%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:13:19 AM UTC 2026
% Result : Unsatisfiable 16.71s 3.35s
% Output : Refutation 16.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 60 unt; 6 def)
% Number of atoms : 60 ( 59 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 : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,negated_conjecture,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f3,negated_conjecture,
! [X0,X1] : multiply(X0,left_division(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_left_division) ).
fof(f4,negated_conjecture,
! [X0,X1] : left_division(X0,multiply(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_division_multiply) ).
fof(f5,negated_conjecture,
! [X0,X1] : multiply(right_division(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_right_division) ).
fof(f6,negated_conjecture,
! [X0,X1] : right_division(multiply(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_division_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,right_inverse(X0)) = identity,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',moufang3) ).
fof(f12,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_moufang1) ).
fof(f13,definition,
sF0 = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f14,plain,
multiply(b,c) = sF0,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF1 = multiply(a,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f16,plain,
multiply(a,sF0) = sF1,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF2 = multiply(sF1,a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f18,plain,
multiply(sF1,a) = sF2,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF3 = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f20,plain,
multiply(a,b) = sF3,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF4 = multiply(c,a),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f22,plain,
multiply(c,a) = 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(f35,plain,
! [X0] : multiply(a,multiply(sF0,multiply(a,X0))) = multiply(multiply(sF1,a),X0),
inference(superposition,[],[f11,f16]) ).
fof(f44,plain,
! [X0] : multiply(a,multiply(sF0,multiply(a,X0))) = multiply(sF2,X0),
inference(forward_demodulation,[],[f35,f18]) ).
fof(f49,plain,
! [X0] : right_inverse(X0) = left_division(X0,identity),
inference(superposition,[],[f4,f8]) ).
fof(f55,plain,
! [X0] : multiply(sF2,left_division(a,X0)) = multiply(a,multiply(sF0,X0)),
inference(superposition,[],[f44,f3]) ).
fof(f70,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,multiply(X0,identity))),
inference(superposition,[],[f11,f2]) ).
fof(f74,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f70,f2]) ).
fof(f82,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(X0,X2))) = multiply(multiply(X0,multiply(X1,X0)),X2),
inference(backward_demodulation,[],[f11,f74]) ).
fof(f88,plain,
! [X0,X1] : multiply(X0,multiply(left_inverse(X0),multiply(X0,X1))) = multiply(multiply(X0,identity),X1),
inference(superposition,[],[f82,f10]) ).
fof(f105,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(left_inverse(X0),multiply(X0,X1))),
inference(forward_demodulation,[],[f88,f2]) ).
fof(f119,plain,
b = right_division(sF0,c),
inference(superposition,[],[f6,f14]) ).
fof(f138,plain,
! [X0] : identity = multiply(X0,multiply(left_inverse(X0),identity)),
inference(superposition,[],[f105,f8]) ).
fof(f153,plain,
! [X0,X1] : left_division(X0,multiply(X0,X1)) = multiply(left_inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f105]) ).
fof(f160,plain,
! [X0,X1] : multiply(left_inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f153,f4]) ).
fof(f166,plain,
! [X0] : identity = multiply(X0,left_inverse(X0)),
inference(forward_demodulation,[],[f138,f2]) ).
fof(f180,plain,
! [X0] : left_inverse(X0) = left_division(X0,identity),
inference(superposition,[],[f4,f166]) ).
fof(f185,plain,
! [X0] : right_inverse(X0) = left_inverse(X0),
inference(forward_demodulation,[],[f180,f49]) ).
fof(f193,plain,
! [X0,X1] : multiply(right_inverse(X0),multiply(X0,X1)) = X1,
inference(backward_demodulation,[],[f160,f185]) ).
fof(f204,plain,
! [X0,X1] : left_division(X1,X0) = multiply(right_inverse(X1),X0),
inference(superposition,[],[f193,f3]) ).
fof(f218,plain,
! [X0,X1] : right_inverse(X1) = right_division(X0,multiply(X1,X0)),
inference(superposition,[],[f6,f193]) ).
fof(f451,plain,
! [X0,X1] : multiply(multiply(X1,X0),right_inverse(X0)) = multiply(X0,multiply(left_division(X0,X1),identity)),
inference(superposition,[],[f32,f8]) ).
