%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP332-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 10:17:31 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 51
% Syntax : Number of formulae : 327 ( 21 unt; 19 def)
% Number of atoms : 1035 ( 302 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1342 ( 634 ~; 689 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c6 != multiply(sk_c8,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f67,f85,f82,f79,f75,f72,f69]) ).
fof(f90,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f64,f94,f90]) ).
fof(f99,definition,
( spl0_9
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f62,f94,f99]) ).
fof(f104,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f60,f94,f104]) ).
fof(f109,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f94,f109]) ).
fof(f114,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f116,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f94,f114]) ).
fof(f118,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f94,f75]) ).
fof(f120,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f122,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f120,f90]) ).
fof(f124,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f120,f99]) ).
fof(f125,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f120,f104]) ).
fof(f126,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f120,f109]) ).
fof(f127,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f120,f114]) ).
fof(f128,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f120,f75]) ).
fof(f130,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f132,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f130,f90]) ).
fof(f134,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f130,f99]) ).
fof(f135,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f130,f104]) ).
fof(f136,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f130,f109]) ).
fof(f137,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f130,f114]) ).
fof(f138,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f130,f75]) ).
fof(f140,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f142,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f140,f90]) ).
fof(f144,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f140,f99]) ).
fof(f145,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f140,f104]) ).
fof(f146,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f140,f109]) ).
fof(f147,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f140,f114]) ).
fof(f148,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f140,f75]) ).
fof(f149,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f85,f90]) ).
fof(f150,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f85,f99]) ).
fof(f151,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f85,f104]) ).
fof(f154,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f75]) ).
fof(f155,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f3,f92]) ).
fof(f156,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f111]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f164,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f167,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f155]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f171,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f168,f101]) ).
fof(f174,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f171,f106]) ).
fof(f178,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f76,f174]) ).
fof(f179,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f87,f174]) ).
fof(f184,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f156,f174]) ).
fof(f192,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f179,f178]) ).
fof(f193,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f195,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(identity)
| ~ spl0_4 ),
inference(superposition,[],[f80,f1]) ).
fof(f203,definition,
( spl0_17
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f204,plain,
( identity = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f205,plain,
( identity != sk_c7
| spl0_17 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f208,definition,
( spl0_18
<=> sk_c7 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f209,plain,
( sk_c7 = inverse(identity)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f210,plain,
( sk_c7 != inverse(identity)
| spl0_18 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f212,definition,
( spl0_19
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f213,plain,
( sk_c7 = sk_c6
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f195,f79,f212,f208]) ).
fof(f293,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f164,f116]) ).
fof(f307,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f293,f111]) ).
fof(f321,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f307,f174]) ).
fof(f329,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f178,f321]) ).
fof(f333,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f164,f321]) ).
fof(f335,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f333,f3]) ).
fof(f345,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f70,f174]) ).
fof(f346,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f329,f114,f109,f104,f99,f90,f75,f212]) ).
fof(f347,plain,
( spl0_17
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f335,f114,f109,f104,f99,f90,f203]) ).
fof(f348,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(sk_c7,multiply(X4,sk_c7)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f345,f174]) ).
fof(f356,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f184,f204]) ).
fof(f364,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f356,f1]) ).
fof(f378,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c7 != multiply(sk_c7,multiply(X4,sk_c7)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f348,f204]) ).
fof(f379,plain,
( ! [X4] :
( identity != multiply(identity,multiply(X4,identity))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f378,f204]) ).
fof(f380,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f379,f1]) ).
fof(f381,plain,
( identity = sk_c6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f213,f204]) ).
fof(f382,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f380,f1]) ).
fof(f386,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f382]) ).
fof(f389,plain,
( sk_c8 = inverse(identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f111,f364]) ).
fof(f398,plain,
( sk_c7 = inverse(identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f389,f174]) ).
fof(f400,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f398,f204]) ).
fof(f401,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f400,f386]) ).
fof(f402,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f401]) ).
fof(f473,plain,
( identity != inverse(identity)
| ~ spl0_17
| spl0_18 ),
inference(forward_demodulation,[],[f210,f204]) ).
fof(f526,plain,
( identity = inverse(sk_c2)
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f122,f204]) ).
fof(f531,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f86,f381]) ).
fof(f541,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f531,f204]) ).
fof(f545,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f541,f1]) ).
fof(f552,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f156,f545]) ).
fof(f555,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_11
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f552,f1]) ).
fof(f566,plain,
( sk_c8 = inverse(identity)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f111,f555]) ).
fof(f571,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f566,f545]) ).
fof(f573,plain,
( $false
| ~ spl0_6
| ~ spl0_11
| ~ spl0_17
| spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f571,f473]) ).
fof(f574,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_17
| spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f573]) ).
fof(f591,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f3,f526]) ).
fof(f592,plain,
( identity = sk_c2
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f591,f1]) ).
fof(f594,plain,
( identity = inverse(identity)
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f526,f592]) ).
fof(f595,plain,
( $false
| ~ spl0_13
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f594,f473]) ).
