%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP346-1 : 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 : n017.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 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 56
% Syntax : Number of formulae : 430 ( 24 unt; 17 def)
% Number of atoms : 1653 ( 386 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2341 (1118 ~;1206 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 65 !; 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_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/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
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,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
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c7) != 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/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,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_c6 != multiply(sk_c7,sk_c5)
| sk_c5 != inverse(sk_c7)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c5 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ),
inference(reorient_equations,[],[f75]) ).
fof(f78,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f79,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f82,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_3
<=> sk_c5 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f85,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( sk_c5 != inverse(sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_4
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f89,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( sk_c6 != multiply(sk_c7,sk_c5)
| spl0_4 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c6,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( sk_c7 != multiply(sk_c6,sk_c5)
| spl0_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_6
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f97,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_7
<=> ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f100,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_8
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f103,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f104,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| spl0_8 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f76,f102,f99,f96,f92,f88,f84,f81,f78]) ).
fof(f107,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f109,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f111,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f113,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f74,f111,f107]) ).
fof(f116,definition,
( spl0_11
<=> sk_c5 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f117,plain,
( sk_c5 != multiply(sk_c4,sk_c7)
| spl0_11 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f118,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_11
| spl0_10 ),
inference(avatar_split_clause,[],[f72,f111,f116]) ).
fof(f121,definition,
( spl0_12
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f122,plain,
( sk_c6 != inverse(sk_c3)
| spl0_12 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_12
| spl0_10 ),
inference(avatar_split_clause,[],[f70,f111,f121]) ).
fof(f126,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_13
| spl0_10 ),
inference(avatar_split_clause,[],[f68,f111,f126]) ).
fof(f130,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f66,f111,f84]) ).
fof(f131,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f64,f111,f88]) ).
fof(f132,plain,
( spl0_5
| spl0_10 ),
inference(avatar_split_clause,[],[f62,f111,f92]) ).
fof(f134,definition,
( spl0_14
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f136,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f60,f134,f107]) ).
fof(f138,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f58,f134,f116]) ).
fof(f139,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f56,f134,f121]) ).
fof(f140,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f54,f134,f126]) ).
fof(f141,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f52,f134,f84]) ).
fof(f142,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f50,f134,f88]) ).
fof(f143,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f134,f92]) ).
fof(f145,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f146,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| spl0_15 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f147,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f46,f145,f107]) ).
fof(f149,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f44,f145,f116]) ).
fof(f150,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f42,f145,f121]) ).
fof(f151,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f145,f126]) ).
fof(f152,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f38,f145,f84]) ).
fof(f153,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f145,f88]) ).
fof(f154,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f145,f92]) ).
fof(f156,definition,
( spl0_16
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f158,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f32,f156,f107]) ).
fof(f160,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f30,f156,f116]) ).
fof(f161,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f156,f121]) ).
fof(f162,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f156,f126]) ).
fof(f163,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f156,f84]) ).
fof(f164,plain,
( spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f156,f88]) ).
fof(f165,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f20,f156,f92]) ).
fof(f166,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f18,f102,f107]) ).
fof(f167,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f16,f102,f116]) ).
fof(f168,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f14,f102,f121]) ).
fof(f169,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f12,f102,f126]) ).
fof(f170,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f10,f102,f84]) ).
fof(f171,plain,
( spl0_4
| spl0_8 ),
inference(avatar_split_clause,[],[f8,f102,f88]) ).
fof(f172,plain,
( spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f6,f102,f92]) ).
fof(f173,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_3 ),
inference(superposition,[],[f3,f85]) ).
fof(f174,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f3,f109]) ).
fof(f177,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f179,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(sk_c7,X0)
| ~ spl0_13 ),
inference(superposition,[],[f4,f128]) ).
fof(f181,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c7,X0))
| ~ spl0_3 ),
inference(superposition,[],[f4,f173]) ).
fof(f182,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f89]) ).
fof(f183,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f93]) ).
fof(f184,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c7,X0)) = X0
| ~ spl0_3 ),
inference(forward_demodulation,[],[f181,f1]) ).
