TSTP Solution File: GRP105-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP105-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:53:24 EDT 2024
% Result : Unsatisfiable 1.58s 0.57s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 3
% Syntax : Number of formulae : 87 ( 77 unt; 0 def)
% Number of atoms : 108 ( 107 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 33 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 190 ( 190 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8108,plain,
$false,
inference(trivial_inequality_removal,[],[f8105]) ).
fof(f8105,plain,
a2 != a2,
inference(superposition,[],[f8070,f424]) ).
fof(f424,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = X1,
inference(superposition,[],[f249,f327]) ).
fof(f327,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f317,f157]) ).
fof(f157,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(superposition,[],[f86,f74]) ).
fof(f74,plain,
! [X0,X1] : double_divide(inverse(multiply(inverse(X0),X0)),inverse(X1)) = X1,
inference(superposition,[],[f40,f53]) ).
fof(f53,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(X1),multiply(inverse(X0),X0)),
inference(superposition,[],[f2,f40]) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f40,plain,
! [X0,X1] : double_divide(multiply(inverse(X1),X1),inverse(X0)) = X0,
inference(superposition,[],[f7,f8]) ).
fof(f8,plain,
! [X2,X0,X1] : inverse(X0) = multiply(X2,multiply(multiply(inverse(X0),X1),double_divide(X1,X2))),
inference(superposition,[],[f2,f5]) ).
fof(f5,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(inverse(X2),X0),double_divide(X0,X1)),X1) = X2,
inference(forward_demodulation,[],[f4,f2]) ).
fof(f4,plain,
! [X2,X0,X1] : double_divide(multiply(inverse(double_divide(X0,inverse(X2))),double_divide(X0,X1)),X1) = X2,
inference(forward_demodulation,[],[f1,f2]) ).
fof(f1,axiom,
! [X2,X0,X1] : double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(X2))))),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f7,plain,
! [X2,X3,X0,X1] : double_divide(multiply(multiply(inverse(X3),multiply(multiply(inverse(X0),X1),double_divide(X1,X2))),X0),X2) = X3,
inference(superposition,[],[f5,f5]) ).
fof(f86,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(multiply(inverse(X1),X0))) = X0,
inference(superposition,[],[f54,f55]) ).
fof(f55,plain,
! [X2,X1] : inverse(X2) = multiply(inverse(X1),multiply(inverse(X2),X1)),
inference(backward_demodulation,[],[f51,f53]) ).
fof(f51,plain,
! [X2,X0,X1] : inverse(X2) = multiply(inverse(X1),multiply(multiply(inverse(X2),multiply(inverse(X0),X0)),X1)),
inference(superposition,[],[f8,f40]) ).
fof(f54,plain,
! [X2,X1] : double_divide(multiply(inverse(X2),X1),inverse(X1)) = X2,
inference(backward_demodulation,[],[f52,f53]) ).
fof(f52,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(inverse(X2),multiply(inverse(X0),X0)),X1),inverse(X1)) = X2,
inference(superposition,[],[f5,f40]) ).
fof(f317,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(multiply(inverse(X1),X1)),X0),
inference(superposition,[],[f253,f70]) ).
fof(f70,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(inverse(X1),X1))) = X0,
inference(superposition,[],[f54,f53]) ).
fof(f253,plain,
! [X2,X0] : inverse(X0) = multiply(X2,double_divide(X0,X2)),
inference(backward_demodulation,[],[f127,f249]) ).
fof(f127,plain,
! [X2,X0,X1] : inverse(X0) = multiply(X2,multiply(multiply(inverse(X1),X1),double_divide(X0,X2))),
inference(superposition,[],[f8,f105]) ).
fof(f105,plain,
! [X0,X1] : multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f74,f70]) ).
fof(f249,plain,
! [X2,X1] : multiply(multiply(inverse(X1),X1),X2) = X2,
inference(forward_demodulation,[],[f237,f2]) ).
fof(f237,plain,
! [X2,X1] : multiply(inverse(double_divide(X1,inverse(X1))),X2) = X2,
inference(superposition,[],[f157,f196]) ).
