%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP595-1 : 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 10:14:56 AM UTC 2026
% Result : Unsatisfiable 3.93s 1.57s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 34 unt; 2 def)
% Number of atoms : 58 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 10 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(X2,X1)))))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f5,definition,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f8,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f3,f5]) ).
fof(f9,plain,
( multiply(multiply(a3,b3),c3) != inverse(double_divide(multiply(b3,c3),a3))
| spl0_1 ),
inference(forward_demodulation,[],[f7,f2]) ).
fof(f10,plain,
( multiply(multiply(a3,b3),c3) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| spl0_1 ),
inference(forward_demodulation,[],[f9,f2]) ).
fof(f11,plain,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,multiply(a3,b3)))
| spl0_1 ),
inference(forward_demodulation,[],[f10,f2]) ).
fof(f12,plain,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| spl0_1 ),
inference(forward_demodulation,[],[f11,f2]) ).
fof(f14,definition,
( spl0_2
<=> inverse(double_divide(inverse(double_divide(c3,b3)),a3)) = inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f16,plain,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| spl0_2 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f17,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f12,f5,f14]) ).
fof(f18,plain,
! [X2,X3,X0,X1] : double_divide(X2,X3) = inverse(double_divide(double_divide(X1,inverse(double_divide(X2,inverse(double_divide(X0,X3))))),inverse(double_divide(X1,X0)))),
inference(superposition,[],[f1,f1]) ).
fof(f19,plain,
! [X2,X0,X1] : inverse(double_divide(double_divide(double_divide(X1,X2),inverse(double_divide(X0,X2))),X0)) = X1,
inference(superposition,[],[f1,f1]) ).
fof(f21,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(double_divide(X1,X2),X0),double_divide(double_divide(X0,X3),inverse(double_divide(X2,X3))))) = X1,
inference(superposition,[],[f19,f19]) ).
fof(f22,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X0,X3),inverse(double_divide(X2,X3))) = inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,X0)))),
inference(superposition,[],[f1,f19]) ).
fof(f40,plain,
! [X2,X3,X0,X1,X4] : double_divide(X1,X2) = inverse(double_divide(double_divide(X3,inverse(double_divide(X1,X0))),inverse(double_divide(X3,double_divide(double_divide(X0,X4),inverse(double_divide(X2,X4))))))),
inference(superposition,[],[f18,f19]) ).
fof(f52,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(double_divide(X0,inverse(double_divide(X1,X2))),X1)),X2) = X0,
inference(superposition,[],[f19,f18]) ).
fof(f65,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(X0,inverse(double_divide(X1,inverse(double_divide(X2,X3))))),X1)) = double_divide(inverse(double_divide(X0,X2)),X3),
inference(superposition,[],[f52,f52]) ).
fof(f66,plain,
! [X2,X0,X1] : double_divide(double_divide(inverse(double_divide(X0,X1)),X2),inverse(double_divide(X1,X2))) = X0,
inference(superposition,[],[f52,f18]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4] : double_divide(inverse(double_divide(double_divide(X0,inverse(double_divide(X1,inverse(double_divide(X2,X3))))),X1)),X3) = inverse(double_divide(double_divide(X4,inverse(X0)),inverse(double_divide(X4,X2)))),
inference(superposition,[],[f18,f52]) ).
fof(f81,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0,inverse(double_divide(X1,inverse(double_divide(X2,X3))))),X1)),X3),inverse(X0))) = X2,
inference(superposition,[],[f1,f52]) ).
fof(f86,plain,
! [X2,X3,X0,X4] : inverse(double_divide(double_divide(X4,inverse(X0)),inverse(double_divide(X4,X2)))) = double_divide(double_divide(inverse(double_divide(X0,X2)),X3),X3),
inference(backward_demodulation,[],[f79,f65]) ).
fof(f88,plain,
! [X2,X3,X0] : inverse(double_divide(double_divide(double_divide(inverse(double_divide(X0,X2)),X3),X3),inverse(X0))) = X2,
inference(backward_demodulation,[],[f81,f65]) ).
fof(f118,plain,
! [X2,X3,X0,X1,X4] : double_divide(inverse(double_divide(X0,X1)),X2) = inverse(double_divide(double_divide(X0,X3),double_divide(double_divide(X3,X4),inverse(double_divide(inverse(double_divide(X1,X2)),X4))))),
inference(superposition,[],[f21,f66]) ).
fof(f137,plain,
! [X2,X0,X1] : double_divide(X0,X2) = double_divide(inverse(double_divide(X1,X0)),inverse(double_divide(inverse(X1),X2))),
inference(superposition,[],[f52,f88]) ).
