%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL049-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:37:45 AM UTC 2026
% Result : Unsatisfiable 6.67s 1.54s
% Output : Refutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% 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 : 5 ( 3 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 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(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
fof(f3,axiom,
! [X0] : apply(m,X0) = apply(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_definition) ).
fof(f4,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f65,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f69,plain,
! [X0,X1] : apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))),
inference(superposition,[],[f4,f1]) ).
fof(f86,plain,
! [X2,X0,X1] : apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2))))) != apply(f(apply(apply(b,apply(apply(b,X0),X1)),X2)),apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2)))))),
inference(superposition,[],[f69,f1]) ).
fof(f193,plain,
! [X0] : apply(m,apply(w,apply(b,X0))) = apply(X0,apply(m,apply(w,apply(b,X0)))),
inference(superposition,[],[f65,f3]) ).
fof(f14091,plain,
apply(m,apply(w,apply(b,f(apply(apply(b,apply(apply(b,m),w)),b))))) != apply(m,apply(w,apply(b,f(apply(apply(b,apply(apply(b,m),w)),b))))),
inference(superposition,[],[f86,f193]) ).
fof(f14092,plain,
$false,
inference(trivial_inequality_removal,[],[f14091]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL049-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.15 % Computer : n012.cluster.edu
% 0.07/0.15 % Model : x86_64 x86_64
% 0.07/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.15 % Memory : 8046.5625MB
% 0.07/0.15 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Mon Sep 28 21:30:49 UTC 2026
% 0.07/0.16 % CPUTime :
% 0.07/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 Running first-order theorem proving
% 0.07/0.19 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
% 6.67/1.54 % (3802355)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.67/1.54 % (3802366)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4238478299:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 6.67/1.54 % (3802365)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=393549513:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 6.67/1.54 % (3802361)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=2272685375:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 6.67/1.54 % (3802360)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=1511573543:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 6.67/1.54 % (3802363)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4002650690:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 6.67/1.54 % (3802362)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1238403128:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 6.67/1.54 % (3802364)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1596190364:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 6.67/1.54 % (3802363)Instruction limit reached!
% 6.67/1.54 % (3802363)------------------------------
% 6.67/1.54 % (3802363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.54 % (3802363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.54 % (3802363)CaDiCaL version: 2.1.3
% 6.67/1.54 % (3802363)Termination reason: Instruction limit
% 6.67/1.54 % (3802363)Termination phase: Saturation
% 6.67/1.54 % (3802363)Time elapsed: 0.070 s
% 6.67/1.54 % (3802363)Peak memory usage: 89 MB
% 6.67/1.54 % (3802363)Instructions burned: 137 (million)
% 6.67/1.54 % (3802364)Instruction limit reached!
% 6.67/1.54 % (3802364)------------------------------
% 6.67/1.54 % (3802364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.54 % (3802364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.54 % (3802364)CaDiCaL version: 2.1.3
% 6.67/1.54 % (3802364)Termination reason: Instruction limit
% 6.67/1.54 % (3802364)Termination phase: Saturation
% 6.67/1.54 % (3802364)Time elapsed: 0.088 s
% 6.67/1.54 % (3802364)Peak memory usage: 88 MB
% 6.67/1.54 % (3802364)Instructions burned: 181 (million)
% 6.67/1.54 % (3802365)Instruction limit reached!
% 6.67/1.54 % (3802365)------------------------------
% 6.67/1.54 % (3802365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.54 % (3802365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.54 % (3802365)CaDiCaL version: 2.1.3
% 6.67/1.54 % (3802365)Termination reason: Instruction limit
% 6.67/1.54 % (3802365)Termination phase: Saturation
% 6.67/1.54 % (3802365)Time elapsed: 0.148 s
% 6.67/1.54 % (3802365)Peak memory usage: 90 MB
% 6.67/1.54 % (3802365)Instructions burned: 258 (million)
% 6.67/1.54 % (3802374)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2834372179:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 6.67/1.54 % (3802375)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4194666700:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 6.67/1.54 % (3802376)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=205959244:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.67/1.54 % (3802366)First to succeed.
% 6.67/1.54 % (3802366)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3802355"
% 6.67/1.54 % (3802376)Instruction limit reached!
% 6.67/1.54 % (3802376)------------------------------
% 6.67/1.54 % (3802376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.54 % (3802376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.54 % (3802376)CaDiCaL version: 2.1.3
% 6.67/1.54 % (3802376)Termination reason: Instruction limit
% 6.67/1.54 % (3802376)Termination phase: Saturation
% 6.67/1.54 % (3802376)Time elapsed: 0.116 s
% 6.67/1.54 % (3802376)Peak memory usage: 89 MB
% 6.67/1.54 % (3802376)Instructions burned: 215 (million)
% 6.67/1.54 % (3802362)Also succeeded, but the first one will report.
% 6.67/1.54 % (3802360)Also succeeded, but the first one will report.
% 6.67/1.54 % (3802361)Also succeeded, but the first one will report.
% 6.67/1.54 % (3802366)Refutation found. Thanks to Tanya!
% 6.67/1.54 % SZS status Unsatisfiable for theBenchmark
% 6.67/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 6.67/1.54 % (3802366)------------------------------
% 6.67/1.54 % (3802366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.54 % (3802366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.54 % (3802366)CaDiCaL version: 2.1.3
% 6.67/1.54 % (3802366)Termination reason: Refutation
% 6.67/1.54 % (3802366)Time elapsed: 0.493 s
% 6.67/1.54 % (3802366)Peak memory usage: 100 MB
% 6.67/1.54 % (3802366)Instructions burned: 1176 (million)
% 6.67/1.54 % (3802366)------------------------------
% 6.67/1.54 % (3802366)------------------------------
% 6.67/1.54 % (3802355)Success in time 0.876 s
% 6.67/1.54 % Vampire exiting
%------------------------------------------------------------------------------