%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP001-4 : 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 : n019.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 10:12:03 AM UTC 2026
% Result : Unsatisfiable 0.18s 1.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 40 unt; 6 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f2,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f3,axiom,
! [X0] : multiply(X0,X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',squareness) ).
fof(f4,plain,
! [X0] : identity = multiply(X0,X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f6,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
fof(f7,plain,
c != multiply(b,a),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = multiply(multiply(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = multiply(X0,multiply(X1,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
! [X2,X0,X1] : sF0(X0,X1,X2) = sF1(X0,X1,X2),
inference(definition_folding,[],[f1,f11,f9]) ).
fof(f13,definition,
! [X0] : sF2(X0) = multiply(identity,X0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f14,plain,
! [X0] : multiply(identity,X0) = sF2(X0),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X0] : sF2(X0) = X0,
inference(definition_folding,[],[f2,f14]) ).
fof(f16,definition,
! [X0] : sF3(X0) = multiply(X0,X0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f17,plain,
! [X0] : multiply(X0,X0) = sF3(X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0] : identity = sF3(X0),
inference(definition_folding,[],[f4,f17]) ).
fof(f19,definition,
sF4 = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f20,plain,
multiply(a,b) = sF4,
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
c = sF4,
inference(definition_folding,[],[f5,f20]) ).
fof(f22,definition,
sF5 = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f23,plain,
multiply(b,a) = sF5,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
c != sF5,
inference(definition_folding,[],[f7,f23]) ).
fof(f25,plain,
! [X0] : identity = multiply(X0,X0),
inference(forward_demodulation,[],[f18,f17]) ).
fof(f26,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f15,f14]) ).
fof(f27,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = sF0(X0,X1,X2),
inference(forward_demodulation,[],[f12,f11]) ).
fof(f28,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[],[f27,f9]) ).
fof(f29,plain,
! [X0,X1] : multiply(X0,multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f28,f25]) ).
fof(f33,plain,
! [X0] : multiply(b,multiply(a,X0)) = multiply(sF5,X0),
inference(superposition,[],[f28,f23]) ).
fof(f38,plain,
! [X0,X1] : multiply(X0,multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f29,f26]) ).
fof(f40,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f38,f25]) ).
fof(f64,plain,
identity = multiply(b,multiply(a,sF5)),
inference(superposition,[],[f33,f25]) ).
fof(f79,plain,
multiply(a,sF5) = multiply(b,identity),
inference(superposition,[],[f38,f64]) ).
fof(f82,plain,
b = multiply(a,sF5),
inference(forward_demodulation,[],[f79,f40]) ).
fof(f86,plain,
multiply(a,b) = sF5,
inference(superposition,[],[f38,f82]) ).
fof(f89,plain,
sF4 = sF5,
inference(forward_demodulation,[],[f86,f20]) ).
fof(f90,plain,
c = sF5,
inference(forward_demodulation,[],[f89,f21]) ).
fof(f95,plain,
c != c,
inference(superposition,[],[f24,f90]) ).
fof(f96,plain,
$false,
inference(trivial_inequality_removal,[],[f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:12:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.56/1.40 % (2821888)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.56/1.40 % (2821895)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2779628719:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.56/1.40 % (2821893)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=3688013470:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.56/1.40 % (2821897)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1671503530:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.56/1.40 % (2821896)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4264742763:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.56/1.40 % (2821894)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=3516182755:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.18/1.40 % (2821899)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4113449248:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.18/1.40 % (2821898)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=652976638:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.18/1.40 % (2821897)First to succeed.
% 0.18/1.40 % (2821899)Also succeeded, but the first one will report.
% 0.18/1.40 % (2821896)Also succeeded, but the first one will report.
% 0.18/1.40 % (2821897)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2821888"
% 0.18/1.40 % (2821898)Also succeeded, but the first one will report.
% 0.18/1.40 % (2821897)Refutation found. Thanks to Tanya!
% 0.18/1.40 % SZS status Unsatisfiable for theBenchmark
% 0.18/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.40 % (2821897)------------------------------
% 0.18/1.40 % (2821897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.40 % (2821897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.40 % (2821897)CaDiCaL version: 2.1.3
% 0.18/1.40 % (2821897)Termination reason: Refutation
% 0.18/1.40 % (2821897)Time elapsed: 0.004 s
% 0.18/1.40 % (2821897)Peak memory usage: 88 MB
% 0.18/1.40 % (2821897)Instructions burned: 4 (million)
% 0.18/1.40 % (2821897)------------------------------
% 0.18/1.40 % (2821897)------------------------------
% 0.18/1.40 % (2821888)Success in time 0.436 s
% 0.18/1.40 % Vampire exiting
%------------------------------------------------------------------------------