%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP450-1 : 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 : n026.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 10:14:02 AM UTC 2026
% Result : Unsatisfiable 2.86s 1.38s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 56 unt; 1 def)
% Number of atoms : 62 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(divide(divide(divide(X1,X1),X1),X2),divide(divide(divide(X1,X1),X0),X2))) = X1,
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,plain,
! [X0,X1] : divide(divide(X1,X1),X0) = inverse(X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f7,definition,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f10,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f5,f7]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f2,f4]) ).
fof(f12,plain,
! [X2,X0,X1] : divide(X0,divide(divide(divide(divide(X1,X1),X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[],[f1,f4]) ).
fof(f13,plain,
! [X2,X0,X1] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[],[f12,f4]) ).
fof(f14,plain,
! [X0,X1] : inverse(X1) = divide(inverse(divide(X0,X0)),X1),
inference(superposition,[],[f4,f4]) ).
fof(f16,plain,
! [X0,X1] : inverse(X1) = divide(multiply(inverse(X0),X0),X1),
inference(superposition,[],[f4,f11]) ).
fof(f17,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(superposition,[],[f4,f11]) ).
fof(f23,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(divide(X1,X1)),X0),
inference(superposition,[],[f11,f14]) ).
fof(f27,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(multiply(inverse(X1),X1),X0),
inference(superposition,[],[f11,f16]) ).
fof(f30,plain,
! [X0,X1] : inverse(inverse(X1)) = multiply(inverse(multiply(inverse(X0),X0)),X1),
inference(superposition,[],[f17,f16]) ).
fof(f36,plain,
! [X2,X0,X1] : divide(X0,divide(divide(inverse(X2),inverse(X1)),multiply(inverse(X0),X1))) = X2,
inference(superposition,[],[f13,f11]) ).
fof(f38,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(superposition,[],[f13,f4]) ).
fof(f51,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[],[f38,f11]) ).
fof(f52,plain,
! [X2,X0,X1] : divide(X0,divide(multiply(inverse(X2),X1),multiply(inverse(X0),X1))) = X2,
inference(forward_demodulation,[],[f36,f11]) ).
fof(f61,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f51,f11]) ).
fof(f63,plain,
! [X0,X1] : multiply(inverse(inverse(X1)),X0) = multiply(X1,X0),
inference(superposition,[],[f61,f61]) ).
fof(f65,plain,
! [X0,X1] : inverse(inverse(multiply(inverse(divide(X1,X1)),X0))) = X0,
inference(superposition,[],[f17,f61]) ).
fof(f66,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[],[f65,f23]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)) = X1,
inference(superposition,[],[f61,f66]) ).
fof(f71,plain,
! [X2,X0,X1] : inverse(inverse(inverse(X0))) = divide(X1,divide(divide(X0,X2),divide(inverse(X1),X2))),
inference(superposition,[],[f13,f66]) ).
fof(f73,plain,
! [X0,X1] : multiply(X1,inverse(inverse(inverse(X0)))) = divide(X1,X0),
inference(superposition,[],[f11,f66]) ).
fof(f85,plain,
! [X2,X0,X1] : multiply(X0,inverse(inverse(inverse(divide(multiply(inverse(X2),X1),multiply(inverse(X0),X1)))))) = X2,
inference(backward_demodulation,[],[f52,f73]) ).
fof(f91,plain,
! [X2,X0,X1] : inverse(inverse(inverse(X0))) = multiply(X1,inverse(inverse(inverse(divide(divide(X0,X2),divide(inverse(X1),X2)))))),
inference(forward_demodulation,[],[f71,f73]) ).
fof(f93,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f69,f63]) ).
fof(f97,plain,
! [X2,X0,X1] : multiply(X0,inverse(inverse(inverse(multiply(multiply(inverse(X2),X1),inverse(inverse(inverse(multiply(inverse(X0),X1))))))))) = X2,
inference(forward_demodulation,[],[f85,f73]) ).
fof(f107,plain,
! [X2,X0,X1] : inverse(inverse(inverse(X0))) = multiply(X1,inverse(inverse(inverse(multiply(divide(X0,X2),inverse(inverse(inverse(divide(inverse(X1),X2))))))))),
inference(forward_demodulation,[],[f91,f73]) ).
fof(f118,plain,
! [X2,X0,X1] : inverse(inverse(inverse(X0))) = multiply(X1,inverse(inverse(inverse(multiply(divide(X0,X2),inverse(inverse(inverse(multiply(inverse(X1),inverse(inverse(inverse(X2)))))))))))),
inference(forward_demodulation,[],[f107,f73]) ).
fof(f126,plain,
! [X2,X0,X1] : inverse(inverse(inverse(X0))) = multiply(X1,inverse(inverse(inverse(multiply(multiply(X0,inverse(inverse(inverse(X2)))),inverse(inverse(inverse(multiply(inverse(X1),inverse(inverse(inverse(X2)))))))))))),
inference(forward_demodulation,[],[f118,f73]) ).
fof(f177,plain,
! [X2,X0,X1] : inverse(X0) = multiply(X2,inverse(inverse(inverse(multiply(multiply(X0,X1),inverse(inverse(inverse(multiply(inverse(X2),X1))))))))),
inference(superposition,[],[f97,f63]) ).
fof(f191,plain,
! [X2,X0,X1] : inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(X0),X1),inverse(inverse(inverse(multiply(inverse(multiply(inverse(X2),X2)),X1)))))))))) = X0,
inference(superposition,[],[f27,f97]) ).
