%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP268-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 10:13:29 AM UTC 2026
% Result : Unsatisfiable 0.53s 1.00s
% Output : Refutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 27
% Syntax : Number of formulae : 180 ( 16 unt; 14 def)
% Number of atoms : 564 ( 168 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 743 ( 359 ~; 370 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c6,sk_c4)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(sk_c6,X2) != sk_c7
| multiply(X3,sk_c6) != X2
| inverse(X3) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(sk_c6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(sk_c6,X2)
| multiply(X3,sk_c6) != X2
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != inverse(sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,plain,
! [X3,X0,X1,X4] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != inverse(sk_c6) ),
inference(equality_resolution,[],[f48]) ).
fof(f51,definition,
( spl0_1
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( sk_c7 != inverse(sk_c6)
| spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl0_2
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f56,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,definition,
( spl0_3
<=> ! [X3] :
( sk_c7 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c6 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f59,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c7 != multiply(sk_c6,multiply(X3,sk_c6)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f62,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f49,f55,f61,f58,f55,f51]) ).
fof(f65,definition,
( spl0_5
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f67,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,plain,
( spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f65,f51]) ).
fof(f70,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f75,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f77,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f80,definition,
( spl0_8
<=> sk_c4 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f82,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,plain,
( spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f40,f80,f51]) ).
fof(f87,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c6,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f89,plain,
( sk_c7 = multiply(sk_c6,sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_1
| spl0_9 ),
inference(avatar_split_clause,[],[f34,f87,f51]) ).
fof(f108,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f110,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_1
| spl0_12 ),
inference(avatar_split_clause,[],[f16,f108,f51]) ).
fof(f112,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f14,f108,f70]) ).
fof(f113,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f12,f108,f75]) ).
fof(f115,definition,
( spl0_13
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f117,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_1
| spl0_13 ),
inference(avatar_split_clause,[],[f10,f115,f51]) ).
fof(f119,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f8,f115,f70]) ).
fof(f120,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f6,f115,f75]) ).
fof(f121,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_5 ),
inference(superposition,[],[f3,f67]) ).
fof(f126,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f127,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(sk_c7,X0)
| ~ spl0_13 ),
inference(superposition,[],[f4,f117]) ).
fof(f129,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f121]) ).
fof(f132,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = X0
| ~ spl0_5 ),
inference(forward_demodulation,[],[f129,f1]) ).
fof(f133,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f126,f1]) ).
fof(f140,plain,
( sk_c6 = multiply(sk_c6,sk_c4)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f132,f82]) ).
fof(f143,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f140,f89]) ).
fof(f148,plain,
( sk_c7 != inverse(sk_c7)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f53,f143]) ).
fof(f193,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f133,f117]) ).
fof(f202,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f133,f89]) ).
fof(f203,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_5 ),
inference(superposition,[],[f133,f121]) ).
fof(f218,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f203,f143]) ).
fof(f219,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f202,f143]) ).
fof(f225,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f193,f110]) ).
fof(f232,plain,
( identity = sk_c4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f219,f3]) ).
fof(f237,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f133,f225]) ).
fof(f239,plain,
( identity = sk_c7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f237,f3]) ).
fof(f241,plain,
( sk_c7 = sk_c4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f239,f232]) ).
fof(f257,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c4)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f218,f232]) ).
fof(f258,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f257,f241]) ).
fof(f259,plain,
( identity = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f258,f3]) ).
fof(f260,plain,
( sk_c4 = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f259,f232]) ).
fof(f261,plain,
( sk_c7 = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f260,f241]) ).
fof(f262,plain,
( sk_c6 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f67,f261]) ).
fof(f275,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f262,f143]) ).
fof(f278,plain,
( $false
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f275,f148]) ).
fof(f279,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f284,plain,
( sk_c8 != sk_c8
| multiply(sk_c1,sk_c8) != sk_c7
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f56,f110]) ).
fof(f288,plain,
( multiply(sk_c1,sk_c8) != sk_c7
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f284]) ).
fof(f300,plain,
( $false
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f288,f117]) ).
fof(f301,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f300]) ).
fof(f357,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_1 ),
inference(superposition,[],[f3,f52]) ).
fof(f358,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f357,f239]) ).
fof(f362,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f133,f77]) ).
fof(f364,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f362,f72]) ).
fof(f365,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f133,f358]) ).
fof(f367,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f365,f3]) ).
fof(f368,plain,
( sk_c7 = sk_c6
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f367,f239]) ).
fof(f379,definition,
( spl0_19
<=> sk_c7 = multiply(sk_c6,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f380,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f381,plain,
( sk_c7 != multiply(sk_c6,sk_c6)
| spl0_19 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f383,definition,
( spl0_20
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f384,plain,
( sk_c7 = sk_c6
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f401,plain,
( spl0_20
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f368,f115,f108,f51,f383]) ).
