%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 2.75s 1.27s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 29
% Syntax : Number of formulae : 185 ( 16 unt; 14 def)
% Number of atoms : 564 ( 183 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 736 ( 357 ~; 365 |; 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 : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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_c7,sk_c4) = sk_c6
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = 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_c7,X2) != sk_c6
| multiply(X3,sk_c7) != X2
| inverse(X3) != sk_c7
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(sk_c6) != sk_c7 ),
file('/export/starexec/sandbox/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_c6 != multiply(sk_c7,X2)
| multiply(X3,sk_c7) != X2
| sk_c7 != 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_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != 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_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f59,plain,
( ! [X3] :
( sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) )
| ~ 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_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ 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_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f67,plain,
( sk_c7 = 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(f73,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f65,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(f78,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f42,f65,f75]) ).
fof(f80,definition,
( spl0_8
<=> sk_c4 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f82,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| ~ 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_c6 = multiply(sk_c7,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f89,plain,
( sk_c6 = multiply(sk_c7,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_c7,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(f129,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f121]) ).
fof(f132,plain,
( ! [X0] : multiply(sk_c7,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_c7 = multiply(sk_c7,sk_c4)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f132,f82]) ).
fof(f147,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f140,f89]) ).
fof(f155,plain,
( sk_c7 != inverse(sk_c7)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f53,f147]) ).
fof(f189,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f133,f117]) ).
fof(f193,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f133,f89]) ).
fof(f194,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_5 ),
inference(superposition,[],[f133,f121]) ).
fof(f212,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f193,f147]) ).
fof(f215,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f189,f110]) ).
fof(f220,plain,
( identity = sk_c4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f212,f3]) ).
fof(f224,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f133,f215]) ).
fof(f226,plain,
( identity = sk_c7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f224,f3]) ).
fof(f228,plain,
( sk_c7 = sk_c4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f226,f220]) ).
fof(f260,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c4)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f194,f220]) ).
fof(f261,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f260,f228]) ).
fof(f262,plain,
( identity = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f261,f3]) ).
fof(f263,plain,
( sk_c4 = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f262,f220]) ).
fof(f264,plain,
( sk_c7 = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f263,f228]) ).
fof(f269,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f67,f264]) ).
fof(f270,plain,
( $false
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f269,f155]) ).
fof(f271,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f279,plain,
( sk_c8 != sk_c8
| multiply(sk_c1,sk_c8) != sk_c7
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f56,f110]) ).
fof(f283,plain,
( multiply(sk_c1,sk_c8) != sk_c7
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f279]) ).
fof(f295,plain,
( $false
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f283,f117]) ).
fof(f296,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f295]) ).
fof(f345,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f194,f226]) ).
fof(f346,plain,
( identity = sk_c3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f345,f3]) ).
fof(f347,plain,
( sk_c7 = sk_c3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f346,f226]) ).
fof(f350,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f67,f347]) ).
fof(f353,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_1 ),
inference(superposition,[],[f3,f52]) ).
fof(f354,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f353,f226]) ).
fof(f358,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f133,f77]) ).
fof(f360,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f358,f72]) ).
fof(f365,plain,
( sk_c7 != sk_c6
| sk_c6 != inverse(identity)
| ~ spl0_4 ),
inference(superposition,[],[f62,f1]) ).
fof(f373,plain,
( sk_c6 != inverse(sk_c7)
| sk_c7 != sk_c6
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f365,f226]) ).
fof(f375,plain,
( sk_c7 != sk_c6
| sk_c7 != sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f373,f350]) ).
fof(f376,plain,
( sk_c7 != sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(duplicate_literal_removal,[],[f375]) ).
fof(f380,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f133,f354]) ).
fof(f383,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f380,f3]) ).
fof(f385,plain,
( sk_c7 = sk_c6
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f383,f226]) ).
fof(f386,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f385,f376]) ).
fof(f387,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f391,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(sk_c7,multiply(X3,sk_c7)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f59,f385]) ).
fof(f399,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c7,multiply(sk_c3,sk_c7))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f391,f67]) ).
fof(f400,plain,
( sk_c7 != multiply(sk_c7,multiply(sk_c3,sk_c7))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f399]) ).
