%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL060-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:37:47 AM UTC 2026
% Result : Unsatisfiable 2.63s 1.16s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 61 ( 61 unt; 16 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 15 con; 0-3 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [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,negated_conjecture,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
fof(f3,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) != apply(y,apply(x,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_q_combinator) ).
fof(f4,definition,
! [X0] : sF0(X0) = apply(b,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f5,plain,
! [X0] : apply(b,X0) = sF0(X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
! [X0,X1] : sF1(X0,X1) = apply(sF0(X0),X1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f7,plain,
! [X0,X1] : apply(sF0(X0),X1) = sF1(X0,X1),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = apply(sF1(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f9,plain,
! [X2,X0,X1] : apply(sF1(X0,X1),X2) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = apply(X0,apply(X1,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f11,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = sF3(X0,X1,X2),
inference(definition_folding,[],[f1,f11,f9,f7,f5]) ).
fof(f13,definition,
! [X0] : sF4(X0) = apply(t,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
! [X0] : apply(t,X0) = sF4(X0),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X0,X1] : sF5(X0,X1) = apply(sF4(X0),X1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
! [X0,X1] : apply(sF4(X0),X1) = sF5(X0,X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,plain,
! [X0,X1] : apply(X1,X0) = sF5(X0,X1),
inference(definition_folding,[],[f2,f16,f14]) ).
fof(f18,definition,
sF6 = apply(t,b),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f19,plain,
apply(t,b) = sF6,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF7 = apply(b,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f21,plain,
apply(b,sF6) = sF7,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF8 = apply(sF7,b),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f23,plain,
apply(sF7,b) = sF8,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF9 = apply(b,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f25,plain,
apply(b,sF8) = sF9,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF10 = apply(sF9,t),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f27,plain,
apply(sF9,t) = sF10,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF11 = apply(sF10,x),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f29,plain,
apply(sF10,x) = sF11,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF12 = apply(sF11,y),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f31,plain,
apply(sF11,y) = sF12,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF13 = apply(sF12,z),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f33,plain,
apply(sF12,z) = sF13,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF14 = apply(x,z),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f35,plain,
apply(x,z) = sF14,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF15 = apply(y,sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f37,plain,
apply(y,sF14) = sF15,
inference(reorient_equations,[],[f36]) ).
fof(f38,plain,
sF13 != sF15,
inference(definition_folding,[],[f3,f37,f35,f33,f31,f29,f27,f25,f23,f21,f19]) ).
fof(f39,plain,
! [X0,X1] : apply(X1,X0) = apply(sF4(X0),X1),
inference(forward_demodulation,[],[f17,f16]) ).
fof(f40,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = sF2(X0,X1,X2),
inference(forward_demodulation,[],[f12,f11]) ).
fof(f41,plain,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
inference(forward_demodulation,[],[f39,f14]) ).
fof(f42,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(sF1(X0,X1),X2),
inference(forward_demodulation,[],[f40,f9]) ).
fof(f43,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(sF0(X0),X1),X2),
inference(forward_demodulation,[],[f42,f7]) ).
fof(f44,plain,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(forward_demodulation,[],[f43,f5]) ).
fof(f45,plain,
! [X0] : apply(X0,b) = apply(sF6,X0),
inference(superposition,[],[f41,f19]) ).
fof(f68,plain,
! [X0,X1] : apply(sF8,apply(X0,X1)) = apply(apply(sF9,X0),X1),
inference(superposition,[],[f44,f25]) ).
fof(f69,plain,
! [X0,X1] : apply(sF6,apply(X0,X1)) = apply(apply(sF7,X0),X1),
inference(superposition,[],[f44,f21]) ).
fof(f70,plain,
! [X2,X0,X1] : apply(X1,apply(X0,X2)) = apply(apply(apply(t,X0),apply(b,X1)),X2),
inference(superposition,[],[f44,f41]) ).
fof(f71,plain,
! [X0,X1] : apply(X0,apply(b,X1)) = apply(apply(sF6,apply(b,X0)),X1),
inference(superposition,[],[f44,f45]) ).
fof(f76,plain,
! [X0] : apply(sF8,apply(t,X0)) = apply(sF10,X0),
inference(superposition,[],[f68,f27]) ).
fof(f82,plain,
sF11 = apply(sF8,apply(t,x)),
inference(superposition,[],[f76,f29]) ).
fof(f88,plain,
! [X0] : apply(sF6,apply(b,X0)) = apply(sF8,X0),
inference(superposition,[],[f69,f23]) ).
fof(f95,plain,
sF11 = apply(sF6,apply(b,apply(t,x))),
inference(superposition,[],[f88,f82]) ).
fof(f181,plain,
! [X0] : apply(apply(t,x),apply(b,X0)) = apply(sF11,X0),
inference(superposition,[],[f71,f95]) ).
fof(f201,plain,
! [X0,X1] : apply(X0,apply(x,X1)) = apply(apply(sF11,X0),X1),
inference(superposition,[],[f70,f181]) ).
fof(f335,plain,
! [X0] : apply(y,apply(x,X0)) = apply(sF12,X0),
inference(superposition,[],[f201,f31]) ).
fof(f353,plain,
apply(y,apply(x,z)) = sF13,
inference(superposition,[],[f33,f335]) ).
fof(f360,plain,
sF13 = apply(y,sF14),
inference(forward_demodulation,[],[f353,f35]) ).
fof(f362,plain,
sF13 = sF15,
inference(forward_demodulation,[],[f360,f37]) ).
fof(f364,plain,
sF13 != sF13,
inference(superposition,[],[f38,f362]) ).
fof(f365,plain,
$false,
inference(trivial_inequality_removal,[],[f364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL060-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n026.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 21:35:08 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running first-order theorem proving
% 0.11/0.24 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
% 2.63/1.16 % (98782)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.63/1.16 % (98927)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2106969244:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.63/1.16 % (98927)First to succeed.
% 2.63/1.16 % (98927)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-98782"
% 2.63/1.16 % (98922)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1379993425:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.63/1.16 % (98930)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2079293387:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.63/1.16 % (98919)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=2401205565:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.63/1.16 % (98921)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=526236641:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.63/1.16 % (98930)Also succeeded, but the first one will report.
% 2.63/1.16 % (98929)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2843690496:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.63/1.16 % (98924)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=718878254:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.63/1.16 % (98924)Also succeeded, but the first one will report.
% 2.63/1.16 % (98929)Also succeeded, but the first one will report.
% 2.63/1.16 % (98927)Refutation found. Thanks to Tanya!
% 2.63/1.16 % SZS status Unsatisfiable for theBenchmark
% 2.63/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.16 % (98927)------------------------------
% 2.63/1.16 % (98927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.16 % (98927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.16 % (98927)CaDiCaL version: 2.1.3
% 2.63/1.16 % (98927)Termination reason: Refutation
% 2.63/1.16 % (98927)Time elapsed: 0.008 s
% 2.63/1.16 % (98927)Peak memory usage: 88 MB
% 2.63/1.16 % (98927)Instructions burned: 22 (million)
% 2.63/1.16 % (98927)------------------------------
% 2.63/1.16 % (98927)------------------------------
% 2.63/1.16 % (98782)Success in time 0.29 s
% 2.63/1.16 % Vampire exiting
%------------------------------------------------------------------------------