fof(f402,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_1
| ~ spl0_20 ),
inference(superposition,[],[f52,f384]) ).
fof(f408,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20 ),
inference(superposition,[],[f358,f384]) ).
fof(f410,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_20 ),
inference(superposition,[],[f62,f402]) ).
fof(f414,plain,
( sk_c7 != multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f410,f384]) ).
fof(f415,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f414,f358]) ).
fof(f416,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f415]) ).
fof(f417,plain,
( ! [X3] :
( sk_c7 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c6 != inverse(X3) )
| ~ spl0_3
| ~ spl0_20 ),
inference(forward_demodulation,[],[f59,f384]) ).
fof(f418,plain,
( ! [X3] :
( sk_c7 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) )
| ~ spl0_3
| ~ spl0_20 ),
inference(forward_demodulation,[],[f417,f384]) ).
fof(f433,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f381,f384]) ).
fof(f448,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f380,f384]) ).
fof(f449,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| sk_c7 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f418,f448]) ).
fof(f453,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f449,f448]) ).
fof(f454,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f453,f402]) ).
fof(f455,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f461,plain,
( $false
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f408,f433]) ).
fof(f462,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f461]) ).
fof(f464,plain,
( sk_c6 = multiply(inverse(sk_c7),identity)
| ~ spl0_1 ),
inference(superposition,[],[f133,f357]) ).
fof(f482,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13 ),
inference(superposition,[],[f127,f364]) ).
fof(f483,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f133,f364]) ).
fof(f485,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f483,f3]) ).
fof(f486,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f482,f117]) ).
fof(f515,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f464,f485]) ).
fof(f516,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f515,f3]) ).
fof(f517,plain,
( sk_c7 = sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f516,f485]) ).
fof(f520,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f433,f486]) ).
fof(f521,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f520]) ).
fof(f532,plain,
( spl0_20
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f517,f75,f70,f51,f383]) ).
fof(f544,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_20 ),
inference(superposition,[],[f357,f384]) ).
fof(f554,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f56,f72]) ).
fof(f557,plain,
( sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f554]) ).
fof(f559,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f557,f77]) ).
fof(f560,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f559]) ).
fof(f566,plain,
( identity != sk_c7
| ~ spl0_1
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f414,f357]) ).
fof(f573,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f566,f485]) ).
fof(f574,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f573]) ).
fof(f585,definition,
( spl0_27
<=> sk_c7 = multiply(sk_c7,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f597,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f544,f485]) ).
fof(f598,plain,
( ~ spl0_27
| spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f433,f383,f379,f585]) ).
fof(f607,plain,
( spl0_27
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f597,f383,f75,f70,f51,f585]) ).
cnf(s1,plain,
( spl0_2
| ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f68]) ).
cnf(s6,plain,
( spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f83]) ).
cnf(s9,plain,
( spl0_1
| spl0_9 ),
inference(sat_conversion,[],[f90]) ).
cnf(s18,plain,
( spl0_1
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s19,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s20,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s21,plain,
( spl0_1
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s22,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s23,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s24,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f279]) ).
cnf(s26,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f301]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f401]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20 ),
inference(sat_conversion,[],[f416]) ).
cnf(s46,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f455]) ).
cnf(s47,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f462]) ).
cnf(s49,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f521]) ).
cnf(s52,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_20 ),
inference(sat_conversion,[],[f532]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f560]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20 ),
inference(sat_conversion,[],[f574]) ).
cnf(s57,plain,
( spl0_19
| ~ spl0_20
| ~ spl0_27 ),
inference(sat_conversion,[],[f598]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| spl0_27 ),
inference(sat_conversion,[],[f607]) ).
cnf(s62,plain,
spl0_1,
inference(rat,[],[s24,s3,s6,s9,s18,s21]) ).
cnf(s63,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s42,s41,s19,s22,s62]) ).
cnf(s65,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s54,s52,s63,s62]) ).
cnf(s66,plain,
~ spl0_4,
inference(rat,[],[s42,s41,s20,s23,s65,s62]) ).
cnf(s67,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_3 ),
inference(rat,[],[s46,s47,s41,s62]) ).
cnf(s68,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s57,s46,s61,s52,s22,s23,s62]) ).
cnf(s69,plain,
( ~ spl0_13
| ~ spl0_3 ),
inference(rat,[],[s49,s46,s52,s19,s20,s67,s62]) ).
cnf(s70,plain,
~ spl0_3,
inference(rat,[],[s69,s68]) ).
cnf(s71,plain,
spl0_2,
inference(rat,[],[s2,s66,s62,s70]) ).
cnf(s72,plain,
spl0_13,
inference(rat,[],[s53,s22,s23,s71]) ).
cnf(s73,plain,
~ spl0_12,
inference(rat,[],[s26,s71,s72]) ).
cnf(s74,plain,
spl0_7,
inference(rat,[],[s20,s73]) ).
cnf(s75,plain,
spl0_6,
inference(rat,[],[s19,s73]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s53,s71,s74,s75]) ).
fof(f608,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP268-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:43:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.53/1.00 % (4163282)Input is clausal, will run a generic CNF schedule.
