%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP532-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 10:14:48 AM UTC 2026
% Result : Unsatisfiable 2.37s 1.17s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 52 unt; 1 def)
% Number of atoms : 58 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn 145 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(X0,divide(X1,X2)),divide(X0,X1)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f6,definition,
( spl0_1
<=> multiply(a,b) = multiply(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f8,plain,
( multiply(a,b) != multiply(b,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f6]) ).
fof(f9,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f4,f6]) ).
fof(f10,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f34,plain,
! [X2,X0,X1] : divide(X0,divide(divide(X1,divide(X2,X0)),X1)) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f38,plain,
! [X2,X0,X1] : divide(divide(X0,divide(inverse(X1),X2)),multiply(X0,X1)) = X2,
inference(superposition,[],[f1,f10]) ).
fof(f40,plain,
! [X2,X3,X0,X1] : divide(divide(divide(X1,divide(X2,X0)),divide(divide(X1,X2),X3)),X0) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f44,plain,
! [X0,X1] : inverse(divide(divide(X1,X0),X1)) = X0,
inference(superposition,[],[f3,f1]) ).
fof(f61,plain,
! [X0,X1] : inverse(X1) = inverse(divide(multiply(X0,X1),X0)),
inference(superposition,[],[f44,f10]) ).
fof(f66,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f44,f3]) ).
fof(f82,plain,
! [X0,X1] : divide(X1,X0) = multiply(X1,inverse(X0)),
inference(superposition,[],[f10,f66]) ).
fof(f94,plain,
! [X2,X0,X1] : divide(X0,divide(divide(X1,multiply(X2,inverse(X0))),X1)) = X2,
inference(backward_demodulation,[],[f34,f82]) ).
fof(f95,plain,
! [X2,X3,X0,X1] : divide(divide(divide(X1,divide(X2,X0)),divide(multiply(X1,inverse(X2)),X3)),X0) = X3,
inference(backward_demodulation,[],[f40,f82]) ).
fof(f101,plain,
! [X2,X0,X1] : divide(multiply(X0,inverse(divide(inverse(X1),X2))),multiply(X0,X1)) = X2,
inference(backward_demodulation,[],[f38,f82]) ).
fof(f104,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(multiply(X0,X1),inverse(X0))),
inference(backward_demodulation,[],[f61,f82]) ).
fof(f112,plain,
! [X2,X0,X1] : multiply(multiply(X0,inverse(divide(inverse(X1),X2))),inverse(multiply(X0,X1))) = X2,
inference(forward_demodulation,[],[f101,f82]) ).
fof(f117,plain,
! [X2,X3,X0,X1] : multiply(divide(divide(X1,divide(X2,X0)),divide(multiply(X1,inverse(X2)),X3)),inverse(X0)) = X3,
inference(forward_demodulation,[],[f95,f82]) ).
fof(f118,plain,
! [X2,X0,X1] : multiply(X0,inverse(divide(divide(X1,multiply(X2,inverse(X0))),X1))) = X2,
inference(forward_demodulation,[],[f94,f82]) ).
fof(f128,plain,
! [X2,X0,X1] : multiply(multiply(X0,inverse(multiply(inverse(X1),inverse(X2)))),inverse(multiply(X0,X1))) = X2,
inference(forward_demodulation,[],[f112,f82]) ).
fof(f133,plain,
! [X2,X3,X0,X1] : multiply(multiply(divide(X1,divide(X2,X0)),inverse(divide(multiply(X1,inverse(X2)),X3))),inverse(X0)) = X3,
inference(forward_demodulation,[],[f117,f82]) ).
fof(f134,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(divide(X1,multiply(X2,inverse(X0))),inverse(X1)))) = X2,
inference(forward_demodulation,[],[f118,f82]) ).
fof(f141,plain,
! [X2,X3,X0,X1] : multiply(multiply(divide(X1,divide(X2,X0)),inverse(multiply(multiply(X1,inverse(X2)),inverse(X3)))),inverse(X0)) = X3,
inference(forward_demodulation,[],[f133,f82]) ).
fof(f142,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(X1,inverse(multiply(X2,inverse(X0)))),inverse(X1)))) = X2,
inference(forward_demodulation,[],[f134,f82]) ).
fof(f145,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(X1,inverse(divide(X2,X0))),inverse(multiply(multiply(X1,inverse(X2)),inverse(X3)))),inverse(X0)) = X3,
inference(forward_demodulation,[],[f141,f82]) ).
fof(f146,plain,
! [X2,X0] : multiply(X0,inverse(inverse(multiply(X2,inverse(X0))))) = X2,
inference(forward_demodulation,[],[f142,f104]) ).
fof(f149,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(X1,inverse(multiply(X2,inverse(X0)))),inverse(multiply(multiply(X1,inverse(X2)),inverse(X3)))),inverse(X0)) = X3,
inference(forward_demodulation,[],[f145,f82]) ).
