%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP347-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 10:17:33 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 48
% Syntax : Number of formulae : 364 ( 24 unt; 15 def)
% Number of atoms : 1425 ( 380 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 2076 (1015 ~;1046 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c6) != sk_c5
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c6
| multiply(X3,sk_c7) != sk_c5
| inverse(X3) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c7 != multiply(sk_c6,sk_c5)
| sk_c5 != inverse(sk_c6)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c5 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_3
<=> sk_c5 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f75,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( sk_c5 != inverse(sk_c6)
| spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl0_4
<=> sk_c7 = multiply(sk_c6,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f79,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( sk_c7 != multiply(sk_c6,sk_c5)
| spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_5
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_7
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f89,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f66,f88,f85,f82,f78,f74,f71,f68]) ).
fof(f93,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f95,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f64,f97,f93]) ).
fof(f102,definition,
( spl0_10
<=> sk_c5 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f62,f97,f102]) ).
fof(f107,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f109,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f60,f97,f107]) ).
fof(f112,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f58,f97,f112]) ).
fof(f116,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f56,f97,f74]) ).
fof(f117,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f54,f97,f78]) ).
fof(f119,definition,
( spl0_13
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f121,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f119,f93]) ).
fof(f123,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f119,f102]) ).
fof(f124,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f119,f107]) ).
fof(f125,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f119,f112]) ).
fof(f126,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f119,f74]) ).
fof(f127,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f119,f78]) ).
fof(f129,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f131,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f129,f93]) ).
fof(f133,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f129,f102]) ).
fof(f134,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f129,f107]) ).
fof(f135,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f129,f112]) ).
fof(f136,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f129,f74]) ).
fof(f137,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f129,f78]) ).
fof(f139,definition,
( spl0_15
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f141,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f139,f93]) ).
fof(f143,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f139,f102]) ).
fof(f144,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f139,f107]) ).
fof(f145,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f139,f112]) ).
fof(f146,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f139,f74]) ).
fof(f147,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f139,f78]) ).
fof(f148,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f88,f93]) ).
fof(f149,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f88,f102]) ).
fof(f150,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f88,f107]) ).
fof(f152,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f88,f74]) ).
fof(f153,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f88,f78]) ).
fof(f154,plain,
( sk_c7 = multiply(sk_c6,inverse(sk_c6))
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f79,f75]) ).
fof(f155,plain,
( multiply(sk_c6,sk_c7) != inverse(sk_c6)
| ~ spl0_3
| spl0_7 ),
inference(forward_demodulation,[],[f90,f75]) ).
fof(f156,plain,
( inverse(sk_c6) = multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_10 ),
inference(forward_demodulation,[],[f104,f75]) ).
fof(f157,plain,
( inverse(sk_c6) != multiply(sk_c6,multiply(sk_c6,inverse(sk_c6)))
| ~ spl0_3
| ~ spl0_4
| spl0_7 ),
inference(forward_demodulation,[],[f155,f154]) ).
fof(f158,plain,
( inverse(sk_c6) = multiply(sk_c4,multiply(sk_c6,inverse(sk_c6)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f156,f154]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f3,f3]) ).
fof(f161,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f109]) ).
fof(f162,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f163,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f162,f4]) ).
fof(f170,plain,
( ! [X0] : multiply(sk_c4,multiply(multiply(sk_c6,inverse(sk_c6)),X0)) = multiply(inverse(sk_c6),X0)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f4,f158]) ).
fof(f171,plain,
( ! [X0] : multiply(inverse(sk_c6),X0) = multiply(sk_c4,multiply(sk_c6,multiply(inverse(sk_c6),X0)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f170,f4]) ).
fof(f177,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f161]) ).
fof(f178,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f177,f1]) ).
fof(f182,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f178,f114]) ).
fof(f185,plain,
( sk_c6 = multiply(sk_c6,multiply(sk_c6,inverse(sk_c6)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f182,f154]) ).
fof(f199,plain,
( identity = multiply(sk_c4,multiply(sk_c6,identity))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f171,f3]) ).
fof(f208,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f163,f3]) ).
fof(f209,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f163,f163]) ).
fof(f210,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f163,f161]) ).
fof(f213,plain,
( multiply(sk_c6,inverse(sk_c6)) = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f163,f185]) ).
fof(f225,plain,
( identity = multiply(sk_c6,inverse(sk_c6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f213,f3]) ).
fof(f226,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f208,f209]) ).