fof(f196,plain,
! [X0,X1] : multiply(inverse(X0),X0) = double_divide(X1,inverse(X1)),
inference(superposition,[],[f54,f157]) ).
fof(f8070,plain,
a2 != multiply(multiply(b2,inverse(b2)),a2),
inference(equality_resolution,[],[f3470]) ).
fof(f3470,plain,
! [X0] :
( multiply(X0,inverse(X0)) != multiply(a1,inverse(a1))
| a2 != multiply(multiply(b2,inverse(b2)),a2) ),
inference(superposition,[],[f2546,f697]) ).
fof(f697,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[],[f458,f424]) ).
fof(f458,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(superposition,[],[f404,f327]) ).
fof(f404,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(superposition,[],[f53,f327]) ).
fof(f2546,plain,
( multiply(b1,inverse(b1)) != multiply(a1,inverse(a1))
| a2 != multiply(multiply(b2,inverse(b2)),a2) ),
inference(trivial_inequality_removal,[],[f2545]) ).
fof(f2545,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1))
| a2 != multiply(multiply(b2,inverse(b2)),a2) ),
inference(forward_demodulation,[],[f2544,f797]) ).
fof(f797,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f777,f327]) ).
fof(f777,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,inverse(inverse(X0))),
inference(superposition,[],[f499,f432]) ).
fof(f432,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(superposition,[],[f358,f327]) ).
fof(f358,plain,
! [X0,X1] : multiply(multiply(inverse(X1),X0),X1) = X0,
inference(backward_demodulation,[],[f334,f321]) ).
fof(f321,plain,
! [X0,X1] : multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[],[f253,f54]) ).
fof(f334,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),X1)),X1) = X0,
inference(forward_demodulation,[],[f318,f327]) ).
fof(f318,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(multiply(inverse(X0),X1)),X1),
inference(superposition,[],[f253,f86]) ).
fof(f499,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[],[f493,f2]) ).
fof(f493,plain,
! [X0,X1] : multiply(inverse(double_divide(X1,X0)),inverse(X1)) = X0,
inference(superposition,[],[f407,f253]) ).
fof(f407,plain,
! [X0,X1] : multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(superposition,[],[f55,f327]) ).
fof(f2544,plain,
( multiply(b1,inverse(b1)) != multiply(a1,inverse(a1))
| a2 != multiply(multiply(b2,inverse(b2)),a2)
| multiply(a4,b4) != multiply(b4,a4) ),
inference(forward_demodulation,[],[f2543,f797]) ).
fof(f2543,plain,
( multiply(inverse(a1),a1) != multiply(b1,inverse(b1))
| a2 != multiply(multiply(b2,inverse(b2)),a2)
| multiply(a4,b4) != multiply(b4,a4) ),
inference(forward_demodulation,[],[f2542,f797]) ).
fof(f2542,plain,
( a2 != multiply(multiply(b2,inverse(b2)),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a4,b4) != multiply(b4,a4) ),
inference(forward_demodulation,[],[f2541,f797]) ).
fof(f2541,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a4,b4) != multiply(b4,a4) ),
inference(trivial_inequality_removal,[],[f2540]) ).
fof(f2540,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a4,b4) != multiply(b4,a4) ),
inference(forward_demodulation,[],[f2521,f797]) ).
fof(f2521,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(c3,b3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a4,b4) != multiply(b4,a4) ),
inference(backward_demodulation,[],[f3,f2475]) ).
fof(f2475,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X2),X1),
inference(forward_demodulation,[],[f2474,f517]) ).
fof(f517,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(superposition,[],[f253,f504]) ).
fof(f504,plain,
! [X0,X1] : double_divide(double_divide(X1,X0),X1) = X0,
inference(superposition,[],[f502,f502]) ).
fof(f502,plain,
! [X0,X1] : double_divide(X1,double_divide(X0,X1)) = X0,
inference(forward_demodulation,[],[f496,f400]) ).