% 0.53/1.00 % (4163291)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=236364310:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.53/1.00 % (4163290)lrs+10_1_sil=8000:sp=occurrence:random_seed=2900551605:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.53/1.00 % (4163293)dis-21_1_sil=8000:lcm=predicate:random_seed=4004846883:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.53/1.00 % (4163288)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3789877640:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.53/1.00 % (4163292)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2540349915:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.53/1.00 % (4163289)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2936073443:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.53/1.00 % (4163287)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2506138465:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.53/1.00 % (4163293)Refutation not found, incomplete strategy
% 0.53/1.00 % (4163293)------------------------------
% 0.53/1.00 % (4163293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.53/1.00 % (4163293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/1.00 % (4163293)CaDiCaL version: 2.1.3
% 0.53/1.00 % (4163293)Termination reason: Refutation not found, incomplete strategy
% 0.53/1.00 % (4163293)Time elapsed: 0.002 s
% 0.53/1.00 % (4163293)Peak memory usage: 88 MB
% 0.53/1.00 % (4163293)Instructions burned: 1 (million)
% 0.53/1.00 % (4163290)Refutation not found, incomplete strategy
% 0.53/1.00 % (4163290)------------------------------
% 0.53/1.00 % (4163290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.53/1.00 % (4163290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/1.00 % (4163290)CaDiCaL version: 2.1.3
% 0.53/1.00 % (4163290)Termination reason: Refutation not found, incomplete strategy
% 0.53/1.00 % (4163290)Time elapsed: 0.003 s
% 0.53/1.00 % (4163290)Peak memory usage: 88 MB
% 0.53/1.00 % (4163290)Instructions burned: 3 (million)
% 0.53/1.00 % (4163292)First to succeed.
% 0.53/1.00 % (4163292)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4163282"
% 0.53/1.00 % (4163291)Instruction limit reached!
% 0.53/1.00 % (4163291)------------------------------
% 0.53/1.00 % (4163291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.53/1.00 % (4163291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/1.00 % (4163291)CaDiCaL version: 2.1.3
% 0.53/1.00 % (4163291)Termination reason: Instruction limit
% 0.53/1.00 % (4163291)Termination phase: Saturation
% 0.53/1.00 % (4163291)Time elapsed: 0.064 s
% 0.53/1.00 % (4163291)Peak memory usage: 89 MB
% 0.53/1.00 % (4163291)Instructions burned: 115 (million)
% 0.53/1.00 % (4163301)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2363355783:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.53/1.00 % (4163301)Refutation not found, incomplete strategy
% 0.53/1.00 % (4163301)------------------------------
% 0.53/1.00 % (4163301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.53/1.00 % (4163301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/1.00 % (4163301)CaDiCaL version: 2.1.3
% 0.53/1.00 % (4163301)Termination reason: Refutation not found, incomplete strategy
% 0.53/1.00 % (4163301)Time elapsed: 0.003 s
% 0.53/1.00 % (4163301)Peak memory usage: 88 MB
% 0.53/1.00 % (4163301)Instructions burned: 3 (million)
% 0.53/1.00 % (4163293)------------------------------
% 0.53/1.00 % (4163293)------------------------------
% 0.53/1.00 % (4163290)------------------------------
% 0.53/1.00 % (4163290)------------------------------
% 0.53/1.00 % (4163292)Refutation found. Thanks to Tanya!
% 0.53/1.00 % SZS status Unsatisfiable for theBenchmark
% 0.53/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 3.13/1.09 % (4163292)------------------------------
% 3.13/1.09 % (4163292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.09 % (4163292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.09 % (4163292)CaDiCaL version: 2.1.3
% 3.13/1.09 % (4163292)Termination reason: Refutation
% 3.13/1.09 % (4163292)Time elapsed: 0.014 s
% 3.13/1.09 % (4163292)Peak memory usage: 89 MB
% 3.13/1.09 % (4163292)Instructions burned: 20 (million)
% 3.13/1.09 % (4163292)------------------------------
% 3.13/1.09 % (4163292)------------------------------
% 3.13/1.09 % (4163282)Success in time 0.408 s
% 3.13/1.09 % Vampire exiting
%------------------------------------------------------------------------------