fof(f236,plain,
( ! [X0] : multiply(sk_c6,multiply(multiply(inverse(sk_c6),identity),X0)) = X0
| ~ spl0_11 ),
inference(superposition,[],[f178,f210]) ).
fof(f238,plain,
( sk_c7 = multiply(multiply(inverse(sk_c6),identity),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f114,f210]) ).
fof(f241,plain,
( sk_c7 = multiply(inverse(sk_c6),multiply(identity,sk_c6))
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f238,f4]) ).
fof(f243,plain,
( ! [X0] : multiply(sk_c6,multiply(inverse(sk_c6),multiply(identity,X0))) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f236,f4]) ).
fof(f245,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f241,f1]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c6,multiply(inverse(sk_c6),X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f243,f1]) ).
fof(f248,plain,
( identity = sk_c7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f245,f3]) ).
fof(f255,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(sk_c7,sk_c4)
| ~ spl0_8 ),
inference(superposition,[],[f159,f95]) ).
fof(f273,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(multiply(sk_c6,inverse(sk_c6)),sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f255,f154]) ).
fof(f279,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(sk_c6,multiply(inverse(sk_c6),sk_c4))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f273,f4]) ).
fof(f282,plain,
( ! [X0] : multiply(inverse(X0),X0) = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f279,f246]) ).
fof(f286,plain,
( sk_c4 = multiply(sk_c7,sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f282,f95]) ).
fof(f293,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f3,f282]) ).
fof(f298,plain,
( ! [X0] : inverse(sk_c6) = multiply(multiply(inverse(X0),X0),multiply(sk_c6,inverse(sk_c6)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f158,f282]) ).
fof(f300,plain,
( ! [X0] : inverse(sk_c6) = multiply(inverse(X0),multiply(X0,multiply(sk_c6,inverse(sk_c6))))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f298,f4]) ).
fof(f305,plain,
( identity = multiply(sk_c7,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f286,f293]) ).
fof(f306,plain,
( inverse(sk_c6) = multiply(sk_c6,inverse(sk_c6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f300,f163]) ).
fof(f310,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f305,f226]) ).
fof(f311,plain,
( identity = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f306,f225]) ).
fof(f326,plain,
( identity = multiply(identity,multiply(sk_c6,identity))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f199,f293]) ).
fof(f329,plain,
( multiply(sk_c6,identity) = multiply(inverse(sk_c4),identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f163,f199]) ).
fof(f332,plain,
( inverse(sk_c4) = multiply(sk_c6,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f329,f226]) ).
fof(f334,plain,
( identity = multiply(sk_c6,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f326,f1]) ).
fof(f335,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f332,f226]) ).
fof(f337,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f334,f226]) ).
fof(f342,plain,
( inverse(identity) != multiply(identity,multiply(identity,inverse(identity)))
| ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f157,f337]) ).
fof(f362,plain,
( inverse(identity) != multiply(identity,inverse(identity))
| ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f342,f1]) ).
fof(f371,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f362,f1]) ).
fof(f372,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f383,plain,
( ! [X1] :
( identity != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f83,f337]) ).
fof(f384,plain,
( multiply(sk_c6,sk_c7) = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f89,f75]) ).
fof(f385,plain,
( ! [X1] :
( sk_c6 != multiply(X1,inverse(sk_c6))
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f383,f75]) ).
fof(f387,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f385,f311]) ).
fof(f389,plain,
( ! [X1] :
( sk_c6 != X1
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f387,f226]) ).
fof(f391,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f389,f337]) ).
fof(f394,plain,
( identity != sk_c7
| identity != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f391,f95]) ).
fof(f397,plain,
( identity != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f394,f248]) ).
fof(f400,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f397,f293]) ).
fof(f401,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f403,plain,
( sk_c6 = multiply(sk_c2,inverse(sk_c6))
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f99,f75]) ).
fof(f408,plain,
( ! [X1] :
( sk_c6 != multiply(X1,inverse(sk_c6))
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f83,f75]) ).
fof(f409,plain,
( inverse(sk_c6) = multiply(sk_c6,multiply(sk_c6,inverse(sk_c6)))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f384,f154]) ).
fof(f415,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f409,f185]) ).
fof(f420,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f3,f121]) ).
fof(f436,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f3,f415]) ).
fof(f473,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f141]) ).
fof(f474,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f163,f131]) ).
fof(f475,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f131]) ).
fof(f476,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f474,f141]) ).