fof(f400,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(multiply(X1,X0)),
inference(superposition,[],[f327,f2]) ).
fof(f496,plain,
! [X0,X1] : double_divide(X1,inverse(multiply(X1,X0))) = X0,
inference(superposition,[],[f54,f407]) ).
fof(f2474,plain,
! [X2,X0,X1] : inverse(double_divide(X0,multiply(X1,X2))) = multiply(multiply(X0,X2),X1),
inference(forward_demodulation,[],[f2433,f1028]) ).
fof(f1028,plain,
! [X2,X3,X0] : double_divide(double_divide(X3,X2),inverse(X0)) = multiply(multiply(X2,X3),X0),
inference(forward_demodulation,[],[f916,f404]) ).
fof(f916,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X3,X2),inverse(X0)) = multiply(multiply(multiply(X2,X3),X0),multiply(inverse(X1),X1)),
inference(superposition,[],[f276,f196]) ).
fof(f276,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(X0,X1),X2),double_divide(X2,X3)) = double_divide(double_divide(X1,X0),X3),
inference(superposition,[],[f255,f6]) ).
fof(f6,plain,
! [X2,X3,X0,X1] : double_divide(X0,X1) = double_divide(multiply(multiply(multiply(X1,X0),X2),double_divide(X2,X3)),X3),
inference(superposition,[],[f5,f2]) ).
fof(f255,plain,
! [X2,X1] : double_divide(double_divide(X2,X1),X1) = X2,
inference(backward_demodulation,[],[f5,f251]) ).
fof(f251,plain,
! [X2,X0,X1] : multiply(multiply(inverse(X0),X1),double_divide(X1,X2)) = double_divide(X0,X2),
inference(backward_demodulation,[],[f129,f249]) ).
fof(f129,plain,
! [X2,X3,X0,X1] : multiply(multiply(inverse(X0),X1),double_divide(X1,X2)) = double_divide(multiply(multiply(inverse(X3),X3),X0),X2),
inference(superposition,[],[f7,f105]) ).
fof(f2433,plain,
! [X2,X0,X1] : inverse(double_divide(X0,multiply(X1,X2))) = double_divide(double_divide(X2,X0),inverse(X1)),
inference(superposition,[],[f405,f1436]) ).
fof(f1436,plain,
! [X2,X0,X1] : double_divide(X0,X2) = multiply(double_divide(X2,multiply(X1,X0)),X1),
inference(backward_demodulation,[],[f965,f1433]) ).
fof(f1433,plain,
! [X2,X0,X1] : double_divide(X2,multiply(X1,X0)) = double_divide(multiply(X2,X1),X0),
inference(backward_demodulation,[],[f969,f1389]) ).
fof(f1389,plain,
! [X2,X0,X1] : double_divide(X2,multiply(X0,X1)) = multiply(double_divide(X1,X2),inverse(X0)),
inference(superposition,[],[f965,f432]) ).
fof(f969,plain,
! [X2,X0,X1] : multiply(double_divide(X0,X2),inverse(X1)) = double_divide(multiply(X2,X1),X0),
inference(backward_demodulation,[],[f774,f960]) ).
fof(f960,plain,
! [X2,X0,X4] : multiply(inverse(X4),double_divide(X0,X2)) = double_divide(multiply(X2,X0),X4),
inference(forward_demodulation,[],[f959,f594]) ).
fof(f594,plain,
! [X2,X0,X1] : multiply(X2,X0) = double_divide(X1,multiply(inverse(X0),double_divide(X1,X2))),
inference(forward_demodulation,[],[f541,f2]) ).
fof(f541,plain,
! [X2,X0,X1] : inverse(double_divide(X0,X2)) = double_divide(X1,multiply(inverse(X0),double_divide(X1,X2))),
inference(superposition,[],[f400,f378]) ).
fof(f378,plain,
! [X2,X0,X1] : double_divide(X0,X2) = multiply(multiply(inverse(X0),double_divide(X1,X2)),X1),
inference(superposition,[],[f255,f256]) ).
