%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP205-1 : TPTP v9.3.1. Released v2.3.0.
% 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 10:13:19 AM UTC 2026
% Result : Unsatisfiable 5.94s 1.91s
% Output : Refutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 72 unt; 6 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,negated_conjecture,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f3,negated_conjecture,
! [X0,X1] : multiply(X0,left_division(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_left_division) ).
fof(f4,negated_conjecture,
! [X0,X1] : left_division(X0,multiply(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_division_multiply) ).
fof(f5,negated_conjecture,
! [X0,X1] : multiply(right_division(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_right_division) ).
fof(f6,negated_conjecture,
! [X0,X1] : right_division(multiply(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_division_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,right_inverse(X0)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f8,plain,
! [X0] : identity = multiply(X0,right_inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : multiply(left_inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f10,plain,
! [X0] : identity = multiply(left_inverse(X0),X0),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,X1),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang3) ).
fof(f12,negated_conjecture,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang4) ).
fof(f13,definition,
sF0 = multiply(y,z),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f14,plain,
multiply(y,z) = sF0,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF1 = multiply(sF0,x),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f16,plain,
multiply(sF0,x) = sF1,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF2 = multiply(x,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f18,plain,
multiply(x,sF1) = sF2,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF3 = multiply(x,y),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f20,plain,
multiply(x,y) = sF3,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF4 = multiply(z,x),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f22,plain,
multiply(z,x) = sF4,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF5 = multiply(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f24,plain,
multiply(sF3,sF4) = sF5,
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
sF2 != sF5,
inference(definition_folding,[],[f12,f24,f22,f20,f18,f16,f14]) ).
fof(f32,plain,
! [X2,X0,X1] : multiply(X1,multiply(left_division(X1,X0),multiply(X1,X2))) = multiply(multiply(X0,X1),X2),
inference(superposition,[],[f11,f3]) ).
fof(f48,plain,
! [X0] : right_inverse(X0) = left_division(X0,identity),
inference(superposition,[],[f4,f8]) ).
fof(f60,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,multiply(X0,identity))),
inference(superposition,[],[f11,f2]) ).
fof(f62,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f60,f2]) ).
fof(f70,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(X0,X2))) = multiply(multiply(X0,multiply(X1,X0)),X2),
inference(backward_demodulation,[],[f11,f62]) ).
fof(f76,plain,
! [X0,X1] : multiply(X0,multiply(left_inverse(X0),multiply(X0,X1))) = multiply(multiply(X0,identity),X1),
inference(superposition,[],[f70,f10]) ).
fof(f81,plain,
! [X0] : multiply(x,multiply(sF0,multiply(x,X0))) = multiply(multiply(x,sF1),X0),
inference(superposition,[],[f70,f16]) ).
fof(f92,plain,
! [X0] : multiply(x,multiply(sF0,multiply(x,X0))) = multiply(sF2,X0),
inference(forward_demodulation,[],[f81,f18]) ).
fof(f93,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(left_inverse(X0),multiply(X0,X1))),
inference(forward_demodulation,[],[f76,f2]) ).
fof(f106,plain,
! [X0] : multiply(sF0,multiply(x,X0)) = left_division(x,multiply(sF2,X0)),
inference(superposition,[],[f4,f92]) ).
fof(f111,plain,
! [X0] : right_division(identity,right_inverse(X0)) = X0,
inference(superposition,[],[f6,f8]) ).
fof(f114,plain,
! [X0] : left_inverse(X0) = right_division(identity,X0),
inference(superposition,[],[f6,f10]) ).
fof(f122,plain,
! [X0] : left_inverse(right_inverse(X0)) = X0,
inference(forward_demodulation,[],[f111,f114]) ).
fof(f137,plain,
! [X0] : identity = multiply(X0,multiply(left_inverse(X0),identity)),
inference(superposition,[],[f93,f8]) ).
fof(f152,plain,
! [X0,X1] : left_division(X0,multiply(X0,X1)) = multiply(left_inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f93]) ).
fof(f159,plain,
! [X0,X1] : multiply(left_inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f152,f4]) ).
fof(f165,plain,
! [X0] : identity = multiply(X0,left_inverse(X0)),
inference(forward_demodulation,[],[f137,f2]) ).
fof(f179,plain,
! [X0] : left_inverse(X0) = left_division(X0,identity),
inference(superposition,[],[f4,f165]) ).
fof(f184,plain,
! [X0] : right_inverse(X0) = left_inverse(X0),
inference(forward_demodulation,[],[f179,f48]) ).