fof(f186,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f177,f1]) ).
fof(f192,plain,
( sk_c5 = multiply(sk_c5,sk_c6)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f184,f89]) ).
fof(f193,plain,
( sk_c4 = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f184,f174]) ).
fof(f196,plain,
( multiply(sk_c7,sk_c5) = multiply(sk_c3,sk_c7)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f179,f93]) ).
fof(f200,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f196,f89]) ).
fof(f209,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f182,f184]) ).
fof(f218,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c6,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[],[f182,f193]) ).
fof(f219,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c5,multiply(identity,X0))
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f4,f193]) ).
fof(f220,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,X0)
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f219,f1]) ).
fof(f221,plain,
( identity = multiply(sk_c6,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f218,f174]) ).
fof(f223,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c7,X0))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f183,f184]) ).
fof(f225,plain,
( multiply(sk_c6,identity) = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f183,f173]) ).
fof(f230,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f225,f221]) ).
fof(f235,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c7,X0))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f4,f230]) ).
fof(f236,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,X0)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f235,f223]) ).
fof(f238,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f236,f1]) ).
fof(f244,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f186,f3]) ).
fof(f250,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c3),multiply(sk_c7,X0))
| ~ spl0_13 ),
inference(superposition,[],[f186,f179]) ).
fof(f252,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f186,f186]) ).
fof(f254,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f186,f192]) ).
fof(f257,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f186,f200]) ).
fof(f258,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_11 ),
inference(superposition,[],[f186,f118]) ).
fof(f267,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f258,f109]) ).
fof(f268,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f257,f123]) ).
fof(f270,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f254,f3]) ).
fof(f273,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f250,f123]) ).
fof(f276,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f244,f252]) ).
fof(f277,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f268,f238]) ).
fof(f279,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,X0)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f273,f209]) ).
fof(f280,plain,
( ! [X0] : multiply(X0,sk_c6) = X0
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f276,f270]) ).
fof(f281,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f279,f238]) ).
fof(f282,plain,
( ! [X0] : multiply(X0,sk_c7) = X0
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f280,f277]) ).
fof(f284,plain,
( sk_c5 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f104,f277]) ).
fof(f285,plain,
( sk_c7 = multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f128,f277]) ).
fof(f287,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c7,X0))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f179,f277]) ).
fof(f290,plain,
( ! [X0] : multiply(sk_c3,X0) = X0
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f287,f281]) ).
fof(f292,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f285,f282]) ).
fof(f293,plain,
( identity != sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f284,f230]) ).
fof(f295,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f293,f270]) ).
fof(f297,plain,
( sk_c7 != sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f295,f277]) ).
fof(f299,plain,
( sk_c6 = sk_c7
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f89,f267]) ).
fof(f302,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f186,f267]) ).
fof(f304,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f302,f3]) ).
fof(f306,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f304,f270]) ).
fof(f307,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f306,f277]) ).
fof(f308,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f307,f297]) ).
fof(f309,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f310,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f97,f277]) ).
fof(f312,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f310,f307]) ).
fof(f313,plain,
( ! [X1] :
( sk_c6 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f312,f282]) ).
fof(f314,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != X1 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f313,f277]) ).
fof(f322,plain,
( sk_c4 = multiply(sk_c7,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f193,f307]) ).
fof(f324,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f322,f281]) ).
fof(f327,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f324,f270]) ).
fof(f328,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f327,f277]) ).
fof(f331,plain,
( sk_c6 != sk_c7
| sk_c7 != sk_c3
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f314,f123]) ).
fof(f334,plain,
( sk_c7 != sk_c3
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f331,f277]) ).
fof(f339,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f334,f292]) ).
fof(f340,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f342,plain,
( sk_c5 != multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_9
| spl0_11 ),
inference(forward_demodulation,[],[f117,f220]) ).
fof(f356,plain,
( identity != sk_c5
| ~ spl0_3
| ~ spl0_9
| spl0_11 ),
inference(forward_demodulation,[],[f342,f173]) ).
fof(f368,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f3,f136]) ).
