%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP614-1 : 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 : n009.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 10:14:59 AM UTC 2026
% Result : Unsatisfiable 0.54s 1.00s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 44 unt; 1 def)
% Number of atoms : 50 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 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 : 96 ( 0 sgn 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(inverse(double_divide(inverse(double_divide(X0,inverse(X1))),X2)),double_divide(X0,X2)) = X1,
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(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f4,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f3]) ).
fof(f6,definition,
( spl0_1
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f8,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_1 ),
inference(avatar_component_clause,[],[f6]) ).
fof(f9,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f4,f6]) ).
fof(f10,plain,
! [X2,X0,X1] : double_divide(multiply(X2,inverse(double_divide(X0,inverse(X1)))),double_divide(X0,X2)) = X1,
inference(backward_demodulation,[],[f1,f2]) ).
fof(f11,plain,
! [X2,X0,X1] : double_divide(multiply(X2,multiply(inverse(X1),X0)),double_divide(X0,X2)) = X1,
inference(forward_demodulation,[],[f10,f2]) ).
fof(f12,plain,
! [X2,X3,X0,X1] : double_divide(X1,X0) = double_divide(multiply(X2,multiply(multiply(X0,X1),X3)),double_divide(X3,X2)),
inference(superposition,[],[f11,f2]) ).
fof(f13,plain,
! [X2,X3,X0,X1] : double_divide(multiply(double_divide(X1,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(X0),X1)))),X0) = X3,
inference(superposition,[],[f11,f11]) ).
fof(f14,plain,
! [X2,X0,X1] : inverse(X0) = multiply(double_divide(X1,X2),multiply(X2,multiply(inverse(X0),X1))),
inference(superposition,[],[f2,f11]) ).
fof(f15,plain,
! [X2,X3,X0,X1] : inverse(X1) = multiply(X0,multiply(double_divide(X3,X2),multiply(inverse(X1),multiply(X2,multiply(inverse(X0),X3))))),
inference(superposition,[],[f14,f11]) ).
fof(f87,plain,
! [X2,X3,X0,X1] : inverse(X1) = multiply(X0,multiply(double_divide(multiply(X2,multiply(inverse(inverse(X1)),X3)),double_divide(X3,X2)),inverse(X0))),
inference(superposition,[],[f15,f15]) ).
fof(f91,plain,
! [X2,X3,X0,X1] : double_divide(multiply(double_divide(multiply(X1,multiply(inverse(inverse(X2)),X3)),double_divide(X3,X1)),inverse(X0)),X0) = X2,
inference(superposition,[],[f13,f15]) ).
fof(f100,plain,
! [X2,X0] : double_divide(multiply(inverse(X2),inverse(X0)),X0) = X2,
inference(forward_demodulation,[],[f91,f11]) ).
fof(f102,plain,
! [X0,X1] : inverse(X1) = multiply(X0,multiply(inverse(X1),inverse(X0))),
inference(forward_demodulation,[],[f87,f11]) ).
fof(f104,plain,
! [X2,X0,X1] : double_divide(multiply(inverse(X2),multiply(X0,X1)),double_divide(X1,X0)) = X2,
inference(superposition,[],[f100,f2]) ).
fof(f115,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(X2,multiply(multiply(X0,X1),inverse(X2))),
inference(superposition,[],[f102,f2]) ).
fof(f120,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(inverse(X1),X1)) = X0,
inference(superposition,[],[f11,f102]) ).
fof(f134,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(multiply(X0,X1),double_divide(inverse(X2),X2)),
inference(superposition,[],[f120,f2]) ).
fof(f360,plain,
! [X2,X3,X0,X1] : double_divide(multiply(X2,multiply(X0,X1)),double_divide(multiply(multiply(X0,X1),inverse(inverse(X3))),X2)) = X3,
inference(superposition,[],[f11,f115]) ).
fof(f370,plain,
! [X2,X3,X0,X1,X4] : double_divide(X2,X3) = double_divide(multiply(X4,multiply(X0,X1)),double_divide(multiply(multiply(X0,X1),inverse(multiply(X3,X2))),X4)),
inference(superposition,[],[f12,f115]) ).
fof(f398,plain,
! [X0,X1] : double_divide(multiply(X0,inverse(X0)),inverse(X1)) = X1,
inference(superposition,[],[f104,f134]) ).
fof(f528,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X0),multiply(X1,inverse(X1))),
inference(superposition,[],[f2,f398]) ).
fof(f529,plain,
! [X2,X0,X1] : double_divide(multiply(inverse(X0),multiply(inverse(X1),multiply(X2,inverse(X2)))),X0) = X1,
inference(superposition,[],[f11,f398]) ).
