%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP262-1 : 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 : n003.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 10:17:19 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 53
% Syntax : Number of formulae : 348 ( 23 unt; 24 def)
% Number of atoms : 1075 ( 301 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1381 ( 654 ~; 703 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 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_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = inverse(sk_c1)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c6 = inverse(sk_c2)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(sk_c5,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f54]) ).
fof(f57,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f61,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_3
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_4
<=> sk_c6 = multiply(sk_c5,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( sk_c6 != multiply(sk_c5,sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_5
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f72,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_6
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f55,f74,f71,f67,f63,f60,f57]) ).
fof(f78,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f79,plain,
( sk_c6 != multiply(sk_c4,sk_c5)
| spl0_7 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f53,f67,f78]) ).
fof(f83,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f85,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f51,f67,f83]) ).
fof(f88,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f49,f67,f88]) ).
fof(f93,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f47,f67,f93]) ).
fof(f97,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f45,f67,f63]) ).
fof(f99,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f101,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f43,f99,f78]) ).
fof(f103,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f41,f99,f83]) ).
fof(f104,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f39,f99,f88]) ).
fof(f105,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f37,f99,f93]) ).
fof(f106,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f35,f99,f63]) ).
fof(f108,definition,
( spl0_12
<=> sk_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f110,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f33,f108,f78]) ).
fof(f112,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f31,f108,f83]) ).
fof(f113,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f29,f108,f88]) ).
fof(f114,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f27,f108,f93]) ).
fof(f115,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f25,f108,f63]) ).
fof(f117,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f119,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f23,f117,f78]) ).
fof(f121,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f21,f117,f83]) ).
fof(f122,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f19,f117,f88]) ).
fof(f123,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f17,f117,f93]) ).
fof(f124,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f15,f117,f63]) ).
fof(f126,definition,
( spl0_14
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f128,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f13,f126,f78]) ).
fof(f130,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f11,f126,f83]) ).
fof(f131,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f9,f126,f88]) ).
fof(f132,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f7,f126,f93]) ).
fof(f133,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f5,f126,f63]) ).
fof(f134,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_8 ),
inference(superposition,[],[f3,f85]) ).
fof(f135,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f95]) ).
fof(f138,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f139,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f64]) ).
fof(f140,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f134]) ).
fof(f141,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f90]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f80]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f140,f1]) ).
fof(f144,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f138,f1]) ).
fof(f153,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f143,f80]) ).
fof(f156,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f141,f64]) ).
fof(f180,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_10 ),
inference(superposition,[],[f144,f135]) ).
fof(f184,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3 ),
inference(superposition,[],[f144,f64]) ).
fof(f186,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f144,f134]) ).
fof(f187,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f144,f90]) ).
fof(f196,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f187,f95]) ).
fof(f197,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f139,f196]) ).
fof(f200,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f197,f153]) ).
fof(f208,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f144,f200]) ).
fof(f210,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f208,f3]) ).
fof(f225,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f180,f210]) ).
fof(f226,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f196,f210]) ).
fof(f228,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f226,f1]) ).
fof(f229,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f225,f3]) ).
fof(f233,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f156,f196]) ).
fof(f242,plain,
( sk_c4 = multiply(inverse(identity),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f186,f228]) ).
fof(f243,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f242,f3]) ).
fof(f257,plain,
( identity = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f233,f228]) ).
fof(f274,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f257,f229]) ).
fof(f275,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f274,f1]) ).
fof(f276,plain,
( sk_c6 != multiply(identity,sk_c7)
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f69,f275]) ).
fof(f290,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f276,f1]) ).
fof(f294,plain,
( identity != sk_c7
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f290,f228]) ).
fof(f297,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f294,f210]) ).
fof(f298,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f315,definition,
( spl0_15
<=> identity = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f316,plain,
( identity = sk_c4
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f325,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f243,f93,f88,f83,f78,f63,f315]) ).
fof(f327,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_11 ),
inference(superposition,[],[f3,f101]) ).
fof(f329,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f119]) ).
fof(f330,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c6)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f142,f68]) ).
fof(f333,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f330,f64]) ).
fof(f334,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f144,f110]) ).
fof(f336,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f334,f101]) ).