fof(f256,plain,
! [X2,X3,X0] : double_divide(multiply(multiply(inverse(X3),double_divide(X0,X2)),X0),X2) = X3,
inference(backward_demodulation,[],[f7,f251]) ).
fof(f959,plain,
! [X2,X0,X1,X4] : multiply(inverse(X4),double_divide(X0,X2)) = double_divide(double_divide(X1,multiply(inverse(X0),double_divide(X1,X2))),X4),
inference(forward_demodulation,[],[f891,f951]) ).
fof(f951,plain,
! [X2,X3,X1] : multiply(inverse(X3),X1) = multiply(multiply(X1,X2),double_divide(X2,X3)),
inference(forward_demodulation,[],[f950,f331]) ).
fof(f331,plain,
! [X0,X1] : multiply(inverse(X1),X0) = double_divide(inverse(X0),X1),
inference(backward_demodulation,[],[f154,f327]) ).
fof(f154,plain,
! [X0,X1] : multiply(inverse(X1),X0) = double_divide(inverse(X0),inverse(inverse(X1))),
inference(superposition,[],[f86,f55]) ).
fof(f950,plain,
! [X2,X3,X1] : multiply(multiply(X1,X2),double_divide(X2,X3)) = double_divide(inverse(X1),X3),
inference(forward_demodulation,[],[f889,f357]) ).
fof(f357,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,multiply(inverse(X1),X0)),
inference(backward_demodulation,[],[f274,f321]) ).
fof(f274,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,inverse(multiply(inverse(X0),X1))),
inference(superposition,[],[f255,f86]) ).
fof(f889,plain,
! [X2,X3,X0,X1] : multiply(multiply(X1,X2),double_divide(X2,X3)) = double_divide(double_divide(X0,multiply(inverse(X0),X1)),X3),
inference(superposition,[],[f276,f358]) ).
fof(f891,plain,
! [X2,X3,X0,X1,X4] : double_divide(double_divide(X1,multiply(inverse(X0),double_divide(X1,X2))),X4) = multiply(multiply(double_divide(X0,X2),X3),double_divide(X3,X4)),
inference(superposition,[],[f276,f378]) ).
fof(f774,plain,
! [X2,X0,X1] : multiply(inverse(X0),double_divide(X1,X2)) = multiply(double_divide(X0,X2),inverse(X1)),
inference(superposition,[],[f499,f378]) ).
fof(f965,plain,
! [X2,X0,X1] : double_divide(X0,X2) = multiply(double_divide(multiply(X2,X1),X0),X1),
inference(backward_demodulation,[],[f378,f960]) ).
fof(f405,plain,
! [X0,X1] : inverse(X0) = double_divide(multiply(X0,X1),inverse(X1)),
inference(superposition,[],[f54,f327]) ).
fof(f3,axiom,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP105-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 20:41:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (10367)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (10371)WARNING: value z3 for option sas not known
% 0.20/0.37 % (10372)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (10370)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (10373)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.37 % (10374)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.37 % (10371)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.37 % (10369)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (10375)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.37 TRYING [1]
% 0.20/0.37 TRYING [2]
% 0.20/0.37 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 TRYING [3]
% 0.20/0.38 TRYING [3]
% 0.20/0.39 TRYING [4]
% 0.20/0.49 TRYING [5]
% 1.58/0.57 % (10374)First to succeed.
% 1.58/0.57 % (10374)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10367"
% 1.58/0.57 % (10374)Refutation found. Thanks to Tanya!
% 1.58/0.57 % SZS status Unsatisfiable for theBenchmark
% 1.58/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.58/0.57 % (10374)------------------------------
% 1.58/0.57 % (10374)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.58/0.57 % (10374)Termination reason: Refutation
% 1.58/0.57
% 1.58/0.57 % (10374)Memory used [KB]: 3132
% 1.58/0.57 % (10374)Time elapsed: 0.196 s
% 1.58/0.57 % (10374)Instructions burned: 444 (million)
% 1.58/0.57 % (10367)Success in time 0.205 s
%------------------------------------------------------------------------------