fof(f403,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f400,f132]) ).
fof(f404,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f418,definition,
( spl0_20
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f419,plain,
( sk_c7 = sk_c6
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f424,definition,
( spl0_21
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f425,plain,
( identity = sk_c7
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f428,definition,
( spl0_22
<=> sk_c6 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f430,plain,
( sk_c6 != inverse(sk_c7)
| spl0_22 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f434,plain,
( identity != sk_c7
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4 ),
inference(superposition,[],[f62,f3]) ).
fof(f437,plain,
( sk_c6 != inverse(sk_c7)
| identity != sk_c7
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f434,f52]) ).
fof(f438,plain,
( ~ spl0_21
| ~ spl0_22
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f437,f61,f51,f428,f424]) ).
fof(f452,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f133,f360]) ).
fof(f454,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f452,f3]) ).
fof(f456,plain,
( spl0_21
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f454,f75,f70,f424]) ).
fof(f458,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_21 ),
inference(superposition,[],[f1,f425]) ).
fof(f466,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_21 ),
inference(superposition,[],[f353,f458]) ).
fof(f473,plain,
( sk_c7 = sk_c6
| ~ spl0_1
| ~ spl0_21 ),
inference(forward_demodulation,[],[f466,f425]) ).
fof(f476,plain,
( spl0_20
| ~ spl0_1
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f473,f424,f51,f418]) ).
fof(f480,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_1
| ~ spl0_20 ),
inference(superposition,[],[f52,f419]) ).
fof(f542,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_20
| spl0_22 ),
inference(superposition,[],[f430,f480]) ).
fof(f547,plain,
( $false
| ~ spl0_1
| ~ spl0_20
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f542,f419]) ).
fof(f548,plain,
( ~ spl0_1
| ~ spl0_20
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f547]) ).
fof(f549,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_3
| ~ spl0_21 ),
inference(forward_demodulation,[],[f59,f458]) ).
fof(f552,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c7) )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f549,f419]) ).
fof(f559,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c6,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f552,f52]) ).
fof(f562,plain,
( sk_c7 != multiply(sk_c6,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f559]) ).
fof(f565,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f562,f419]) ).
fof(f575,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f565,f458]) ).
fof(f576,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f575]) ).
fof(f582,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f56,f72]) ).
fof(f585,plain,
( sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f582]) ).
fof(f586,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f585,f77]) ).
fof(f587,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f586]) ).
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(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f73]) ).
cnf(s5,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f78]) ).
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,[],[f271]) ).
cnf(s26,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f296]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f387]) ).
cnf(s40,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f404]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f438]) ).
cnf(s46,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_21 ),
inference(sat_conversion,[],[f456]) ).
cnf(s47,plain,
( ~ spl0_1
| spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f476]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_20
| spl0_22 ),
inference(sat_conversion,[],[f548]) ).
cnf(s55,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f576]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f587]) ).
cnf(s58,plain,
spl0_1,
inference(rat,[],[s24,s3,s6,s9,s18,s21]) ).
cnf(s59,plain,
( spl0_6
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s39,s19,s22,s58]) ).
cnf(s60,plain,
( ~ spl0_21
| ~ spl0_4 ),
inference(rat,[],[s50,s45,s47,s58]) ).
cnf(s61,plain,
( ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s39,s20,s23,s46,s59,s60,s58]) ).
cnf(s62,plain,
~ spl0_4,
inference(rat,[],[s46,s4,s5,s61,s60]) ).
cnf(s63,plain,
( ~ spl0_21
| ~ spl0_3 ),
inference(rat,[],[s55,s47,s58]) ).
cnf(s64,plain,
( spl0_7
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s40,s20,s23,s58]) ).
cnf(s65,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s40,s19,s22,s46,s64,s63,s58]) ).
cnf(s66,plain,
~ spl0_3,
inference(rat,[],[s46,s4,s5,s65,s63]) ).
cnf(s67,plain,
spl0_2,
inference(rat,[],[s2,s62,s58,s66]) ).
cnf(s68,plain,
spl0_7,
inference(rat,[],[s26,s20,s23,s67]) ).
cnf(s69,plain,
~ spl0_6,
inference(rat,[],[s57,s67,s68]) ).
cnf(s70,plain,
spl0_13,
inference(rat,[],[s22,s69]) ).
cnf(s71,plain,
spl0_12,
inference(rat,[],[s19,s69]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s26,s67,s70,s71]) ).
fof(f588,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n015.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:47:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.75/1.27 % (1411923)Input is clausal, will run a generic CNF schedule.