fof(f370,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f158]) ).
fof(f372,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f186,f103]) ).
fof(f374,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f186,f113]) ).
fof(f375,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f113]) ).
fof(f376,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f374,f136]) ).
fof(f377,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f186,f147]) ).
fof(f378,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f147]) ).
fof(f379,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f377,f158]) ).
fof(f381,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c2)
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f97,f113]) ).
fof(f385,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_6
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f381]) ).
fof(f404,plain,
( $false
| ~ spl0_6
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f385,f136]) ).
fof(f405,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f411,definition,
( spl0_22
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f412,plain,
( sk_c6 = sk_c7
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f413,plain,
( sk_c6 != sk_c7
| spl0_22 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f415,plain,
( multiply(sk_c3,identity) = multiply(sk_c7,sk_c2)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f179,f368]) ).
fof(f416,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_14 ),
inference(superposition,[],[f186,f368]) ).
fof(f419,plain,
( sk_c2 = inverse(sk_c6)
| ~ spl0_14 ),
inference(forward_demodulation,[],[f416,f276]) ).
fof(f420,plain,
( sk_c3 = multiply(sk_c7,sk_c2)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f415,f276]) ).
fof(f421,plain,
( sk_c1 = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f184,f370]) ).
fof(f422,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_16 ),
inference(superposition,[],[f186,f370]) ).
fof(f425,plain,
( inverse(sk_c7) = sk_c1
| ~ spl0_16 ),
inference(forward_demodulation,[],[f422,f276]) ).
fof(f426,plain,
( sk_c5 = sk_c1
| ~ spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[],[f421,f276]) ).
fof(f430,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f158,f426]) ).
fof(f449,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c2,identity)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f375,f173]) ).
fof(f454,plain,
( multiply(sk_c6,sk_c7) = sk_c2
| ~ spl0_3
| ~ spl0_10 ),
inference(forward_demodulation,[],[f449,f276]) ).
fof(f458,plain,
( sk_c5 = sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f454,f103]) ).
fof(f462,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f368,f458]) ).
fof(f464,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f136,f458]) ).
fof(f465,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f464,f430]) ).
fof(f466,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f462,f93]) ).
fof(f467,plain,
( spl0_22
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f465,f156,f134,f111,f102,f84,f411]) ).
fof(f469,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_22 ),
inference(superposition,[],[f103,f412]) ).
fof(f474,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_14
| ~ spl0_22 ),
inference(superposition,[],[f368,f412]) ).
fof(f479,plain,
( identity = sk_c3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f474,f420]) ).
fof(f481,plain,
( sk_c6 = sk_c5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f469,f379]) ).
fof(f483,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f479,f466]) ).
fof(f484,plain,
( sk_c7 = sk_c5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f481,f412]) ).
fof(f485,plain,
( sk_c6 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(superposition,[],[f122,f483]) ).
fof(f490,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f485,f85]) ).
fof(f491,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f490,f484]) ).
fof(f492,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f491,f412]) ).
fof(f493,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f492]) ).
fof(f496,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| spl0_4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f90,f484]) ).
fof(f510,plain,
( $false
| spl0_4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f496,f379]) ).
fof(f511,plain,
( spl0_4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f524,plain,
( sk_c5 != sk_c1
| spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f86,f425]) ).
fof(f526,plain,
( identity = multiply(sk_c1,sk_c7)
| ~ spl0_16 ),
inference(superposition,[],[f3,f425]) ).
fof(f531,plain,
( multiply(sk_c7,sk_c2) = multiply(sk_c1,identity)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f378,f368]) ).
fof(f536,plain,
( sk_c1 = multiply(sk_c7,sk_c2)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f531,f276]) ).
fof(f542,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f186,f376]) ).
fof(f544,plain,
( sk_c6 = sk_c7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f542,f372]) ).
fof(f546,plain,
( $false
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f544,f413]) ).
fof(f547,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f558,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_14
| ~ spl0_22 ),
inference(superposition,[],[f368,f412]) ).
fof(f567,plain,
( identity = sk_c1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f558,f536]) ).