fof(f477,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_13 ),
inference(superposition,[],[f163,f420]) ).
fof(f480,plain,
( inverse(sk_c6) = sk_c2
| ~ spl0_13 ),
inference(forward_demodulation,[],[f477,f226]) ).
fof(f483,plain,
( identity = multiply(sk_c6,inverse(sk_c6))
| ~ spl0_13 ),
inference(superposition,[],[f420,f480]) ).
fof(f487,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_15 ),
inference(superposition,[],[f163,f473]) ).
fof(f490,plain,
( sk_c1 = inverse(sk_c7)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f487,f226]) ).
fof(f515,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f408,f403]) ).
fof(f516,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f515]) ).
fof(f517,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f516,f121]) ).
fof(f518,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f517]) ).
fof(f548,plain,
( sk_c6 = multiply(sk_c2,multiply(sk_c6,sk_c7))
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f99,f89]) ).
fof(f550,plain,
( sk_c7 != multiply(sk_c6,multiply(sk_c6,sk_c7))
| spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f80,f89]) ).
fof(f551,plain,
( sk_c6 = multiply(inverse(sk_c6),multiply(sk_c6,sk_c7))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f548,f480]) ).
fof(f552,plain,
( sk_c6 = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f551,f163]) ).
fof(f554,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f476,f552]) ).
fof(f580,plain,
( sk_c6 != multiply(sk_c6,multiply(sk_c6,sk_c6))
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f550,f552]) ).
fof(f581,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f580,f554]) ).
fof(f582,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f581,f554]) ).
fof(f583,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f582]) ).
fof(f624,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c7),multiply(sk_c6,X0))
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f475,f490]) ).
fof(f625,plain,
( multiply(sk_c7,sk_c2) = multiply(sk_c1,identity)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f475,f420]) ).
fof(f630,plain,
( sk_c1 = multiply(sk_c7,sk_c2)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f625,f226]) ).
fof(f631,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c6),multiply(sk_c6,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f624,f552]) ).
fof(f634,plain,
( sk_c1 = multiply(sk_c7,inverse(sk_c6))
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f630,f480]) ).
fof(f635,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f631,f163]) ).
fof(f638,plain,
( sk_c1 = multiply(sk_c6,inverse(sk_c6))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f634,f552]) ).
fof(f640,plain,
( identity = sk_c1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f638,f483]) ).
fof(f643,plain,
( identity = inverse(sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f490,f640]) ).
fof(f644,plain,
( identity = multiply(sk_c7,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f473,f640]) ).
fof(f648,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f644,f226]) ).
fof(f649,plain,
( identity = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f643,f552]) ).
fof(f678,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f552,f648]) ).
fof(f774,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f69,f552]) ).
fof(f777,plain,
( ! [X3] :
( sk_c5 != multiply(X3,identity)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f774,f678]) ).
fof(f779,plain,
( ! [X3] :
( sk_c5 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f777,f226]) ).
fof(f780,plain,
( ! [X3] :
( multiply(sk_c6,sk_c7) != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f779,f89]) ).
fof(f781,plain,
( ! [X3] :
( sk_c7 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f780,f635]) ).
fof(f782,plain,
( ! [X3] :
( sk_c6 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f781,f552]) ).
fof(f783,plain,
( ! [X3] :
( identity != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f782,f678]) ).
fof(f784,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| identity != X3 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f783,f552]) ).
fof(f785,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f784,f678]) ).
fof(f788,plain,
( identity != sk_c7
| identity != sk_c1
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f785,f141]) ).
fof(f791,plain,
( identity != sk_c1
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f788,f648]) ).
fof(f794,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f791,f640]) ).
fof(f795,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f794]) ).
fof(f796,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f86,f552]) ).
fof(f797,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f796,f678]) ).
fof(f798,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f797,f678]) ).
fof(f799,plain,
( ! [X0] :
( sk_c7 != X0
| identity != inverse(X0) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f798,f226]) ).
fof(f800,plain,
( ! [X0] :
( sk_c6 != X0
| identity != inverse(X0) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f799,f552]) ).
fof(f801,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f800,f678]) ).
fof(f804,plain,
( identity != sk_c7
| identity != sk_c1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f801,f141]) ).
fof(f807,plain,
( identity != sk_c1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f804,f648]) ).
fof(f810,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f807,f640]) ).
fof(f811,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f810]) ).
fof(f812,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f72,f678]) ).
fof(f813,plain,
( ! [X2] :
( sk_c7 != X2
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f812,f226]) ).