% 2.75/1.27 % (1411928)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=2573433194:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.75/1.27 % (1411932)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1051583661:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.75/1.27 % (1411929)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3067796938:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.75/1.27 % (1411930)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=363844664:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.75/1.27 % (1411931)lrs+10_1_sil=8000:sp=occurrence:random_seed=149155019:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.75/1.27 % (1411931)Refutation not found, incomplete strategy
% 2.75/1.27 % (1411931)------------------------------
% 2.75/1.27 % (1411931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.27 % (1411931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.27 % (1411931)CaDiCaL version: 2.1.3
% 2.75/1.27 % (1411931)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.27 % (1411931)Time elapsed: 0.003 s
% 2.75/1.27 % (1411931)Peak memory usage: 88 MB
% 2.75/1.27 % (1411931)Instructions burned: 3 (million)
% 2.75/1.27 % (1411934)dis-21_1_sil=8000:lcm=predicate:random_seed=3096075863: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)
% 2.75/1.27 % (1411933)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2202505567:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.75/1.27 % (1411934)Refutation not found, incomplete strategy
% 2.75/1.27 % (1411934)------------------------------
% 2.75/1.27 % (1411934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.27 % (1411934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.27 % (1411934)CaDiCaL version: 2.1.3
% 2.75/1.27 % (1411934)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.27 % (1411934)Time elapsed: 0.002 s
% 2.75/1.27 % (1411934)Peak memory usage: 88 MB
% 2.75/1.27 % (1411934)Instructions burned: 1 (million)
% 2.75/1.27 % (1411933)First to succeed.
% 2.75/1.27 % (1411933)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1411923"
% 2.75/1.27 % (1411932)Instruction limit reached!
% 2.75/1.27 % (1411932)------------------------------
% 2.75/1.27 % (1411932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.27 % (1411932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.27 % (1411932)CaDiCaL version: 2.1.3
% 2.75/1.27 % (1411932)Termination reason: Instruction limit
% 2.75/1.27 % (1411932)Termination phase: Saturation
% 2.75/1.27 % (1411932)Time elapsed: 0.066 s
% 2.75/1.27 % (1411932)Peak memory usage: 89 MB
% 2.75/1.27 % (1411932)Instructions burned: 115 (million)
% 2.75/1.27 % (1411942)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=4164157674:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.75/1.27 % (1411942)Refutation not found, incomplete strategy
% 2.75/1.27 % (1411942)------------------------------
% 2.75/1.27 % (1411942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.27 % (1411942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.27 % (1411942)CaDiCaL version: 2.1.3
% 2.75/1.27 % (1411942)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.27 % (1411942)Time elapsed: 0.003 s
% 2.75/1.27 % (1411942)Peak memory usage: 88 MB
% 2.75/1.27 % (1411942)Instructions burned: 3 (million)
% 2.75/1.27 % (1411931)------------------------------
% 2.75/1.27 % (1411931)------------------------------
% 2.75/1.27 % (1411934)------------------------------
% 2.75/1.27 % (1411934)------------------------------
% 2.75/1.27 % (1411933)Refutation found. Thanks to Tanya!
% 2.75/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.75/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.47 % (1411933)------------------------------
% 3.59/1.47 % (1411933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.47 % (1411933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.47 % (1411933)CaDiCaL version: 2.1.3
% 3.59/1.47 % (1411933)Termination reason: Refutation
% 3.59/1.47 % (1411933)Time elapsed: 0.015 s
% 3.59/1.47 % (1411933)Peak memory usage: 89 MB
% 3.59/1.47 % (1411933)Instructions burned: 19 (million)
% 3.59/1.47 % (1411933)------------------------------
% 3.59/1.47 % (1411933)------------------------------
% 3.59/1.47 % (1411923)Success in time 0.429 s
% 3.59/1.47 % Vampire exiting
%------------------------------------------------------------------------------