fof(f191,plain,
! [X0,X1] : multiply(right_inverse(X0),multiply(X0,X1)) = X1,
inference(backward_demodulation,[],[f159,f184]) ).
fof(f196,plain,
! [X0] : right_inverse(right_inverse(X0)) = X0,
inference(backward_demodulation,[],[f122,f184]) ).
fof(f202,plain,
! [X0,X1] : left_division(X1,X0) = multiply(right_inverse(X1),X0),
inference(superposition,[],[f191,f3]) ).
fof(f216,plain,
! [X0,X1] : right_inverse(X1) = right_division(X0,multiply(X1,X0)),
inference(superposition,[],[f6,f191]) ).
fof(f249,plain,
! [X0,X1] : right_inverse(X0) = right_division(left_division(X0,X1),X1),
inference(superposition,[],[f6,f202]) ).
fof(f299,plain,
! [X0] : left_division(x,X0) = multiply(sF0,multiply(x,left_division(sF2,X0))),
inference(superposition,[],[f106,f3]) ).
fof(f382,plain,
! [X0,X1] : multiply(multiply(X1,X0),right_inverse(X0)) = multiply(X0,multiply(left_division(X0,X1),identity)),
inference(superposition,[],[f32,f8]) ).
fof(f418,plain,
! [X0,X1] : multiply(X0,left_division(X0,X1)) = multiply(multiply(X1,X0),right_inverse(X0)),
inference(forward_demodulation,[],[f382,f2]) ).
fof(f431,plain,
! [X0,X1] : multiply(multiply(X1,X0),right_inverse(X0)) = X1,
inference(forward_demodulation,[],[f418,f3]) ).
fof(f441,plain,
! [X0,X1] : right_division(X0,X1) = multiply(X0,right_inverse(X1)),
inference(superposition,[],[f431,f5]) ).
fof(f457,plain,
! [X0,X1] : right_inverse(multiply(X0,X1)) = right_division(right_inverse(X1),X0),
inference(superposition,[],[f216,f431]) ).
fof(f460,plain,
! [X0,X1] : right_inverse(X1) = left_division(multiply(X0,X1),X0),
inference(superposition,[],[f4,f431]) ).
fof(f549,plain,
! [X0,X1] : right_division(right_inverse(X0),X1) = left_division(X0,right_inverse(X1)),
inference(superposition,[],[f202,f441]) ).
fof(f557,plain,
! [X0,X1] : right_inverse(multiply(X0,X1)) = left_division(X1,right_inverse(X0)),
inference(backward_demodulation,[],[f457,f549]) ).
fof(f587,plain,
right_inverse(z) = left_division(sF0,y),
inference(superposition,[],[f460,f14]) ).
fof(f644,plain,
right_inverse(sF4) = left_division(x,right_inverse(z)),
inference(superposition,[],[f557,f22]) ).
fof(f646,plain,
left_division(sF4,right_inverse(sF3)) = right_inverse(sF5),
inference(superposition,[],[f557,f24]) ).
fof(f1312,plain,
! [X0] : multiply(x,left_division(sF2,X0)) = left_division(sF0,left_division(x,X0)),
inference(superposition,[],[f4,f299]) ).
fof(f1339,plain,
! [X0] : left_division(sF0,X0) = multiply(x,left_division(sF2,multiply(x,X0))),
inference(superposition,[],[f1312,f4]) ).
fof(f1372,plain,
! [X0] : left_division(x,left_division(sF0,X0)) = left_division(sF2,multiply(x,X0)),
inference(superposition,[],[f4,f1339]) ).
fof(f1992,plain,
left_division(sF2,sF3) = left_division(x,left_division(sF0,y)),
inference(superposition,[],[f1372,f20]) ).
fof(f2015,plain,
left_division(x,right_inverse(z)) = left_division(sF2,sF3),
inference(forward_demodulation,[],[f1992,f587]) ).
fof(f2023,plain,
right_inverse(sF4) = left_division(sF2,sF3),
inference(forward_demodulation,[],[f2015,f644]) ).
fof(f2033,plain,
right_inverse(sF2) = right_division(right_inverse(sF4),sF3),
inference(superposition,[],[f249,f2023]) ).
fof(f2036,plain,
right_inverse(sF2) = left_division(sF4,right_inverse(sF3)),
inference(forward_demodulation,[],[f2033,f549]) ).
