%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP511-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:14:45 AM UTC 2026
% Result : Unsatisfiable 2.63s 1.28s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 47 unt; 2 def)
% Number of atoms : 63 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 6 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 3 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f4,definition,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f6,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(avatar_component_clause,[],[f4]) ).
fof(f7,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2,f4]) ).
fof(f8,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(X0,X3),inverse(multiply(multiply(multiply(X1,X0),X2),X3))),
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f10,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(multiply(multiply(X1,X0),X2),X3),inverse(multiply(X1,X2))),inverse(X0)) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f14,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X0)))) = multiply(X1,inverse(multiply(multiply(X2,X1),inverse(X0)))),
inference(superposition,[],[f9,f9]) ).
fof(f17,plain,
! [X2,X3,X0,X1] : multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(X3,multiply(X1,X2)),inverse(multiply(X3,X0))))))) = X2,
inference(superposition,[],[f1,f9]) ).
fof(f20,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(multiply(multiply(X1,X3),X2),inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X0))))))),
inference(superposition,[],[f8,f9]) ).
fof(f32,plain,
! [X2,X0,X1] : inverse(multiply(X0,multiply(X1,inverse(multiply(multiply(X0,X1),X2))))) = X2,
inference(superposition,[],[f9,f8]) ).
fof(f42,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X3,multiply(X1,X2)),inverse(multiply(X3,X0)))) = inverse(multiply(X1,multiply(X2,inverse(X0)))),
inference(superposition,[],[f32,f9]) ).
fof(f44,plain,
! [X2,X0,X1] : inverse(multiply(multiply(X0,X1),inverse(multiply(X0,multiply(X1,X2))))) = X2,
inference(superposition,[],[f32,f8]) ).
fof(f52,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(X1,inverse(multiply(X1,multiply(X2,inverse(X0))))))) = X2,
inference(backward_demodulation,[],[f17,f42]) ).
fof(f88,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3)))) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(superposition,[],[f8,f10]) ).
fof(f101,plain,
! [X2,X0] : inverse(X2) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(forward_demodulation,[],[f88,f1]) ).
fof(f110,plain,
! [X3,X0] : multiply(multiply(X3,X0),inverse(X3)) = X0,
inference(superposition,[],[f101,f44]) ).
fof(f111,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(multiply(X1,X0),X2))),
inference(superposition,[],[f101,f1]) ).
fof(f112,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(X0,X2),X1),X3)) = multiply(inverse(multiply(X0,X1)),inverse(multiply(X2,X3))),
inference(superposition,[],[f101,f8]) ).
fof(f115,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))),
inference(superposition,[],[f101,f101]) ).
fof(f122,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))),inverse(X2)),
inference(superposition,[],[f10,f101]) ).
fof(f133,plain,
! [X2,X0,X1] : inverse(multiply(inverse(X0),inverse(multiply(multiply(X1,inverse(X0)),multiply(inverse(X1),X2))))) = X2,
inference(superposition,[],[f44,f101]) ).
fof(f137,plain,
! [X2,X1] : inverse(multiply(X1,X2)) = multiply(inverse(X1),inverse(X2)),
inference(backward_demodulation,[],[f122,f115]) ).
fof(f163,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(X1,X2)) = multiply(X0,multiply(inverse(multiply(X1,X2)),inverse(multiply(X3,inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X0)))))))),
inference(backward_demodulation,[],[f20,f112]) ).
fof(f176,plain,
! [X2,X1] : inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(backward_demodulation,[],[f9,f111]) ).
fof(f177,plain,
! [X2,X3,X0] : inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X0)))) = inverse(multiply(X2,inverse(X0))),
inference(backward_demodulation,[],[f14,f111]) ).
fof(f178,plain,
! [X2,X1] : inverse(inverse(multiply(X1,multiply(inverse(X1),X2)))) = X2,
inference(backward_demodulation,[],[f133,f111]) ).
fof(f192,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(multiply(X1,X2),multiply(X3,inverse(multiply(multiply(X4,X3),inverse(multiply(X4,X0)))))))),
inference(forward_demodulation,[],[f163,f137]) ).
fof(f227,plain,
! [X2,X0,X1] : inverse(multiply(X1,multiply(X2,inverse(X0)))) = inverse(multiply(multiply(X1,X2),inverse(X0))),
inference(backward_demodulation,[],[f42,f177]) ).
fof(f230,plain,
! [X2,X0] : multiply(X0,multiply(X2,inverse(X0))) = X2,
inference(backward_demodulation,[],[f52,f176]) ).
fof(f239,plain,
! [X2,X0,X1,X4] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(multiply(X1,X2),inverse(multiply(X4,inverse(multiply(X4,X0))))))),
inference(forward_demodulation,[],[f192,f111]) ).