fof(f493,plain,
! [X0,X1] : multiply(X0,left_division(X0,X1)) = multiply(multiply(X1,X0),right_inverse(X0)),
inference(forward_demodulation,[],[f451,f2]) ).
fof(f507,plain,
! [X0,X1] : multiply(multiply(X1,X0),right_inverse(X0)) = X1,
inference(forward_demodulation,[],[f493,f3]) ).
fof(f521,plain,
! [X0,X1] : right_division(X0,X1) = multiply(X0,right_inverse(X1)),
inference(superposition,[],[f507,f5]) ).
fof(f542,plain,
! [X0,X1] : right_inverse(multiply(X0,X1)) = right_division(right_inverse(X1),X0),
inference(superposition,[],[f218,f507]) ).
fof(f648,plain,
! [X0,X1] : right_division(right_inverse(X0),X1) = left_division(X0,right_inverse(X1)),
inference(superposition,[],[f204,f521]) ).
fof(f658,plain,
! [X0,X1] : right_inverse(multiply(X0,X1)) = left_division(X1,right_inverse(X0)),
inference(backward_demodulation,[],[f542,f648]) ).
fof(f763,plain,
right_inverse(sF4) = left_division(a,right_inverse(c)),
inference(superposition,[],[f658,f22]) ).
fof(f2404,plain,
multiply(a,multiply(sF0,right_inverse(c))) = multiply(sF2,right_inverse(sF4)),
inference(superposition,[],[f55,f763]) ).
fof(f2417,plain,
multiply(a,multiply(sF0,right_inverse(c))) = right_division(sF2,sF4),
inference(forward_demodulation,[],[f2404,f521]) ).
fof(f2423,plain,
right_division(sF2,sF4) = multiply(a,right_division(sF0,c)),
inference(forward_demodulation,[],[f2417,f521]) ).
fof(f2424,plain,
multiply(a,b) = right_division(sF2,sF4),
inference(forward_demodulation,[],[f2423,f119]) ).
fof(f2425,plain,
sF3 = right_division(sF2,sF4),
inference(forward_demodulation,[],[f2424,f20]) ).
fof(f2430,plain,
sF2 = multiply(sF3,sF4),
inference(superposition,[],[f5,f2425]) ).
fof(f2431,plain,
sF2 = sF5,
inference(backward_demodulation,[],[f24,f2430]) ).
fof(f2434,plain,
$false,
inference(forward_subsumption_resolution,[],[f2431,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 09:37:17 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 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
% 16.11/3.09 % (3741963)Detected a unit-equality problem, will run specialized UEQ schedule.
% 16.11/3.09 % (3741976)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=813950401:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 16.11/3.09 % (3741973)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=806656561:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 16.11/3.09 % (3741971)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=3086577881:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 16.11/3.09 % (3741975)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2486484848:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 16.11/3.09 % (3741970)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=2574967111:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 16.11/3.09 % (3741972)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1933507320:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 16.11/3.09 % (3741974)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1906985523:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 16.11/3.09 % (3741973)Instruction limit reached!
% 16.11/3.09 % (3741973)------------------------------
% 16.11/3.09 % (3741973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.11/3.09 % (3741973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.11/3.09 % (3741973)CaDiCaL version: 2.1.3
% 16.11/3.09 % (3741973)Termination reason: Instruction limit
% 16.11/3.09 % (3741973)Termination phase: Saturation
% 16.11/3.09 % (3741973)Time elapsed: 0.120 s
% 16.11/3.09 % (3741973)Peak memory usage: 88 MB
% 16.11/3.09 % (3741973)Instructions burned: 136 (million)
% 16.11/3.09 % (3741974)Instruction limit reached!
% 16.11/3.09 % (3741974)------------------------------
% 16.11/3.09 % (3741974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.11/3.09 % (3741974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.11/3.09 % (3741974)CaDiCaL version: 2.1.3
% 16.11/3.09 % (3741974)Termination reason: Instruction limit
% 16.11/3.09 % (3741974)Termination phase: Saturation
% 16.11/3.09 % (3741974)Time elapsed: 0.174 s
% 16.11/3.09 % (3741974)Peak memory usage: 89 MB
% 16.11/3.09 % (3741974)Instructions burned: 181 (million)
% 16.11/3.09 % (3741975)Instruction limit reached!