fof(f576,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_4 ),
inference(superposition,[],[f186,f89]) ).
fof(f579,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f576,f412]) ).
fof(f582,plain,
( identity = sk_c5
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f579,f3]) ).
fof(f584,plain,
( identity = sk_c7
| ~ spl0_4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f582,f484]) ).
fof(f601,plain,
( sk_c7 = sk_c1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f567,f584]) ).
fof(f622,plain,
( sk_c7 != sk_c5
| spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f524,f601]) ).
fof(f630,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f622,f484]) ).
fof(f631,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f651,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f270,f412]) ).
fof(f652,plain,
( ! [X0] : multiply(X0,sk_c7) = X0
| ~ spl0_3
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f280,f412]) ).
fof(f654,plain,
( sk_c7 = sk_c2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f458,f484]) ).
fof(f655,plain,
( identity != sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f356,f484]) ).
fof(f656,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_7
| ~ spl0_22 ),
inference(forward_demodulation,[],[f100,f412]) ).
fof(f663,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f655,f584]) ).
fof(f664,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f663]) ).
fof(f665,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_22 ),
inference(forward_demodulation,[],[f656,f652]) ).
fof(f674,plain,
( sk_c7 != sk_c2
| sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_22 ),
inference(superposition,[],[f665,f419]) ).
fof(f675,plain,
( sk_c7 != sk_c1
| sk_c7 != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f665,f425]) ).
fof(f676,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f665,f109]) ).
fof(f680,plain,
( sk_c7 != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f676]) ).
fof(f681,plain,
( sk_c7 != sk_c1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_16
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f675]) ).
fof(f687,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f681,f601]) ).
fof(f688,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f687]) ).
fof(f689,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f674,f654]) ).
fof(f692,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f689,f412]) ).
fof(f693,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f692]) ).
fof(f694,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c7)
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_22 ),
inference(forward_demodulation,[],[f82,f412]) ).
fof(f695,plain,
( ! [X2] :
( sk_c7 != X2
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f694,f652]) ).
fof(f696,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != X2 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f695,f412]) ).
fof(f709,plain,
( sk_c7 != sk_c1
| sk_c7 != sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f696,f425]) ).
fof(f710,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f696,f109]) ).
fof(f714,plain,
( sk_c7 != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f710]) ).
fof(f715,plain,
( sk_c7 != sk_c1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f709]) ).
fof(f721,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f715,f601]) ).
fof(f722,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f721]) ).
fof(f728,plain,
( ! [X3] :
( sk_c5 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[],[f79,f652]) ).
fof(f729,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != X3 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f728,f484]) ).
fof(f737,plain,
( sk_c7 != sk_c1
| sk_c7 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f729,f425]) ).
fof(f743,plain,
( sk_c7 != sk_c1
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f737]) ).
fof(f749,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f743,f601]) ).
fof(f750,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f749]) ).
fof(f756,plain,
( sk_c7 != multiply(sk_c6,sk_c7)
| spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f94,f484]) ).
fof(f762,plain,
( sk_c7 != sk_c5
| spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f756,f103]) ).
fof(f767,plain,
( $false
| spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f762,f484]) ).
fof(f768,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f767]) ).
fof(f795,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f680,f328]) ).
fof(f796,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f795]) ).
fof(f807,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f146,f412]) ).
fof(f842,plain,
( identity != sk_c7
| spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f807,f526]) ).
fof(f878,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f714,f328]) ).
fof(f879,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f878]) ).
fof(f887,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f842,f651]) ).
fof(f888,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f887]) ).
fof(f914,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f299,f413]) ).
fof(f915,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f914]) ).
fof(f925,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f128,f290]) ).
fof(f946,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f925,f413]) ).
fof(f947,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f946]) ).
fof(f956,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != X3 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f728,f307]) ).
fof(f986,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c4
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f956,f109]) ).
fof(f987,plain,
( sk_c7 != sk_c4
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f986]) ).
fof(f991,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f987,f328]) ).
fof(f992,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f991]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f105]) ).
