%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP356-1 : 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 : n012.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 10:17:35 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.36s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 50
% Syntax : Number of formulae : 313 ( 21 unt; 16 def)
% Number of atoms : 1018 ( 304 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1325 ( 620 ~; 689 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 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_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| 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,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(X1,sk_c8) != sk_c6
| inverse(X1) != sk_c8
| 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_c6) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| 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_c6) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| 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_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c8 != 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_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| 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_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c8 = inverse(sk_c2)
| ~ 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_c6 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f122,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| ~ 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(f152,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f85,f109]) ).
fof(f153,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f85,f114]) ).
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(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f76]) ).
fof(f162,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f116]) ).
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(f178,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f106,f171]) ).
fof(f185,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f76,f178]) ).
fof(f238,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f164,f3]) ).
fof(f239,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f164,f164]) ).
fof(f245,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f164,f171]) ).
fof(f251,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f164,f116]) ).
fof(f258,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f251,f178]) ).
fof(f263,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f245,f3]) ).
fof(f267,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f238,f239]) ).
fof(f268,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f258,f111]) ).
fof(f274,plain,
( ! [X0] : multiply(X0,sk_c5) = X0
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f267,f263]) ).
fof(f278,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f162,f268]) ).
fof(f279,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f164,f268]) ).
fof(f281,plain,
( identity = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f279,f3]) ).
fof(f282,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f278,f178]) ).
fof(f284,plain,
( sk_c6 = multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f282,f185]) ).
fof(f285,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f284,f116]) ).
fof(f286,plain,
( sk_c6 = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f285,f178]) ).
fof(f288,plain,
( sk_c8 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f263,f281]) ).
fof(f290,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1,f281]) ).
fof(f297,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f87,f286]) ).
fof(f298,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f297,f178]) ).
fof(f299,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f298,f268]) ).
fof(f300,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f301,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f80,f286]) ).
fof(f308,plain,
( sk_c7 != sk_c8
| sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f301,f116]) ).
fof(f313,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f308,f178]) ).
fof(f318,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f313,f111]) ).
fof(f319,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f324,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f96]) ).
fof(f326,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f132]) ).
fof(f329,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f86]) ).
fof(f333,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f164,f142]) ).
fof(f334,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f142]) ).
fof(f335,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f333,f132]) ).
fof(f338,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_8 ),
inference(superposition,[],[f164,f324]) ).
fof(f341,plain,
( sk_c2 = inverse(sk_c8)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f338,f267]) ).
fof(f349,plain,
( sk_c6 != sk_c6
| sk_c8 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f80,f122]) ).
fof(f350,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f349]) ).
fof(f351,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f350,f96]) ).
fof(f352,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f360,definition,
( spl0_17
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f361,plain,
( sk_c6 = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f366,plain,
( identity = multiply(sk_c2,sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f3,f341]) ).
fof(f367,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f366,f122]) ).
fof(f370,plain,
( sk_c7 != multiply(sk_c8,identity)
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1 ),
inference(superposition,[],[f70,f3]) ).
fof(f372,plain,
( sk_c7 != multiply(sk_c8,sk_c5)
| sk_c8 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f70,f101]) ).
fof(f388,plain,
( sk_c7 != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f370,f267]) ).
fof(f402,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f1,f367]) ).
fof(f403,plain,
( multiply(sk_c8,identity) = multiply(sk_c6,sk_c1)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f160,f326]) ).
fof(f404,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_14 ),
inference(superposition,[],[f164,f326]) ).
fof(f407,plain,
( sk_c1 = inverse(sk_c7)
| ~ spl0_14 ),
inference(forward_demodulation,[],[f404,f267]) ).
fof(f408,plain,
( sk_c1 = multiply(sk_c8,identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f403,f402]) ).
fof(f409,plain,
( sk_c8 = sk_c1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f408,f267]) ).
fof(f410,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f326,f409]) ).
fof(f413,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f410,f335]) ).
fof(f415,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c7),multiply(sk_c8,X0))
| ~ spl0_6 ),
inference(superposition,[],[f164,f329]) ).
fof(f418,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f415,f407]) ).
fof(f425,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f367,f413]) ).
fof(f426,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f1,f413]) ).
fof(f433,plain,
( identity != sk_c7
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2 ),
inference(superposition,[],[f73,f3]) ).
fof(f434,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f73,f116]) ).
fof(f437,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f434]) ).
fof(f439,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f437,f111]) ).
fof(f440,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f441,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f433,f413]) ).
fof(f445,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f441,f341]) ).
fof(f446,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f445,f96]) ).
fof(f447,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f446]) ).
fof(f450,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f86,f425]) ).
fof(f451,plain,
( sk_c7 = sk_c8
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f450,f426]) ).
fof(f454,plain,
( sk_c7 != sk_c8
| sk_c7 != inverse(identity)
| ~ spl0_5 ),
inference(superposition,[],[f83,f1]) ).
fof(f458,plain,
( sk_c8 != sk_c8
| sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[],[f83,f142]) ).
fof(f459,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f458]) ).
fof(f460,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f459,f132]) ).
fof(f461,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f460]) ).
fof(f487,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f388,f451]) ).
fof(f498,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f487,f341]) ).
fof(f503,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f498,f96]) ).
fof(f504,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f503]) ).
fof(f505,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c8,X0)) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f418,f402]) ).
fof(f508,plain,
( identity = multiply(sk_c1,sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f3,f407]) ).
fof(f509,plain,
( identity = sk_c8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f508,f142]) ).
fof(f523,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(sk_c8,multiply(sk_c6,X0))
| ~ spl0_6
| ~ spl0_15 ),
inference(superposition,[],[f334,f329]) ).
fof(f528,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f523,f402]) ).