fof(f814,plain,
( ! [X2] :
( sk_c6 != X2
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f813,f552]) ).
fof(f815,plain,
( ! [X2] :
( identity != X2
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f814,f678]) ).
fof(f816,plain,
( ! [X2] :
( identity != inverse(X2)
| identity != X2 )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f815,f678]) ).
fof(f826,plain,
( identity != sk_c7
| identity != sk_c1
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f816,f141]) ).
fof(f829,plain,
( identity != sk_c1
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f826,f648]) ).
fof(f832,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f829,f640]) ).
fof(f833,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f832]) ).
fof(f834,plain,
( identity != sk_c5
| spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f76,f649]) ).
fof(f839,plain,
( identity != multiply(sk_c6,sk_c7)
| spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f834,f89]) ).
fof(f846,plain,
( identity != sk_c7
| spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f839,f635]) ).
fof(f848,plain,
( $false
| spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f846,f648]) ).
fof(f849,plain,
( spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f848]) ).
fof(f961,plain,
( sk_c6 = inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f335,f293]) ).
fof(f1016,plain,
( ! [X0,X1] :
( sk_c7 != multiply(X0,multiply(X1,sk_c6))
| sk_c6 != inverse(multiply(X0,X1)) )
| ~ spl0_2 ),
inference(superposition,[],[f72,f4]) ).
fof(f1017,plain,
( ! [X0,X1] :
( sk_c7 != multiply(X0,multiply(X1,identity))
| sk_c6 != inverse(multiply(X0,X1)) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1016,f337]) ).
fof(f1018,plain,
( ! [X0,X1] :
( multiply(X0,X1) != sk_c7
| sk_c6 != inverse(multiply(X0,X1)) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1017,f226]) ).
fof(f1019,plain,
( ! [X0,X1] :
( identity != multiply(X0,X1)
| sk_c6 != inverse(multiply(X0,X1)) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1018,f310]) ).
fof(f1020,plain,
( ! [X0,X1] :
( identity != inverse(multiply(X0,X1))
| identity != multiply(X0,X1) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1019,f337]) ).
fof(f1047,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1020,f436]) ).
fof(f1051,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1047]) ).
fof(f1059,plain,
( ! [X3] :
( sk_c5 != multiply(X3,identity)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f69,f310]) ).
fof(f1060,plain,
( ! [X3] :
( sk_c5 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1059,f226]) ).
fof(f1061,plain,
( ! [X3] :
( multiply(sk_c6,sk_c7) != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1060,f89]) ).
fof(f1062,plain,
( ! [X3] :
( multiply(sk_c6,identity) != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1061,f310]) ).
fof(f1063,plain,
( ! [X3] :
( sk_c6 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1062,f226]) ).
fof(f1064,plain,
( ! [X3] :
( identity != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1063,f337]) ).
fof(f1065,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1064,f310]) ).
fof(f1067,plain,
( identity != sk_c6
| identity != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1065,f415]) ).
fof(f1069,plain,
( identity != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(duplicate_literal_removal,[],[f1067]) ).
fof(f1071,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1069,f337]) ).
fof(f1072,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1071]) ).
fof(f1075,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f86,f310]) ).
fof(f1076,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1075,f337]) ).
fof(f1077,plain,
( ! [X0] :
( sk_c7 != X0
| identity != inverse(X0) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1076,f226]) ).
fof(f1078,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1077,f310]) ).
fof(f1089,plain,
( identity != sk_c6
| identity != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1078,f415]) ).
fof(f1091,plain,
( identity != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(duplicate_literal_removal,[],[f1089]) ).
fof(f1096,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1091,f337]) ).
fof(f1097,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1096]) ).
fof(f1111,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f961,f337]) ).
fof(f1135,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1111,f1051]) ).
fof(f1136,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1135]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f91]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f100]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f110]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f116]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s10,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s11,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s13,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s14,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s16,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s17,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s18,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s19,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s20,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f142]) ).
cnf(s21,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s22,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s23,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s24,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s25,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s26,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f148]) ).
cnf(s27,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f149]) ).
cnf(s28,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f150]) ).
cnf(s30,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f152]) ).
cnf(s31,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f153]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f372]) ).
cnf(s35,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f401]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f518]) ).
cnf(s43,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f583]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f795]) ).
cnf(s51,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f811]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f833]) ).
cnf(s56,plain,
( spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f849]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f1072]) ).