cnf(s2,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f114]) ).
cnf(s3,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f119]) ).
cnf(s4,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f124]) ).
cnf(s5,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s6,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f130]) ).
cnf(s7,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f131]) ).
cnf(s8,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f132]) ).
cnf(s9,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s10,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s11,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s12,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s13,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f141]) ).
cnf(s14,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f142]) ).
cnf(s15,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f143]) ).
cnf(s16,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s17,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s18,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f150]) ).
cnf(s19,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f151]) ).
cnf(s20,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f152]) ).
cnf(s21,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f153]) ).
cnf(s22,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s23,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f159]) ).
cnf(s24,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f160]) ).
cnf(s25,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f161]) ).
cnf(s26,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f162]) ).
cnf(s27,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f163]) ).
cnf(s28,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f164]) ).
cnf(s29,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s30,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f166]) ).
cnf(s31,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f167]) ).
cnf(s32,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f168]) ).
cnf(s33,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f169]) ).
cnf(s34,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f170]) ).
cnf(s35,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f171]) ).
cnf(s36,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f172]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f309]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f340]) ).
cnf(s45,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_14 ),
inference(sat_conversion,[],[f405]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_16
| spl0_22 ),
inference(sat_conversion,[],[f467]) ).
cnf(s48,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f493]) ).
cnf(s49,plain,
( spl0_4
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f511]) ).
cnf(s50,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| spl0_22 ),
inference(sat_conversion,[],[f547]) ).
cnf(s51,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f631]) ).
cnf(s52,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f664]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f688]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f693]) ).
cnf(s60,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f722]) ).
cnf(s65,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f750]) ).
cnf(s68,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f768]) ).
cnf(s70,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f796]) ).
cnf(s80,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f879]) ).
cnf(s81,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f888]) ).
cnf(s88,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_11
| spl0_22 ),
inference(sat_conversion,[],[f915]) ).
cnf(s98,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| spl0_22 ),
inference(sat_conversion,[],[f947]) ).
cnf(s101,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f992]) ).
cnf(s102,plain,
spl0_3,
inference(rat,[],[s51,s49,s50,s6,s13,s20,s27,s34]) ).
cnf(s103,plain,
( spl0_8
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s37,s30,s31,s32,s33,s102]) ).
cnf(s104,plain,
( spl0_13
| ~ spl0_22
| ~ spl0_7
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s55,s12,s19,s26,s102]) ).
cnf(s105,plain,
( ~ spl0_11
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s48,s4,s11,s18,s25,s70,s104,s88,s103,s102]) ).
cnf(s106,plain,
( ~ spl0_15
| ~ spl0_16
| ~ spl0_14
| ~ spl0_10
| ~ spl0_4
| ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s50,s57,s102]) ).
cnf(s107,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s106,s3,s10,s17,s24]) ).
cnf(s108,plain,
( ~ spl0_7
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s106,s2,s9,s16,s23,s105,s107,s103]) ).
cnf(s109,plain,
( spl0_10
| ~ spl0_6
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s40,s2,s3,s4,s5,s102]) ).
cnf(s110,plain,
( ~ spl0_6
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s40,s9,s10,s11,s12,s45,s109,s102]) ).
cnf(s111,plain,
( spl0_7
| ~ spl0_5
| spl0_1
| ~ spl0_4
| spl0_2
| ~ spl0_8 ),
inference(rat,[],[s110,s1,s102]) ).
cnf(s113,plain,
spl0_5,
inference(rat,[],[s47,s68,s8,s15,s22,s29,s36,s102]) ).
cnf(s114,plain,
spl0_4,
inference(rat,[],[s47,s49,s7,s14,s21,s28,s35,s102]) ).
cnf(s116,plain,
spl0_8,
inference(rat,[],[s103,s113,s114]) ).
cnf(s117,plain,
~ spl0_7,
inference(rat,[],[s108,s113,s114]) ).
cnf(s119,plain,
( spl0_13
| ~ spl0_22
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s60,s19,s26,s102,s114,s116]) ).