fof(f192,plain,
! [X2,X0,X1] : multiply(X1,X0) = inverse(inverse(inverse(multiply(multiply(inverse(X0),X2),inverse(inverse(inverse(multiply(inverse(inverse(X1)),X2)))))))),
inference(superposition,[],[f61,f97]) ).
fof(f195,plain,
! [X2,X0,X1] : multiply(X1,X0) = inverse(inverse(inverse(multiply(multiply(inverse(X0),X2),inverse(inverse(inverse(multiply(X1,X2)))))))),
inference(forward_demodulation,[],[f192,f63]) ).
fof(f196,plain,
! [X2,X0,X1] : inverse(multiply(multiply(inverse(X0),X1),inverse(inverse(inverse(multiply(inverse(multiply(inverse(X2),X2)),X1)))))) = X0,
inference(forward_demodulation,[],[f191,f66]) ).
fof(f207,plain,
! [X2] : inverse(inverse(X2)) = X2,
inference(backward_demodulation,[],[f97,f177]) ).
fof(f208,plain,
! [X0] : inverse(X0) = inverse(inverse(inverse(X0))),
inference(backward_demodulation,[],[f126,f177]) ).
fof(f212,plain,
! [X0,X1] : inverse(multiply(multiply(inverse(X0),X1),inverse(inverse(inverse(inverse(inverse(X1))))))) = X0,
inference(forward_demodulation,[],[f196,f30]) ).
fof(f230,plain,
! [X2,X0,X1] : multiply(X1,X0) = inverse(multiply(multiply(inverse(X0),X2),inverse(inverse(inverse(multiply(X1,X2)))))),
inference(backward_demodulation,[],[f195,f208]) ).
fof(f237,plain,
! [X0,X1] : inverse(multiply(multiply(inverse(X0),X1),inverse(inverse(inverse(X1))))) = X0,
inference(forward_demodulation,[],[f212,f207]) ).
fof(f244,plain,
! [X2,X0,X1] : multiply(X1,X0) = inverse(multiply(multiply(inverse(X0),X2),inverse(multiply(X1,X2)))),
inference(forward_demodulation,[],[f230,f207]) ).
fof(f254,plain,
! [X0,X1] : inverse(multiply(multiply(inverse(X0),X1),inverse(X1))) = X0,
inference(forward_demodulation,[],[f237,f207]) ).
fof(f397,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X1,X0)))) = X1,
inference(superposition,[],[f254,f93]) ).
fof(f565,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
inference(superposition,[],[f397,f397]) ).
fof(f1065,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1),
inference(superposition,[],[f207,f565]) ).
fof(f1595,plain,
! [X2,X0,X1] : inverse(inverse(multiply(X0,X2))) = multiply(multiply(X0,X1),multiply(inverse(X1),X2)),
inference(superposition,[],[f1065,f244]) ).
fof(f1619,plain,
! [X2,X0,X1] : multiply(X0,X2) = multiply(multiply(X0,X1),multiply(inverse(X1),X2)),
inference(forward_demodulation,[],[f1595,f207]) ).
fof(f4738,plain,
! [X2,X0,X1] : multiply(X1,multiply(X2,X0)) = multiply(multiply(X1,X2),X0),
inference(superposition,[],[f1619,f93]) ).
fof(f4780,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f9,f4738]) ).
fof(f4840,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f4780]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f4840]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3]) ).
fof(f5064,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP450-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n026.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:07:56 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.86/1.38 % (2595842)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.86/1.38 % (2595852)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3757035418:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.86/1.38 % (2595847)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=3066442869:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.86/1.38 % (2595849)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=200399688:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.86/1.38 % (2595848)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=2345250388:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.86/1.38 % (2595850)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=479048225:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.86/1.38 % (2595853)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3497500211:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.86/1.38 % (2595851)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1849226213:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.86/1.38 % (2595852)First to succeed.
% 2.86/1.38 % (2595852)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2595842"
% 2.86/1.38 % (2595850)Also succeeded, but the first one will report.
% 2.86/1.38 % (2595851)Instruction limit reached!
% 2.86/1.38 % (2595851)------------------------------
% 2.86/1.38 % (2595851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.38 % (2595851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.38 % (2595851)CaDiCaL version: 2.1.3
% 2.86/1.38 % (2595851)Termination reason: Instruction limit
% 2.86/1.38 % (2595851)Termination phase: Saturation
% 2.86/1.38 % (2595851)Time elapsed: 0.104 s
% 2.86/1.38 % (2595851)Peak memory usage: 89 MB
% 2.86/1.38 % (2595851)Instructions burned: 182 (million)
% 2.86/1.38 % (2595852)Refutation found. Thanks to Tanya!
% 2.86/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.86/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.86/1.38 % (2595852)------------------------------
% 2.86/1.38 % (2595852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.38 % (2595852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.38 % (2595852)CaDiCaL version: 2.1.3
% 2.86/1.38 % (2595852)Termination reason: Refutation
% 2.86/1.38 % (2595852)Time elapsed: 0.058 s
% 2.86/1.38 % (2595852)Peak memory usage: 90 MB
% 2.86/1.38 % (2595852)Instructions burned: 180 (million)
% 2.86/1.38 % (2595852)------------------------------
% 2.86/1.38 % (2595852)------------------------------
% 2.86/1.38 % (2595842)Success in time 0.323 s
% 2.86/1.38 % Vampire exiting
%------------------------------------------------------------------------------