cnf(s65,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f1097]) ).
cnf(s77,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f1136]) ).
cnf(s79,plain,
spl0_3,
inference(rat,[],[s56,s6,s12,s18,s24,s30]) ).
cnf(s80,plain,
spl0_4,
inference(rat,[],[s43,s7,s13,s19,s25,s31]) ).
cnf(s81,plain,
spl0_7,
inference(rat,[],[s33,s26,s27,s28,s79,s80]) ).
cnf(s82,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_6 ),
inference(rat,[],[s51,s11,s17,s23,s81]) ).
cnf(s83,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_6 ),
inference(rat,[],[s51,s10,s16,s22,s81]) ).
cnf(s84,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6 ),
inference(rat,[],[s51,s9,s15,s21,s65,s83,s82,s81,s79,s80]) ).
cnf(s85,plain,
( ~ spl0_8
| ~ spl0_6 ),
inference(rat,[],[s65,s3,s4,s5,s84,s81,s80,s79]) ).
cnf(s86,plain,
~ spl0_6,
inference(rat,[],[s51,s2,s8,s14,s20,s85,s81]) ).
cnf(s87,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s35,s9,s10,s11,s79,s80]) ).
cnf(s88,plain,
( ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s35,s3,s4,s5,s39,s87,s80,s79]) ).
cnf(s89,plain,
~ spl0_5,
inference(rat,[],[s39,s2,s8,s88,s79]) ).
cnf(s90,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s53,s11,s17,s23,s81]) ).
cnf(s91,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s53,s10,s16,s22,s81]) ).
cnf(s92,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s53,s9,s15,s21,s77,s91,s90,s81,s79,s80]) ).
cnf(s93,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s77,s3,s4,s5,s92,s81,s80,s79]) ).
cnf(s94,plain,
~ spl0_2,
inference(rat,[],[s53,s2,s8,s14,s20,s93,s81]) ).
cnf(s95,plain,
spl0_1,
inference(rat,[],[s1,s81,s86,s79,s80,s89,s94]) ).
cnf(s96,plain,
( spl0_12
| ~ spl0_9 ),
inference(rat,[],[s49,s11,s17,s23,s81,s95]) ).
cnf(s97,plain,
( spl0_11
| ~ spl0_9 ),
inference(rat,[],[s49,s10,s16,s22,s81,s95]) ).
cnf(s98,plain,
( ~ spl0_9
| ~ spl0_8 ),
inference(rat,[],[s49,s9,s15,s21,s62,s97,s96,s81,s95,s79,s80]) ).
cnf(s99,plain,
~ spl0_8,
inference(rat,[],[s62,s3,s4,s5,s98,s79,s80,s81,s95]) ).
cnf(s100,plain,
spl0_15,
inference(rat,[],[s20,s99]) ).
cnf(s101,plain,
spl0_14,
inference(rat,[],[s14,s99]) ).
cnf(s102,plain,
spl0_13,
inference(rat,[],[s8,s99]) ).
cnf(s103,plain,
spl0_9,
inference(rat,[],[s2,s99]) ).
cnf(s104,plain,
$false,
inference(rat,[],[s49,s103,s95,s81,s102,s100,s101]) ).
fof(f1143,plain,
$false,
inference(avatar_sat_refutation,[],[s104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP347-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:54:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.45 % (3261778)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (3261788)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3965483980:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.45 % (3261783)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2312915036_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.45 % (3261787)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2489777881:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.45 % (3261785)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3579715816:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.45 % (3261786)dis+10_1_sil=32000:sp=arity:random_seed=4004342766:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.45 % (3261789)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1142416585:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.45 % (3261788) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3261778-3261788"...
% 0.15/0.45 % TRYING [1]
% 0.15/0.45 % TRYING [2]
% 0.15/0.45 % (3261784)% WARNING: option uhcvi not known.
% 0.15/0.45 % TRYING [3]
% 0.15/0.45 % (3261788)...printing done.
% 0.15/0.45 % (3261788)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (3261788)------------------------------
% 0.15/0.46 % (3261788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (3261788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (3261788)CaDiCaL version: 2.1.3
% 0.15/0.46 % (3261788)Termination reason: Refutation
% 0.15/0.46 % (3261788)Time elapsed: 0.012 s
% 0.15/0.46 % (3261788)Peak memory usage: 12 MB
% 0.15/0.46 % (3261788)Instructions burned: 35 (million)
% 0.15/0.46 % (3261778)Success in time 0.037 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------