fof(f541,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X0) = X1,
inference(backward_demodulation,[],[f529,f528]) ).
fof(f556,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f398,f541]) ).
fof(f559,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),X1))) = X0,
inference(superposition,[],[f134,f541]) ).
fof(f579,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(X1,inverse(X1))) = X0,
inference(forward_demodulation,[],[f559,f2]) ).
fof(f620,plain,
! [X2,X3,X0,X1] : double_divide(multiply(X2,multiply(X0,X1)),double_divide(multiply(multiply(X0,X1),X3),X2)) = X3,
inference(backward_demodulation,[],[f360,f556]) ).
fof(f634,plain,
! [X2,X3] : double_divide(X2,X3) = inverse(multiply(X3,X2)),
inference(backward_demodulation,[],[f370,f620]) ).
fof(f828,plain,
! [X0,X1] : inverse(multiply(multiply(X1,inverse(X1)),inverse(X0))) = X0,
inference(backward_demodulation,[],[f579,f634]) ).
fof(f1148,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X1))) = X0,
inference(superposition,[],[f102,f556]) ).
fof(f1157,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(superposition,[],[f1148,f556]) ).
fof(f1160,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(superposition,[],[f1157,f1157]) ).
fof(f1192,plain,
! [X0,X1] : multiply(inverse(X1),inverse(X0)) = inverse(multiply(X1,X0)),
inference(superposition,[],[f1157,f1160]) ).
fof(f1276,plain,
! [X0,X1] : multiply(inverse(multiply(X1,inverse(X1))),inverse(inverse(X0))) = X0,
inference(backward_demodulation,[],[f828,f1192]) ).
fof(f1304,plain,
! [X0,X1] : multiply(inverse(multiply(X1,inverse(X1))),X0) = X0,
inference(forward_demodulation,[],[f1276,f556]) ).
fof(f1378,plain,
! [X0,X1] : multiply(multiply(inverse(X1),inverse(inverse(X1))),X0) = X0,
inference(forward_demodulation,[],[f1304,f1192]) ).
fof(f1436,plain,
! [X0,X1] : multiply(multiply(inverse(X1),X1),X0) = X0,
inference(forward_demodulation,[],[f1378,f556]) ).
fof(f1485,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f8,f1436]) ).
fof(f1486,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1485]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f9]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1486]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
fof(f1680,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP614-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n009.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 10:09:30 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.54/1.00 % (1798709)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.54/1.00 % (1798719)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2949747402:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.54/1.00 % (1798717)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=727749855:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.54/1.00 % (1798720)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4169603770:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.54/1.00 % (1798716)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3981409092:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.54/1.00 % (1798715)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=4162443054:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.54/1.00 % (1798714)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=3046044224:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.54/1.00 % (1798718)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4074245522:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.54/1.00 % (1798719)First to succeed.
% 0.54/1.00 % (1798719)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1798709"
% 0.54/1.00 % (1798720)Also succeeded, but the first one will report.
% 0.54/1.00 % (1798718)Also succeeded, but the first one will report.
% 0.54/1.00 % (1798717)Instruction limit reached!
% 0.54/1.00 % (1798717)------------------------------
% 0.54/1.00 % (1798717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/1.00 % (1798717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/1.00 % (1798717)CaDiCaL version: 2.1.3
% 0.54/1.00 % (1798717)Termination reason: Instruction limit
% 0.54/1.00 % (1798717)Termination phase: Saturation
% 0.54/1.00 % (1798717)Time elapsed: 0.082 s
% 0.54/1.00 % (1798717)Peak memory usage: 88 MB
% 0.54/1.00 % (1798717)Instructions burned: 137 (million)
% 0.54/1.00 % (1798719)Refutation found. Thanks to Tanya!
% 0.54/1.00 % SZS status Unsatisfiable for theBenchmark
% 0.54/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 0.54/1.00 % (1798719)------------------------------
% 0.54/1.00 % (1798719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/1.00 % (1798719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/1.00 % (1798719)CaDiCaL version: 2.1.3
% 0.54/1.00 % (1798719)Termination reason: Refutation
% 0.54/1.00 % (1798719)Time elapsed: 0.051 s
% 0.54/1.00 % (1798719)Peak memory usage: 90 MB
% 0.54/1.00 % (1798719)Instructions burned: 158 (million)
% 0.54/1.00 % (1798719)------------------------------
% 0.54/1.00 % (1798719)------------------------------
% 0.54/1.00 % (1798709)Success in time 0.314 s
% 0.54/1.00 % Vampire exiting
%------------------------------------------------------------------------------