cnf(s120,plain,
( ~ spl0_15
| ~ spl0_22
| spl0_12
| ~ spl0_14
| ~ spl0_13
| ~ spl0_16 ),
inference(rat,[],[s4,s48,s116,s113,s102]) ).
cnf(s121,plain,
( ~ spl0_11
| ~ spl0_9
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s120,s18,s25,s80,s119,s88,s102,s114,s113]) ).
cnf(s122,plain,
( spl0_11
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s60,s47,s3,s17,s24,s102,s114,s116]) ).
cnf(s123,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s60,s47,s2,s16,s23,s121,s116,s114,s102]) ).
cnf(s124,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s123,s122]) ).
cnf(s125,plain,
~ spl0_2,
inference(rat,[],[s80,s98,s9,s10,s11,s12,s124,s102,s114,s113]) ).
cnf(s126,plain,
spl0_1,
inference(rat,[],[s111,s113,s125,s114,s116,s117]) ).
cnf(s127,plain,
( spl0_16
| ~ spl0_9
| ~ spl0_11 ),
inference(rat,[],[s101,s25,s26,s88,s102,s114,s113,s126]) ).
cnf(s128,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_14 ),
inference(rat,[],[s65,s81,s127,s88,s102,s114,s116,s126]) ).
cnf(s129,plain,
( spl0_9
| ~ spl0_14 ),
inference(rat,[],[s65,s47,s2,s16,s23,s102,s114,s116,s126]) ).
cnf(s130,plain,
( ~ spl0_9
| ~ spl0_14 ),
inference(rat,[],[s52,s47,s3,s17,s24,s128,s116,s114,s102]) ).
cnf(s131,plain,
~ spl0_14,
inference(rat,[],[s130,s129]) ).
cnf(s132,plain,
spl0_13,
inference(rat,[],[s12,s131]) ).
cnf(s133,plain,
spl0_12,
inference(rat,[],[s11,s131]) ).
cnf(s134,plain,
spl0_11,
inference(rat,[],[s10,s131]) ).
cnf(s135,plain,
spl0_9,
inference(rat,[],[s9,s131]) ).
cnf(s136,plain,
spl0_22,
inference(rat,[],[s98,s132,s135,s113,s114,s102,s133]) ).
cnf(s137,plain,
$false,
inference(rat,[],[s101,s132,s135,s126,s113,s114,s102,s134,s136,s133]) ).
fof(f993,plain,
$false,
inference(avatar_sat_refutation,[],[s137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP346-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.38 % Computer : n017.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Sep 27 09:50:20 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42 Running first-order model finding
% 0.14/0.42 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
% 0.19/0.46 % (2298016)Will run a generic schedule for satisfiability detection.
% 0.19/0.46 % (2298032)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3997338382:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.46 % (2298029)% WARNING: option uhcvi not known.
% 0.19/0.46 % (2298027)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2715828015_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.46 % (2298029)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2215146115:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.46 % (2298031)dis+10_1_sil=32000:sp=arity:random_seed=2995806077:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.46 % (2298030)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2347600147:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.46 % (2298033)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=503747182:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.46 % (2298034)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3942236505:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.46 % (2298032) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2298016-2298032"...
% 0.19/0.46 % TRYING [1]
% 0.19/0.46 % TRYING [2]
% 0.19/0.46 % TRYING [3]
% 0.19/0.46 % (2298032)...printing done.
% 0.19/0.46 % (2298032)Refutation found. Thanks to Tanya!
% 0.19/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46 % (2298032)------------------------------
% 0.19/0.46 % (2298032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.46 % (2298032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.46 % (2298032)CaDiCaL version: 2.1.3
% 0.19/0.46 % (2298032)Termination reason: Refutation
% 0.19/0.46 % (2298032)Time elapsed: 0.012 s
% 0.19/0.46 % (2298032)Peak memory usage: 12 MB
% 0.19/0.46 % (2298032)Instructions burned: 32 (million)
% 0.19/0.46 % (2298016)Success in time 0.028 s
% 0.19/0.46 % Vampire exiting
%------------------------------------------------------------------------------