%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP118-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 10:12:38 AM UTC 2026
% Result : Unsatisfiable 0.87s 0.91s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 52 unt; 2 def)
% Number of atoms : 72 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 8 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 111 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),X2)),multiply(identity,multiply(X2,X2)))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order3) ).
fof(f4,definition,
( spl0_1
<=> multiply(multiply(a,b),c) = multiply(a,multiply(b,c)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f6,plain,
( multiply(multiply(a,b),c) != multiply(a,multiply(b,c))
| spl0_1 ),
inference(avatar_component_clause,[],[f4]) ).
fof(f7,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2,f4]) ).
fof(f11,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(multiply(identity,X0),multiply(identity,X0))))),X0)) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f15,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(X0,X0)))),multiply(multiply(identity,multiply(multiply(identity,X0),multiply(identity,multiply(multiply(identity,X3),multiply(identity,X3))))),X3))) = X2,
inference(superposition,[],[f11,f11]) ).
fof(f17,plain,
! [X2,X0,X1] : multiply(multiply(X1,X0),multiply(identity,X2)) = multiply(X1,multiply(X0,X2)),
inference(superposition,[],[f11,f1]) ).
fof(f19,plain,
! [X2,X0,X1] : multiply(multiply(X1,X0),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2)))) = multiply(X1,multiply(X0,multiply(identity,multiply(X2,X2)))),
inference(superposition,[],[f1,f11]) ).
fof(f20,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X0,X3)),multiply(identity,multiply(X3,X3)))) = multiply(multiply(X1,multiply(multiply(X1,X0),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))),X2),
inference(superposition,[],[f1,f11]) ).
fof(f22,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X0,X3)),multiply(identity,multiply(X3,X3)))) = multiply(multiply(X1,multiply(X1,multiply(X0,multiply(identity,multiply(X2,X2))))),X2),
inference(backward_demodulation,[],[f20,f19]) ).
fof(f28,plain,
! [X2,X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),X2),multiply(X2,X2)))) = X1,
inference(backward_demodulation,[],[f1,f17]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(X0,X0)))),multiply(multiply(identity,multiply(identity,multiply(X0,multiply(multiply(identity,X3),multiply(identity,X3))))),X3))) = X2,
inference(forward_demodulation,[],[f15,f17]) ).
fof(f37,plain,
! [X2,X3,X0,X1] : multiply(multiply(X1,multiply(X1,multiply(X0,multiply(identity,multiply(X2,X2))))),X2) = multiply(X1,multiply(X1,multiply(multiply(X0,X3),multiply(X3,X3)))),
inference(forward_demodulation,[],[f22,f17]) ).
fof(f42,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(X0,X0)))),multiply(multiply(identity,multiply(identity,multiply(X0,multiply(identity,multiply(X3,X3))))),X3))) = X2,
inference(forward_demodulation,[],[f32,f17]) ).
fof(f46,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X1,multiply(X2,multiply(X0,X0)))),multiply(multiply(identity,multiply(identity,multiply(X0,multiply(identity,multiply(X3,X3))))),X3))) = X2,
inference(forward_demodulation,[],[f42,f17]) ).
fof(f56,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),multiply(identity,identity)))) = X1,
inference(superposition,[],[f28,f17]) ).
fof(f59,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,multiply(X1,identity)))) = X1,
inference(forward_demodulation,[],[f56,f17]) ).
fof(f64,plain,
! [X2,X0,X1] : multiply(X1,multiply(X1,multiply(X0,identity))) = multiply(X1,multiply(X1,multiply(multiply(X0,X2),multiply(X2,X2)))),
inference(superposition,[],[f28,f59]) ).
fof(f65,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X1,multiply(X0,identity))),X2)) = multiply(X0,multiply(identity,X2)),
inference(superposition,[],[f17,f59]) ).
fof(f67,plain,
! [X2,X0,X1] : multiply(multiply(X1,X2),X0) = multiply(X1,multiply(X2,multiply(identity,multiply(identity,multiply(X0,identity))))),
inference(superposition,[],[f17,f59]) ).
fof(f68,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),identity))) = X1,
inference(backward_demodulation,[],[f28,f64]) ).
