%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL003-1 : 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 : n005.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 09:37:34 AM UTC 2026
% Result : Unsatisfiable 14.11s 3.32s
% Output : Refutation 14.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 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,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f4,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,[],[f3,f1]) ).
fof(f10,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f12,plain,
! [X0,X1] : apply(X0,apply(X1,X1)) = apply(apply(w,apply(b,X0)),X1),
inference(superposition,[],[f1,f2]) ).
fof(f14,plain,
! [X2,X0,X1] : apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1)))))) != apply(f(apply(apply(b,X2),apply(apply(b,X0),X1))),apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1))))))),
inference(superposition,[],[f4,f1]) ).
fof(f20,plain,
! [X2,X3,X0,X1] : apply(X0,apply(X1,apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3))))))) != apply(f(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3))),apply(X0,apply(X1,apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3)))))))),
inference(superposition,[],[f14,f1]) ).
fof(f83,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,f12]) ).
fof(f120,plain,
! [X0] : apply(apply(w,w),apply(w,apply(b,apply(b,X0)))) = apply(X0,apply(apply(w,w),apply(w,apply(b,apply(b,X0))))),
inference(superposition,[],[f83,f10]) ).
fof(f220,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,f(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b))))))) != apply(apply(w,w),apply(w,apply(b,apply(b,f(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b))))))),
inference(superposition,[],[f20,f120]) ).
fof(f221,plain,
$false,
inference(trivial_inequality_removal,[],[f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 % Computer : n005.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Mon Sep 28 21:28:46 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.34 Running first-order theorem proving
% 0.28/0.34 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
% 14.11/3.32 % (1201231)Detected a unit-equality problem, will run specialized UEQ schedule.
% 14.11/3.32 % (1201249)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1922995618:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 14.11/3.32 % (1201247)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2312675645:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 14.11/3.32 % (1201246)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=4095175508:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 14.11/3.32 % (1201245)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=2919051106:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 14.11/3.32 % (1201250)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1780464619:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 14.11/3.32 % (1201251)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=35836358:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 14.11/3.32 % (1201248)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1404296490:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 14.11/3.32 % (1201249)Instruction limit reached!
% 14.11/3.32 % (1201249)------------------------------
% 14.11/3.32 % (1201249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.11/3.32 % (1201249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.11/3.32 % (1201249)CaDiCaL version: 2.1.3
% 14.11/3.32 % (1201249)Termination reason: Instruction limit
% 14.11/3.32 % (1201249)Termination phase: Saturation
% 14.11/3.32 % (1201249)Time elapsed: 0.091 s
% 14.11/3.32 % (1201249)Peak memory usage: 89 MB
% 14.11/3.32 % (1201249)Instructions burned: 184 (million)
% 14.11/3.32 % (1201248)Instruction limit reached!
% 14.11/3.32 % (1201248)------------------------------
% 14.11/3.32 % (1201248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.11/3.32 % (1201248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.11/3.32 % (1201248)CaDiCaL version: 2.1.3
% 14.11/3.32 % (1201248)Termination reason: Instruction limit
% 14.11/3.32 % (1201248)Termination phase: Saturation
% 14.11/3.32 % (1201248)Time elapsed: 0.137 s
% 14.11/3.32 % (1201248)Peak memory usage: 89 MB
% 14.11/3.32 % (1201248)Instructions burned: 136 (million)
% 14.11/3.32 % (1201259)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3145650704:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 14.11/3.32 % (1201250)Instruction limit reached!
% 14.11/3.32 % (1201250)------------------------------
% 14.11/3.32 % (1201250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.11/3.32 % (1201250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.11/3.32 % (1201250)CaDiCaL version: 2.1.3
% 14.11/3.32 % (1201250)Termination reason: Instruction limit
% 14.11/3.32 % (1201250)Termination phase: Saturation
% 14.11/3.32 % (1201250)Time elapsed: 0.263 s
% 14.11/3.32 % (1201250)Peak memory usage: 90 MB
% 14.11/3.32 % (1201250)Instructions burned: 257 (million)
% 14.11/3.32 % (1201260)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1597781559:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 14.11/3.32 % (1201262)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=486604361:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 14.11/3.32 % (1201262)Instruction limit reached!
% 14.11/3.32 % (1201262)------------------------------
% 14.11/3.32 % (1201262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.11/3.32 % (1201262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.11/3.32 % (1201262)CaDiCaL version: 2.1.3
% 14.11/3.32 % (1201262)Termination reason: Instruction limit
% 14.11/3.32 % (1201262)Termination phase: Saturation
% 14.11/3.32 % (1201262)Time elapsed: 0.208 s
% 14.11/3.32 % (1201262)Peak memory usage: 89 MB
% 14.11/3.32 % (1201262)Instructions burned: 216 (million)
% 14.11/3.32 % (1201265)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=1158967101:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 14.11/3.32 % (1201251)Instruction limit reached!
% 14.11/3.32 % (1201251)------------------------------
% 14.11/3.32 % (1201251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.11/3.32 % (1201251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.11/3.32 % (1201251)CaDiCaL version: 2.1.3
% 14.11/3.32 % (1201251)Termination reason: Instruction limit
% 14.11/3.32 % (1201251)Termination phase: Saturation
% 14.11/3.32 % (1201251)Time elapsed: 1.043 s
% 14.11/3.32 % (1201251)Peak memory usage: 99 MB
% 14.11/3.32 % (1201251)Instructions burned: 1187 (million)
% 14.11/3.32 % (1201245)First to succeed.
% 14.11/3.32 % (1201245)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1201231"
% 14.11/3.32 % (1201246)Also succeeded, but the first one will report.
% 14.11/3.32 % (1201265)Instruction limit reached!
% 14.11/3.32 % (1201265)------------------------------
% 14.11/3.32 % (1201265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.11/3.32 % (1201265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.11/3.32 % (1201265)CaDiCaL version: 2.1.3
% 14.11/3.32 % (1201265)Termination reason: Instruction limit
% 14.11/3.32 % (1201265)Termination phase: Saturation
% 14.11/3.32 % (1201265)Time elapsed: 0.165 s
% 14.11/3.32 % (1201265)Peak memory usage: 93 MB
% 14.11/3.32 % (1201265)Instructions burned: 318 (million)
% 14.11/3.32 % (1201267)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=96944388:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 14.11/3.32 % (1201270)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=491865809:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2985 on theBenchmark for (2985ds/2836Mi)
% 14.11/3.32 % (1201245)Refutation found. Thanks to Tanya!
% 14.11/3.32 % SZS status Unsatisfiable for theBenchmark
% 14.11/3.32 % SZS output start Proof for theBenchmark
% See solution above
% 14.11/3.33 % (1201245)------------------------------
% 14.11/3.33 % (1201245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.11/3.33 % (1201245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.11/3.33 % (1201245)CaDiCaL version: 2.1.3
% 14.11/3.33 % (1201245)Termination reason: Refutation
% 14.11/3.33 % (1201245)Time elapsed: 1.107 s
% 14.11/3.33 % (1201245)Peak memory usage: 129 MB
% 14.11/3.33 % (1201245)Instructions burned: 1040 (million)
% 14.11/3.33 % (1201245)------------------------------
% 14.11/3.33 % (1201245)------------------------------
% 14.11/3.33 % (1201231)Success in time 1.83 s
% 14.11/3.33 % Vampire exiting
%------------------------------------------------------------------------------