fof(f266,plain,
! [X2,X0,X1,X4] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(X1,multiply(X2,inverse(multiply(X4,inverse(multiply(X4,X0)))))))),
inference(forward_demodulation,[],[f239,f227]) ).
fof(f282,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(X1,multiply(X2,X0)))),
inference(forward_demodulation,[],[f266,f176]) ).
fof(f321,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f110,f110]) ).
fof(f334,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f176,f321]) ).
fof(f338,plain,
! [X2,X1] : multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(backward_demodulation,[],[f178,f334]) ).
fof(f352,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X1,X0))),
inference(superposition,[],[f334,f176]) ).
fof(f359,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,inverse(inverse(X1))),
inference(superposition,[],[f338,f230]) ).
fof(f364,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f359,f334]) ).
fof(f405,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| spl0_1 ),
inference(superposition,[],[f6,f364]) ).
fof(f408,definition,
( spl0_2
<=> multiply(a3,multiply(b3,c3)) = multiply(c3,multiply(a3,b3)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f410,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| spl0_2 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f411,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f405,f4,f408]) ).
fof(f789,plain,
! [X2,X0,X1] : inverse(inverse(multiply(X0,multiply(X1,X2)))) = multiply(X2,inverse(inverse(multiply(X0,X1)))),
inference(superposition,[],[f352,f282]) ).
fof(f792,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = inverse(inverse(multiply(X0,multiply(X1,X2)))),
inference(forward_demodulation,[],[f789,f334]) ).
fof(f812,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X0,X1)),
inference(forward_demodulation,[],[f792,f334]) ).
fof(f831,plain,
( $false
| spl0_2 ),
inference(backward_subsumption_resolution,[],[f410,f812]) ).
fof(f832,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f831]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f7]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f411]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f832]) ).
cnf(s5,plain,
spl0_1,
inference(rat,[],[s2,s4]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5]) ).
fof(f850,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP511-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:06:19 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.63/1.28 % (2859127)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.63/1.28 % (2859187)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1623700587:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 2.63/1.28 % (2859190)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2157677863:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 2.63/1.28 % (2859182)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=1049445369:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 2.63/1.28 % (2859186)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2300635335:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 2.63/1.28 % (2859184)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2773787267:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 2.63/1.28 % (2859181)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=62319582:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 2.63/1.28 % (2859189)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2753605236:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 2.63/1.28 % (2859187)Instruction limit reached!
% 2.63/1.28 % (2859187)------------------------------
% 2.63/1.28 % (2859187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.28 % (2859187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.28 % (2859187)CaDiCaL version: 2.1.3
% 2.63/1.28 % (2859187)Termination reason: Instruction limit
% 2.63/1.28 % (2859187)Termination phase: Saturation
% 2.63/1.28 % (2859187)Time elapsed: 0.057 s
% 2.63/1.28 % (2859187)Peak memory usage: 90 MB
% 2.63/1.28 % (2859187)Instructions burned: 189 (million)
% 2.63/1.28 % (2859189)First to succeed.
% 2.63/1.28 % (2859189)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2859127"
% 2.63/1.28 % (2859186)Instruction limit reached!
% 2.63/1.28 % (2859186)------------------------------
% 2.63/1.28 % (2859186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.28 % (2859186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.28 % (2859186)CaDiCaL version: 2.1.3
% 2.63/1.28 % (2859186)Termination reason: Instruction limit
% 2.63/1.28 % (2859186)Termination phase: Saturation
% 2.63/1.28 % (2859186)Time elapsed: 0.057 s
% 2.63/1.28 % (2859186)Peak memory usage: 88 MB
% 2.63/1.28 % (2859186)Instructions burned: 139 (million)
% 2.63/1.28 % (2859218)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=945313430:i=4948:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/4948Mi)
% 2.63/1.28 % (2859212)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1046833723:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 2.63/1.28 % (2859190)Also succeeded, but the first one will report.
% 2.63/1.28 % (2859189)Refutation found. Thanks to Tanya!
% 2.63/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.63/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.47 % (2859189)------------------------------
% 3.72/1.47 % (2859189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.47 % (2859189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.47 % (2859189)CaDiCaL version: 2.1.3
% 3.72/1.47 % (2859189)Termination reason: Refutation
% 3.72/1.47 % (2859189)Time elapsed: 0.041 s
% 3.72/1.47 % (2859189)Peak memory usage: 89 MB
% 3.72/1.47 % (2859189)Instructions burned: 64 (million)
% 3.72/1.47 % (2859189)------------------------------
% 3.72/1.47 % (2859189)------------------------------
% 3.72/1.47 % (2859127)Success in time 0.435 s
% 3.72/1.47 % Vampire exiting
%------------------------------------------------------------------------------