fof(f71,plain,
! [X2,X0,X1] : multiply(multiply(X1,multiply(X1,multiply(X0,multiply(identity,multiply(X2,X2))))),X2) = multiply(X1,multiply(X1,multiply(X0,identity))),
inference(backward_demodulation,[],[f37,f64]) ).
fof(f74,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X1,multiply(X2,multiply(X0,X0)))),multiply(identity,multiply(identity,multiply(X0,identity))))) = X2,
inference(backward_demodulation,[],[f46,f71]) ).
fof(f82,plain,
! [X2,X0,X1] : multiply(X1,multiply(X1,multiply(multiply(X1,multiply(X2,multiply(X0,X0))),multiply(identity,multiply(X0,identity))))) = X2,
inference(forward_demodulation,[],[f74,f17]) ).
fof(f83,plain,
! [X2,X0,X1] : multiply(X1,multiply(X1,multiply(X1,multiply(multiply(X2,multiply(X0,X0)),multiply(X0,identity))))) = X2,
inference(forward_demodulation,[],[f82,f17]) ).
fof(f85,plain,
! [X0,X1] : multiply(X1,multiply(X1,multiply(X0,identity))) = multiply(X1,multiply(multiply(X1,X0),identity)),
inference(superposition,[],[f68,f68]) ).
fof(f93,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),identity),identity))) = multiply(X0,multiply(multiply(X0,multiply(X0,multiply(X1,identity))),identity)),
inference(superposition,[],[f85,f85]) ).
fof(f95,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(multiply(X0,X1),identity),X2)) = multiply(multiply(X0,multiply(X0,multiply(X1,identity))),multiply(identity,X2)),
inference(superposition,[],[f17,f85]) ).
fof(f98,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(multiply(X0,X1),identity),X2)) = multiply(X0,multiply(multiply(X0,multiply(X1,identity)),X2)),
inference(forward_demodulation,[],[f95,f17]) ).
fof(f99,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),identity),identity))) = multiply(X1,multiply(identity,identity)),
inference(forward_demodulation,[],[f93,f65]) ).
fof(f102,plain,
! [X0,X1] : multiply(X1,multiply(identity,identity)) = multiply(X0,multiply(X0,multiply(multiply(X0,multiply(X1,identity)),identity))),
inference(forward_demodulation,[],[f99,f98]) ).
fof(f104,plain,
! [X0,X1] : multiply(X1,multiply(identity,identity)) = multiply(X0,multiply(X0,multiply(X0,multiply(multiply(X1,identity),identity)))),
inference(forward_demodulation,[],[f102,f85]) ).
fof(f106,plain,
! [X1] : multiply(X1,identity) = multiply(X1,multiply(identity,identity)),
inference(forward_demodulation,[],[f104,f59]) ).
fof(f108,plain,
! [X0] : identity = multiply(X0,multiply(X0,multiply(X0,identity))),
inference(superposition,[],[f59,f106]) ).
fof(f118,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f59,f108]) ).
fof(f122,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,X1))) = X1,
inference(backward_demodulation,[],[f59,f118]) ).
fof(f127,plain,
! [X2,X0,X1] : multiply(multiply(X1,X2),X0) = multiply(X1,multiply(X2,multiply(identity,multiply(identity,X0)))),
inference(backward_demodulation,[],[f67,f118]) ).
fof(f131,plain,
! [X2,X0,X1] : multiply(X1,multiply(X1,multiply(X1,multiply(multiply(X2,multiply(X0,X0)),X0)))) = X2,
inference(backward_demodulation,[],[f83,f118]) ).
fof(f134,plain,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
inference(backward_demodulation,[],[f108,f118]) ).
fof(f143,plain,
! [X2,X0,X1] : multiply(X1,multiply(X1,multiply(X1,multiply(X2,multiply(multiply(X0,X0),multiply(identity,multiply(identity,X0))))))) = X2,
inference(backward_demodulation,[],[f131,f127]) ).
fof(f150,plain,
( multiply(a,multiply(b,c)) != multiply(a,multiply(b,multiply(identity,multiply(identity,c))))
| spl0_1 ),
inference(backward_demodulation,[],[f6,f127]) ).