fof(f532,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f528,f505]) ).
fof(f534,plain,
( sk_c6 = sk_c8
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f367,f509]) ).
fof(f536,plain,
( spl0_17
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f534,f140,f130,f120,f94,f360]) ).
fof(f539,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f86,f361]) ).
fof(f614,plain,
( sk_c7 != sk_c6
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f77,f532]) ).
fof(f622,plain,
( sk_c7 != sk_c8
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f614,f361]) ).
fof(f640,plain,
( sk_c7 = sk_c8
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f539,f335]) ).
fof(f649,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f640,f622]) ).
fof(f650,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f649]) ).
fof(f657,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f372,f106]) ).
fof(f670,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f274,f288]) ).
fof(f690,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f657,f92]) ).
fof(f691,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f717,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f458]) ).
fof(f719,plain,
( sk_c7 != inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f454,f178]) ).
fof(f722,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f717,f178]) ).
fof(f730,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f333,f670]) ).
fof(f736,plain,
( sk_c7 != inverse(sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f719,f281]) ).
fof(f741,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f730,f178]) ).
fof(f745,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f736,f178]) ).
fof(f748,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f741,f722]) ).
fof(f749,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f748]) ).
fof(f773,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f3,f92]) ).
fof(f774,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f773,f290]) ).
fof(f782,plain,
( sk_c8 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f774,f281]) ).
fof(f794,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f92,f782]) ).
fof(f795,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f794,f745]) ).
fof(f796,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f795]) ).
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(s29,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f300]) ).
cnf(s34,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f319]) ).
cnf(s35,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f352]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f440]) ).
cnf(s43,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f447]) ).
cnf(s44,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f461]) ).
cnf(s51,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f504]) ).
cnf(s52,plain,
( ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f536]) ).
cnf(s60,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f650]) ).
cnf(s63,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f691]) ).
cnf(s71,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(sat_conversion,[],[f749]) ).
cnf(s75,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f796]) ).
cnf(s76,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(rat,[],[s52,s60]) ).
cnf(s77,plain,
spl0_3,
inference(rat,[],[s76,s7,s13,s19,s25,s31]) ).
cnf(s78,plain,
( spl0_15
| ~ spl0_5 ),
inference(rat,[],[s75,s20,s21,s22,s23,s24]) ).
cnf(s79,plain,
( ~ spl0_15
| ~ spl0_5 ),
inference(rat,[],[s71,s14,s15,s16,s17,s18,s44]) ).
cnf(s80,plain,
~ spl0_5,
inference(rat,[],[s79,s78]) ).
cnf(s81,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s34,s8,s9,s10,s11,s12,s77]) ).
cnf(s82,plain,
( ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s34,s2,s3,s4,s5,s6,s35,s77]) ).
cnf(s83,plain,
~ spl0_4,
inference(rat,[],[s82,s81]) ).
cnf(s84,plain,
spl0_6,
inference(rat,[],[s32,s26,s27,s28,s29,s30,s77]) ).
cnf(s85,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s43,s6,s12,s18,s24,s77]) ).
cnf(s86,plain,
( ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s43,s5,s11,s17,s23,s41,s77]) ).
cnf(s87,plain,
~ spl0_2,
inference(rat,[],[s86,s85]) ).
cnf(s88,plain,
spl0_1,
inference(rat,[],[s1,s80,s77,s83,s84,s87]) ).
cnf(s90,plain,
spl0_15,
inference(rat,[],[s63,s20,s21,s22,s88]) ).
cnf(s91,plain,
spl0_14,
inference(rat,[],[s63,s14,s15,s16,s88]) ).
cnf(s92,plain,
spl0_13,
inference(rat,[],[s63,s8,s9,s10,s88]) ).
cnf(s93,plain,
spl0_8,
inference(rat,[],[s63,s2,s3,s4,s88]) ).
cnf(s94,plain,
$false,
inference(rat,[],[s51,s90,s88,s84,s77,s91,s93,s92]) ).
fof(f797,plain,
$false,
inference(avatar_sat_refutation,[],[s94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP356-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 09:55:35 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 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
% 0.07/0.36 % (2129879)Will run a generic schedule for satisfiability detection.
% 0.07/0.36 % (2129885)% WARNING: option uhcvi not known.
% 0.07/0.36 % (2129885)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=407943833:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.07/0.36 % (2129886)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2120140559:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.07/0.36 % (2129889)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1196358128:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.07/0.36 % (2129887)dis+10_1_sil=32000:sp=arity:random_seed=240602993:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.07/0.36 % (2129890)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2061221503:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.07/0.36 % (2129888)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1296017390:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.07/0.36 % (2129884)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2166436870_3000 on theBenchmark for (3000ds/0Mi)
% 0.07/0.36 % TRYING [1]
% 0.07/0.36 % TRYING [2]
% 0.07/0.36 % (2129888) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2129879-2129888"...
% 0.07/0.36 % TRYING [3]
% 0.07/0.36 % (2129887) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2129879-2129887"...
% 0.07/0.36 % (2129888)...printing done.
% 0.07/0.36 % (2129888)Refutation found. Thanks to Tanya!
% 0.07/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.36 % (2129888)------------------------------
% 0.07/0.36 % (2129888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.36 % (2129888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.36 % (2129888)CaDiCaL version: 2.1.3
% 0.07/0.36 % (2129888)Termination reason: Refutation
% 0.07/0.36 % (2129888)Time elapsed: 0.009 s
% 0.07/0.36 % (2129888)Peak memory usage: 12 MB
% 0.07/0.36 % (2129888)Instructions burned: 28 (million)
% 0.07/0.36 % (2129879)Success in time 0.023 s
% 0.07/0.36 % Vampire exiting
%------------------------------------------------------------------------------