% 16.11/3.09 % (3741975)------------------------------
% 16.11/3.09 % (3741975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.11/3.09 % (3741975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.11/3.09 % (3741975)CaDiCaL version: 2.1.3
% 16.11/3.09 % (3741975)Termination reason: Instruction limit
% 16.11/3.09 % (3741975)Termination phase: Saturation
% 16.11/3.09 % (3741975)Time elapsed: 0.180 s
% 16.11/3.09 % (3741975)Peak memory usage: 91 MB
% 16.11/3.09 % (3741975)Instructions burned: 257 (million)
% 16.11/3.09 % (3741986)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3208927773:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 16.11/3.09 % (3741976)Instruction limit reached!
% 16.11/3.09 % (3741976)------------------------------
% 16.11/3.09 % (3741976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.11/3.09 % (3741976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.11/3.09 % (3741976)CaDiCaL version: 2.1.3
% 16.11/3.09 % (3741976)Termination reason: Instruction limit
% 16.11/3.09 % (3741976)Termination phase: Saturation
% 16.11/3.09 % (3741976)Time elapsed: 0.535 s
% 16.11/3.09 % (3741976)Peak memory usage: 101 MB
% 16.11/3.09 % (3741976)Instructions burned: 1189 (million)
% 16.11/3.09 % (3741987)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3349254306:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 16.11/3.09 % (3741988)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1949075513:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 16.71/3.35 % (3741988)Instruction limit reached!
% 16.71/3.35 % (3741988)------------------------------
% 16.71/3.35 % (3741988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.71/3.35 % (3741988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.71/3.35 % (3741988)CaDiCaL version: 2.1.3
% 16.71/3.35 % (3741988)Termination reason: Instruction limit
% 16.71/3.35 % (3741988)Termination phase: Saturation
% 16.71/3.35 % (3741988)Time elapsed: 0.192 s
% 16.71/3.35 % (3741988)Peak memory usage: 90 MB
% 16.71/3.35 % (3741988)Instructions burned: 216 (million)
% 16.71/3.35 % (3741990)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=2963669194:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 16.71/3.35 % (3741990)Instruction limit reached!
% 16.71/3.35 % (3741990)------------------------------
% 16.71/3.35 % (3741990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.71/3.35 % (3741990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.71/3.35 % (3741990)CaDiCaL version: 2.1.3
% 16.71/3.35 % (3741990)Termination reason: Instruction limit
% 16.71/3.35 % (3741990)Termination phase: Saturation
% 16.71/3.35 % (3741990)Time elapsed: 0.186 s
% 16.71/3.35 % (3741990)Peak memory usage: 94 MB
% 16.71/3.35 % (3741990)Instructions burned: 318 (million)
% 16.71/3.35 % (3741994)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=962027456:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 16.71/3.35 % (3741995)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=620522764:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2988 on theBenchmark for (2988ds/2836Mi)
% 16.71/3.35 % (3741972)First to succeed.
% 16.71/3.35 % (3741972)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3741963"
% 16.71/3.35 % (3741986)Also succeeded, but the first one will report.
% 16.71/3.35 % (3741972)Refutation found. Thanks to Tanya!
% 16.71/3.35 % SZS status Unsatisfiable for theBenchmark
% 16.71/3.35 % SZS output start Proof for theBenchmark
% See solution above
% 16.71/3.35 % (3741972)------------------------------
% 16.71/3.35 % (3741972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.71/3.35 % (3741972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.71/3.35 % (3741972)CaDiCaL version: 2.1.3
% 16.71/3.35 % (3741972)Termination reason: Refutation
% 16.71/3.35 % (3741972)Time elapsed: 1.468 s
% 16.71/3.35 % (3741972)Peak memory usage: 133 MB
% 16.71/3.35 % (3741972)Instructions burned: 1396 (million)
% 16.71/3.35 % (3741972)------------------------------
% 16.71/3.35 % (3741972)------------------------------
% 16.71/3.35 % (3741963)Success in time 2.265 s
% 16.71/3.35 % Vampire exiting
%------------------------------------------------------------------------------