fof(f2042,plain,
right_inverse(sF2) = right_inverse(sF5),
inference(backward_demodulation,[],[f646,f2036]) ).
fof(f2050,plain,
sF5 = right_inverse(right_inverse(sF2)),
inference(superposition,[],[f196,f2042]) ).
fof(f2053,plain,
sF2 = sF5,
inference(forward_demodulation,[],[f2050,f196]) ).
fof(f2060,plain,
$false,
inference(forward_subsumption_resolution,[],[f2053,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP205-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:37:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 3.90/1.72 % (2736792)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.90/1.72 % (2736826)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=680583157:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.90/1.72 % (2736829)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1755957336:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.90/1.72 % (2736825)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=573250936:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.90/1.72 % (2736824)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=1291318874:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.90/1.72 % (2736827)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4156560537:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.90/1.72 % (2736830)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3026268062:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.90/1.72 % (2736827)Instruction limit reached!
% 3.90/1.72 % (2736827)------------------------------
% 3.90/1.72 % (2736827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.72 % (2736827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.72 % (2736827)CaDiCaL version: 2.1.3
% 3.90/1.72 % (2736827)Termination reason: Instruction limit
% 3.90/1.72 % (2736827)Termination phase: Saturation
% 3.90/1.72 % (2736827)Time elapsed: 0.061 s
% 3.90/1.72 % (2736827)Peak memory usage: 89 MB
% 3.90/1.72 % (2736827)Instructions burned: 137 (million)
% 3.90/1.72 % (2736828)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2315977520:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.90/1.72 % (2736829)Instruction limit reached!
% 3.90/1.72 % (2736829)------------------------------
% 3.90/1.72 % (2736829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.72 % (2736829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.72 % (2736829)CaDiCaL version: 2.1.3
% 3.90/1.72 % (2736829)Termination reason: Instruction limit
% 3.90/1.72 % (2736829)Termination phase: Saturation
% 3.90/1.72 % (2736829)Time elapsed: 0.110 s
% 3.90/1.72 % (2736829)Peak memory usage: 91 MB
% 3.90/1.72 % (2736829)Instructions burned: 257 (million)
% 3.90/1.72 % (2736828)Instruction limit reached!
% 3.90/1.72 % (2736828)------------------------------
% 3.90/1.72 % (2736828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.72 % (2736828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.72 % (2736828)CaDiCaL version: 2.1.3
% 3.90/1.72 % (2736828)Termination reason: Instruction limit
% 3.90/1.72 % (2736828)Termination phase: Saturation
% 3.90/1.72 % (2736828)Time elapsed: 0.120 s
% 3.90/1.72 % (2736828)Peak memory usage: 89 MB
% 3.90/1.72 % (2736828)Instructions burned: 183 (million)
% 3.90/1.72 % (2736837)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3798395335:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.90/1.72 % (2736839)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1736467384:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.90/1.72 % (2736840)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=356116201:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 3.90/1.72 % (2736826)First to succeed.
% 3.90/1.72 % (2736826)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2736792"
% 3.90/1.72 % (2736840)Instruction limit reached!
% 3.90/1.72 % (2736840)------------------------------
% 3.90/1.72 % (2736840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.72 % (2736840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.72 % (2736840)CaDiCaL version: 2.1.3
% 5.94/1.91 % (2736840)Termination reason: Instruction limit
% 5.94/1.91 % (2736840)Termination phase: Saturation
% 5.94/1.91 % (2736840)Time elapsed: 0.118 s
% 5.94/1.91 % (2736840)Peak memory usage: 90 MB
% 5.94/1.91 % (2736840)Instructions burned: 216 (million)
% 5.94/1.91 % (2736826)Refutation found. Thanks to Tanya!
% 5.94/1.91 % SZS status Unsatisfiable for theBenchmark
% 5.94/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 5.94/1.91 % (2736826)------------------------------
% 5.94/1.91 % (2736826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.91 % (2736826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.91 % (2736826)CaDiCaL version: 2.1.3
% 5.94/1.91 % (2736826)Termination reason: Refutation
% 5.94/1.91 % (2736826)Time elapsed: 0.453 s
% 5.94/1.91 % (2736826)Peak memory usage: 132 MB
% 5.94/1.91 % (2736826)Instructions burned: 1283 (million)
% 5.94/1.91 % (2736826)------------------------------
% 5.94/1.91 % (2736826)------------------------------
% 5.94/1.91 % (2736792)Success in time 0.748 s
% 5.94/1.91 % Vampire exiting
%------------------------------------------------------------------------------