fof(f596,plain,
( ~ spl0_13
| ~ spl0_17
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f595]) ).
fof(f597,plain,
( identity = inverse(identity)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f209,f204]) ).
fof(f608,plain,
( ! [X4] :
( identity != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f70,f204]) ).
fof(f636,plain,
( ! [X4] :
( identity != multiply(identity,multiply(X4,identity))
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f608,f545]) ).
fof(f637,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f636,f1]) ).
fof(f638,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f637,f545]) ).
fof(f639,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f638,f1]) ).
fof(f643,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f639]) ).
fof(f654,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f643,f597]) ).
fof(f655,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f654]) ).
fof(f656,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f83,f204]) ).
fof(f657,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f656,f545]) ).
fof(f658,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f657,f204]) ).
fof(f661,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f658,f3]) ).
fof(f662,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f661]) ).
fof(f664,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f662,f597]) ).
fof(f667,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f664,f597]) ).
fof(f668,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f669,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f73,f545]) ).
fof(f670,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f669,f204]) ).
fof(f671,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f670,f545]) ).
fof(f674,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f671,f3]) ).
fof(f675,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f674]) ).
fof(f677,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f675,f597]) ).
fof(f680,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f677,f597]) ).
fof(f681,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f682,plain,
( sk_c6 != multiply(sk_c8,identity)
| spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f77,f204]) ).
fof(f683,plain,
( sk_c6 != multiply(identity,identity)
| spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f682,f545]) ).
fof(f684,plain,
( identity != sk_c6
| spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f683,f1]) ).
fof(f685,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f684,f381]) ).
fof(f686,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f685]) ).
fof(f692,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_19 ),
inference(forward_demodulation,[],[f86,f213]) ).
fof(f696,plain,
( sk_c7 = multiply(sk_c2,sk_c7)
| ~ spl0_8
| ~ spl0_19 ),
inference(forward_demodulation,[],[f96,f213]) ).
fof(f697,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f164,f142]) ).
fof(f699,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f697,f132]) ).
fof(f700,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_19 ),
inference(superposition,[],[f164,f692]) ).
fof(f702,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_19 ),
inference(forward_demodulation,[],[f700,f3]) ).
fof(f708,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_8
| ~ spl0_19 ),
inference(superposition,[],[f164,f696]) ).
fof(f710,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f708,f122]) ).
fof(f713,plain,
( ! [X0] :
( identity != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_19 ),
inference(forward_demodulation,[],[f83,f702]) ).
fof(f720,plain,
( identity != sk_c8
| sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f713,f142]) ).
fof(f723,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f720,f702]) ).
fof(f724,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f723,f132]) ).
fof(f725,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f724]) ).
fof(f777,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f86,f699]) ).
fof(f785,plain,
( spl0_19
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f777,f140,f130,f85,f212]) ).
fof(f797,plain,
( sk_c7 != sk_c5
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f73,f101]) ).
fof(f801,definition,
( spl0_21
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f804,plain,
( ~ spl0_7
| ~ spl0_21
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f797,f99,f72,f801,f90]) ).
fof(f818,plain,
( sk_c7 = multiply(identity,sk_c5)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_19 ),
inference(superposition,[],[f106,f702]) ).
fof(f822,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_10
| ~ spl0_19 ),
inference(forward_demodulation,[],[f818,f1]) ).
fof(f827,plain,
( spl0_21
| ~ spl0_6
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f822,f212,f104,f85,f801]) ).
fof(f857,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_19 ),
inference(superposition,[],[f164,f710]) ).
fof(f859,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f857,f3]) ).
fof(f860,plain,
( $false
| ~ spl0_8
| ~ spl0_13
| spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f859,f205]) ).
fof(f861,plain,
( ~ spl0_8
| ~ spl0_13
| spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f860]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s7,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s9,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s10,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s15,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s16,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s18,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s19,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s21,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s22,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f149]) ).
cnf(s27,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f150]) ).
cnf(s28,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f151]) ).
cnf(s31,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f193]) ).
cnf(s34,plain,
( ~ spl0_4
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f215]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f346]) ).
cnf(s41,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f347]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f402]) ).
cnf(s45,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_17
| spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f574]) ).
cnf(s46,plain,
( ~ spl0_13
| ~ spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f596]) ).
cnf(s48,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f655]) ).
cnf(s50,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f668]) ).
cnf(s52,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f681]) ).
cnf(s53,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f686]) ).
cnf(s54,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f725]) ).
cnf(s60,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f785]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_21 ),
inference(sat_conversion,[],[f804]) ).
cnf(s65,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_19
| spl0_21 ),
inference(sat_conversion,[],[f827]) ).
cnf(s67,plain,
( ~ spl0_8
| ~ spl0_13
| spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f861]) ).
cnf(s68,plain,
spl0_3,
inference(rat,[],[s53,s67,s60,s7,s13,s19,s25,s31]) ).