fof(f156,definition,
( spl0_2
<=> multiply(a,multiply(b,c)) = multiply(a,multiply(b,multiply(identity,multiply(identity,c)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f158,plain,
( multiply(a,multiply(b,c)) != multiply(a,multiply(b,multiply(identity,multiply(identity,c))))
| spl0_2 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f150,f4,f156]) ).
fof(f165,plain,
! [X2,X0] : multiply(X2,multiply(multiply(X0,X0),multiply(identity,multiply(identity,X0)))) = X2,
inference(forward_demodulation,[],[f143,f122]) ).
fof(f174,plain,
! [X2,X0] : multiply(X2,multiply(X0,multiply(X0,multiply(identity,multiply(identity,multiply(identity,multiply(identity,X0))))))) = X2,
inference(forward_demodulation,[],[f165,f127]) ).
fof(f183,plain,
! [X2,X0] : multiply(X2,multiply(X0,multiply(X0,multiply(identity,X0)))) = X2,
inference(forward_demodulation,[],[f174,f122]) ).
fof(f231,plain,
! [X0] : identity = multiply(multiply(X0,multiply(X0,multiply(identity,X0))),multiply(X0,multiply(X0,multiply(identity,X0)))),
inference(superposition,[],[f134,f183]) ).
fof(f237,plain,
! [X0] : identity = multiply(X0,multiply(X0,multiply(identity,X0))),
inference(forward_demodulation,[],[f231,f183]) ).
fof(f283,plain,
! [X0] : multiply(identity,X0) = multiply(X0,identity),
inference(superposition,[],[f122,f237]) ).
fof(f286,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f283,f118]) ).
fof(f296,plain,
( multiply(a,multiply(b,c)) != multiply(a,multiply(b,multiply(identity,c)))
| spl0_2 ),
inference(backward_demodulation,[],[f158,f286]) ).
fof(f300,plain,
( multiply(a,multiply(b,c)) != multiply(a,multiply(b,c))
| spl0_2 ),
inference(forward_demodulation,[],[f296,f286]) ).
fof(f301,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f300]) ).
fof(f302,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f301]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f7]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f159]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f302]) ).
cnf(s4,plain,
spl0_1,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f332,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP118-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:21:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.87/0.91 % (242089)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.87/0.91 % (242099)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2661672018:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.87/0.91 % (242099)First to succeed.
% 0.87/0.91 % (242099)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-242089"
% 0.87/0.91 % (242094)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=473261127:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.87/0.91 % (242097)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1327482633:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.87/0.91 % (242100)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=56680838:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.87/0.91 % (242098)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3653412242:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.87/0.91 % (242095)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=773883274:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.87/0.91 % (242096)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=794449208:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.87/0.91 % (242100)Also succeeded, but the first one will report.
% 0.87/0.91 % (242097)Also succeeded, but the first one will report.
% 0.87/0.91 % (242098)Instruction limit reached!
% 0.87/0.91 % (242098)------------------------------
% 0.87/0.91 % (242098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.87/0.91 % (242098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.91 % (242098)CaDiCaL version: 2.1.3
% 0.87/0.91 % (242098)Termination reason: Instruction limit
% 0.87/0.91 % (242098)Termination phase: Saturation
% 0.87/0.91 % (242098)Time elapsed: 0.097 s
% 0.87/0.91 % (242098)Peak memory usage: 89 MB
% 0.87/0.91 % (242098)Instructions burned: 183 (million)
% 0.87/0.91 % (242099)Refutation found. Thanks to Tanya!
% 0.87/0.91 % SZS status Unsatisfiable for theBenchmark
% 0.87/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/1.10 % (242099)------------------------------
% 2.47/1.10 % (242099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.10 % (242099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.10 % (242099)CaDiCaL version: 2.1.3
% 2.47/1.10 % (242099)Termination reason: Refutation
% 2.47/1.10 % (242099)Time elapsed: 0.010 s
% 2.47/1.10 % (242099)Peak memory usage: 89 MB
% 2.47/1.10 % (242099)Instructions burned: 26 (million)
% 2.47/1.10 % (242099)------------------------------
% 2.47/1.10 % (242099)------------------------------
% 2.47/1.10 % (242089)Success in time 0.298 s
% 2.47/1.10 % Vampire exiting
%------------------------------------------------------------------------------