1.54 % (220952)------------------------------
% 5.38/1.54 % (220952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.54 % (220952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.54 % (220952)CaDiCaL version: 2.1.3
% 5.38/1.54 % (220952)Termination reason: Refutation
% 5.38/1.54 % (220952)Time elapsed: 0.174 s
% 5.38/1.54 % (220952)Peak memory usage: 90 MB
% 5.38/1.54 % (220952)Instructions burned: 190 (million)
% 5.38/1.54 % (220952)------------------------------
% 5.38/1.54 % (220952)------------------------------
% 5.38/1.54 % (220925)Success in time 0.663 s
% 5.38/1.54 % Vampire exiting
%------------------------------------------------------------------------------