fof(f184,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,X2)))),X1)) = X2,
inference(superposition,[],[f19,f22]) ).
fof(f255,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(double_divide(X1,X0),inverse(double_divide(double_divide(X2,X3),inverse(double_divide(X2,X0)))))),X3) = X1,
inference(superposition,[],[f52,f184]) ).
fof(f275,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(inverse(double_divide(X1,X2)),X3))) = double_divide(inverse(double_divide(X1,inverse(double_divide(X0,X2)))),X3),
inference(superposition,[],[f137,f1]) ).
fof(f295,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(inverse(X2),X1))))) = X2,
inference(superposition,[],[f66,f137]) ).
fof(f343,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X2,X3),inverse(double_divide(inverse(double_divide(double_divide(X1,X0),inverse(double_divide(X2,X0)))),X3))) = X1,
inference(backward_demodulation,[],[f255,f275]) ).
fof(f359,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X2,X3),inverse(double_divide(X2,inverse(double_divide(inverse(double_divide(double_divide(X1,X0),X0)),X3))))) = X1,
inference(forward_demodulation,[],[f343,f275]) ).
fof(f362,plain,
! [X0,X1] : double_divide(double_divide(X1,X0),X0) = X1,
inference(forward_demodulation,[],[f359,f295]) ).
fof(f376,plain,
! [X2,X0,X4] : inverse(double_divide(X0,X2)) = inverse(double_divide(double_divide(X4,inverse(X0)),inverse(double_divide(X4,X2)))),
inference(backward_demodulation,[],[f86,f362]) ).
fof(f416,plain,
! [X2,X0,X1,X4] : double_divide(X1,X2) = inverse(double_divide(double_divide(X1,X0),double_divide(double_divide(X0,X4),inverse(double_divide(X2,X4))))),
inference(backward_demodulation,[],[f40,f376]) ).
fof(f496,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(X1,X2))) = double_divide(inverse(double_divide(X0,X1)),X2),
inference(backward_demodulation,[],[f118,f416]) ).
fof(f609,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| spl0_2 ),
inference(backward_demodulation,[],[f16,f496]) ).
fof(f610,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f609]) ).
fof(f611,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f610]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f8]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f17]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f611]) ).
cnf(s4,plain,
spl0_1,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f663,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP595-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.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 10:10:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 3.93/1.57 % (2603859)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.93/1.57 % (2603887)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2507488959:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.93/1.57 % (2603889)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4289082203:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.93/1.57 % (2603885)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=739009903:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.93/1.57 % (2603891)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2856841379:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.93/1.57 % (2603884)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=2127131759:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.93/1.57 % (2603890)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1901389539:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.93/1.57 % (2603893)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3403080109:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.93/1.57 % (2603891)First to succeed.
% 3.93/1.57 % (2603889)Also succeeded, but the first one will report.
% 3.93/1.57 % (2603891)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2603859"
% 3.93/1.57 % (2603890)Instruction limit reached!
% 3.93/1.57 % (2603890)------------------------------
% 3.93/1.57 % (2603890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.57 % (2603890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.57 % (2603890)CaDiCaL version: 2.1.3
% 3.93/1.57 % (2603890)Termination reason: Instruction limit
% 3.93/1.57 % (2603890)Termination phase: Saturation
% 3.93/1.57 % (2603890)Time elapsed: 0.100 s
% 3.93/1.57 % (2603890)Peak memory usage: 90 MB
% 3.93/1.57 % (2603890)Instructions burned: 182 (million)
% 3.93/1.57 % (2603970)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1377215417:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.93/1.57 % (2603891)Refutation found. Thanks to Tanya!
% 3.93/1.57 % SZS status Unsatisfiable for theBenchmark
% 3.93/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 3.93/1.57 % (2603891)------------------------------
% 3.93/1.57 % (2603891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.57 % (2603891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.57 % (2603891)CaDiCaL version: 2.1.3
% 3.93/1.57 % (2603891)Termination reason: Refutation
% 3.93/1.57 % (2603891)Time elapsed: 0.070 s
% 3.93/1.57 % (2603891)Peak memory usage: 90 MB
% 3.93/1.57 % (2603891)Instructions burned: 115 (million)
% 3.93/1.57 % (2603891)------------------------------
% 3.93/1.57 % (2603891)------------------------------
% 3.93/1.57 % (2603859)Success in time 0.463 s
% 3.93/1.57 % Vampire exiting
%------------------------------------------------------------------------------