fof(f150,plain,
! [X2,X0] : multiply(X0,multiply(X2,inverse(X0))) = X2,
inference(forward_demodulation,[],[f146,f66]) ).
fof(f189,plain,
! [X2,X0,X1] : multiply(X1,inverse(multiply(inverse(X2),inverse(X0)))) = multiply(multiply(X1,X2),X0),
inference(superposition,[],[f150,f128]) ).
fof(f195,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(X1,inverse(multiply(X2,inverse(X0)))),inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(inverse(X3))))))),inverse(X0)) = X3,
inference(backward_demodulation,[],[f149,f189]) ).
fof(f219,plain,
! [X2,X3,X0,X1] : multiply(multiply(X1,inverse(multiply(X2,inverse(X0)))),inverse(multiply(inverse(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(inverse(X3))))))),inverse(inverse(X0))))) = X3,
inference(forward_demodulation,[],[f195,f189]) ).
fof(f241,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),inverse(inverse(multiply(inverse(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(inverse(X3))))))),inverse(inverse(X0)))))))) = X3,
inference(forward_demodulation,[],[f219,f189]) ).
fof(f259,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(inverse(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(inverse(X3))))))),inverse(inverse(X0)))))) = X3,
inference(forward_demodulation,[],[f241,f66]) ).
fof(f273,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(inverse(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(inverse(X3))))))),X0)))) = X3,
inference(forward_demodulation,[],[f259,f66]) ).
fof(f281,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(inverse(X3))))),X0)))) = X3,
inference(forward_demodulation,[],[f273,f66]) ).
fof(f287,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(X1,inverse(multiply(inverse(inverse(multiply(inverse(inverse(X2)),inverse(inverse(X3))))),inverse(X0))))))) = X3,
inference(forward_demodulation,[],[f281,f189]) ).
fof(f291,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(X1,inverse(multiply(multiply(inverse(inverse(X2)),inverse(inverse(X3))),inverse(X0))))))) = X3,
inference(forward_demodulation,[],[f287,f66]) ).
fof(f295,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(inverse(inverse(inverse(X3))),inverse(inverse(X0)))))))))) = X3,
inference(forward_demodulation,[],[f291,f189]) ).
fof(f298,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(inverse(inverse(inverse(X3))),X0)))))))) = X3,
inference(forward_demodulation,[],[f295,f66]) ).
fof(f300,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(inverse(X3),X0)))))))) = X3,
inference(forward_demodulation,[],[f298,f66]) ).
fof(f302,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X0)))),multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X3),X0)))))))) = X3,
inference(forward_demodulation,[],[f300,f66]) ).
fof(f304,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(multiply(X2,inverse(X0)),multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X3),X0)))))))) = X3,
inference(forward_demodulation,[],[f302,f66]) ).
fof(f306,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(inverse(X0)),inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X3),X0))))))))))) = X3,
inference(forward_demodulation,[],[f304,f189]) ).
fof(f307,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(multiply(X2,inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X3),X0))))))))))) = X3,
inference(forward_demodulation,[],[f306,f66]) ).
fof(f741,plain,
! [X0,X1] : multiply(X1,inverse(X0)) = multiply(inverse(X0),X1),
inference(superposition,[],[f307,f307]) ).
fof(f962,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f741,f66]) ).
fof(f1004,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f8,f962]) ).
fof(f1005,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1004]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f9]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1005]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
fof(f1015,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP532-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.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 10:10:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 2.37/1.17 % (1429431)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.37/1.17 % (1429488)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1689372344:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.37/1.17 % (1429488)First to succeed.
% 2.37/1.17 % (1429488)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1429431"
% 2.37/1.17 % (1429486)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1420079841:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.37/1.17 % (1429484)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=2703457629:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.37/1.17 % (1429483)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=3748235966:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.37/1.17 % (1429485)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=456159038:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.37/1.17 % (1429487)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2409583672:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.37/1.17 % (1429489)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3399174564:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.37/1.17 % (1429486)Also succeeded, but the first one will report.
% 2.37/1.17 % (1429489)Also succeeded, but the first one will report.
% 2.37/1.17 % (1429487)Also succeeded, but the first one will report.
% 2.37/1.17 % (1429488)Refutation found. Thanks to Tanya!
% 2.37/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.37/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.36 % (1429488)------------------------------
% 2.80/1.36 % (1429488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.36 % (1429488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.36 % (1429488)CaDiCaL version: 2.1.3
% 2.80/1.36 % (1429488)Termination reason: Refutation
% 2.80/1.36 % (1429488)Time elapsed: 0.017 s
% 2.80/1.36 % (1429488)Peak memory usage: 89 MB
% 2.80/1.36 % (1429488)Instructions burned: 46 (million)
% 2.80/1.36 % (1429488)------------------------------
% 2.80/1.36 % (1429488)------------------------------
% 2.80/1.36 % (1429431)Success in time 0.31 s
% 2.80/1.36 % Vampire exiting
%------------------------------------------------------------------------------