cnf(s69,plain,
spl0_6,
inference(rat,[],[s32,s26,s27,s28,s68]) ).
cnf(s70,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s50,s45,s39,s41,s69,s68]) ).
cnf(s71,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s54,s60,s18,s24,s69]) ).
cnf(s72,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s54,s60,s17,s23,s69]) ).
cnf(s73,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s54,s60,s16,s22,s69]) ).
cnf(s74,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s54,s60,s15,s21,s69]) ).
cnf(s75,plain,
( ~ spl0_9
| ~ spl0_5
| ~ spl0_12
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s54,s60,s14,s20,s70,s69]) ).
cnf(s76,plain,
~ spl0_5,
inference(rat,[],[s75,s74,s73,s72,s71]) ).
cnf(s77,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s45,s34,s41,s39,s69,s68]) ).
cnf(s78,plain,
( spl0_12
| ~ spl0_4 ),
inference(rat,[],[s34,s46,s67,s60,s6,s12,s18,s24,s69]) ).
cnf(s79,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s34,s46,s67,s60,s5,s11,s17,s23,s69]) ).
cnf(s80,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s34,s46,s67,s60,s4,s10,s16,s22,s69]) ).
cnf(s81,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s34,s46,s67,s60,s3,s9,s15,s21,s69]) ).
cnf(s82,plain,
( ~ spl0_9
| ~ spl0_4
| ~ spl0_12
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s34,s46,s67,s60,s2,s8,s14,s20,s77,s69]) ).
cnf(s83,plain,
~ spl0_4,
inference(rat,[],[s82,s81,s80,s79,s78]) ).
cnf(s84,plain,
( spl0_12
| spl0_19 ),
inference(rat,[],[s60,s18,s24,s69]) ).
cnf(s85,plain,
( ~ spl0_12
| spl0_19
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(rat,[],[s60,s17,s23,s39,s68,s69]) ).
cnf(s86,plain,
( ~ spl0_10
| spl0_21
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s85,s84,s65,s69]) ).
cnf(s87,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s52,s46,s67,s60,s4,s10,s16,s22,s69]) ).
cnf(s88,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s86,s62,s87]) ).
cnf(s89,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s52,s46,s67,s60,s3,s9,s15,s21,s69]) ).
cnf(s90,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s52,s46,s67,s60,s2,s8,s14,s20,s88,s69]) ).
cnf(s91,plain,
~ spl0_2,
inference(rat,[],[s90,s89]) ).
cnf(s92,plain,
spl0_1,
inference(rat,[],[s1,s69,s68,s76,s83,s91]) ).
cnf(s93,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s41,s42,s92]) ).
cnf(s94,plain,
( ~ spl0_13
| ~ spl0_8
| ~ spl0_19 ),
inference(rat,[],[s48,s46,s67,s92,s69]) ).
cnf(s95,plain,
( spl0_11
| ~ spl0_19 ),
inference(rat,[],[s94,s5,s11]) ).
cnf(s96,plain,
( spl0_12
| ~ spl0_19 ),
inference(rat,[],[s94,s6,s12]) ).
cnf(s97,plain,
( ~ spl0_19
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s94,s4,s10,s93,s96,s95]) ).
cnf(s98,plain,
( ~ spl0_12
| spl0_19
| ~ spl0_7
| ~ spl0_9 ),
inference(rat,[],[s60,s16,s22,s85,s69]) ).
cnf(s99,plain,
( ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s98,s84,s97]) ).
cnf(s100,plain,
spl0_9,
inference(rat,[],[s94,s60,s3,s9,s15,s21,s69]) ).
cnf(s101,plain,
~ spl0_7,
inference(rat,[],[s99,s100]) ).
cnf(s102,plain,
spl0_15,
inference(rat,[],[s20,s101]) ).
cnf(s103,plain,
spl0_14,
inference(rat,[],[s14,s101]) ).
cnf(s104,plain,
spl0_13,
inference(rat,[],[s8,s101]) ).
cnf(s105,plain,
spl0_8,
inference(rat,[],[s2,s101]) ).
cnf(s106,plain,
spl0_19,
inference(rat,[],[s60,s102,s69,s103]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s94,s106,s105,s104]) ).
fof(f862,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP332-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:55:53 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 % (2088041)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2088049)dis+10_1_sil=32000:sp=arity:random_seed=3899931485:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2088047)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2088046)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2073176231_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2088047)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1628162149:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2088048)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1165548890:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2088051)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2792454181:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2088050)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3185277982:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2088052)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3061561746:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (2088049) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2088041-2088049"...
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % (2088049)...printing done.
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (2088049)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (2088049)------------------------------
% 0.17/0.48 % (2088049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2088049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2088049)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2088049)Termination reason: Refutation
% 0.17/0.48 % (2088049)Time elapsed: 0.011 s
% 0.17/0.48 % (2088049)Peak memory usage: 12 MB
% 0.17/0.48 % (2088049)Instructions burned: 31 (million)
% 0.17/0.48 % (2088041)Success in time 0.036 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------