fof(f337,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f144,f128]) ).
fof(f339,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f337,f119]) ).
fof(f344,plain,
( sk_c7 != sk_c5
| sk_c6 != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f72,f90]) ).
fof(f345,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f72,f110]) ).
fof(f346,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f345]) ).
fof(f348,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f346,f101]) ).
fof(f349,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f348]) ).
fof(f355,definition,
( spl0_18
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f357,plain,
( sk_c7 != sk_c5
| spl0_18 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f360,definition,
( spl0_19
<=> sk_c6 = inverse(inverse(sk_c6)) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f362,plain,
( sk_c6 != inverse(inverse(sk_c6))
| spl0_19 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f364,definition,
( spl0_20
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f365,plain,
( identity = sk_c5
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f373,definition,
( spl0_22
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f374,plain,
( sk_c6 = sk_c5
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f375,plain,
( sk_c6 != sk_c5
| spl0_22 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f378,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f144,f327]) ).
fof(f381,plain,
( sk_c4 = sk_c2
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f378,f186]) ).
fof(f385,plain,
( sk_c7 != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f58,f184]) ).
fof(f386,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f58,f80]) ).
fof(f387,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f386]) ).
fof(f388,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f387,f85]) ).
fof(f389,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f391,definition,
( spl0_23
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f392,plain,
( sk_c7 = sk_c6
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f394,plain,
( ~ spl0_19
| ~ spl0_23
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f385,f63,f57,f391,f360]) ).
fof(f400,definition,
( spl0_25
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f401,plain,
( identity = sk_c6
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f411,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f75,f128]) ).
fof(f412,plain,
( sk_c6 != sk_c5
| sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f75,f64]) ).
fof(f415,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f411]) ).
fof(f421,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f415,f119]) ).
fof(f422,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f421]) ).
fof(f429,definition,
( spl0_28
<=> sk_c7 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f430,plain,
( sk_c7 = inverse(identity)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f431,plain,
( sk_c7 != inverse(identity)
| spl0_28 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f441,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f61,f90]) ).
fof(f442,plain,
( sk_c7 != sk_c5
| sk_c7 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f61,f110]) ).
fof(f443,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f441]) ).
fof(f444,plain,
( sk_c7 != sk_c6
| sk_c7 != sk_c5
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f442,f101]) ).
fof(f451,definition,
( spl0_30
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f452,plain,
( identity = sk_c7
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f456,plain,
( ~ spl0_18
| ~ spl0_23
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f444,f108,f99,f60,f391,f355]) ).
fof(f464,plain,
( sk_c7 != sk_c5
| sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f61,f333]) ).
fof(f471,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f144,f336]) ).
fof(f473,plain,
( identity = sk_c5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f471,f3]) ).
fof(f475,plain,
( spl0_20
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f473,f108,f99,f364]) ).
fof(f476,plain,
( sk_c6 = multiply(identity,sk_c7)
| ~ spl0_4
| ~ spl0_20 ),
inference(superposition,[],[f68,f365]) ).
fof(f482,plain,
( identity != sk_c7
| spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f357,f365]) ).
fof(f483,plain,
( ~ spl0_30
| spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f482,f364,f355,f451]) ).
fof(f486,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f476,f1]) ).
fof(f489,plain,
( spl0_23
| ~ spl0_4
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f486,f364,f67,f391]) ).
fof(f516,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f339,f392]) ).
fof(f524,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(superposition,[],[f144,f516]) ).
fof(f526,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f524,f3]) ).
fof(f535,plain,
( spl0_25
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f228,f93,f88,f83,f78,f63,f400]) ).
fof(f540,plain,
( spl0_30
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f210,f93,f88,f83,f78,f63,f451]) ).
fof(f546,plain,
( spl0_30
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f526,f391,f126,f117,f451]) ).
fof(f547,plain,
( identity != sk_c7
| sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f464,f365]) ).
fof(f548,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f443,f88,f60,f93]) ).
fof(f554,plain,
( sk_c7 != sk_c6
| identity != sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20 ),
inference(forward_demodulation,[],[f547,f85]) ).
fof(f557,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f554,f392]) ).
fof(f558,plain,
( ~ spl0_30
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f557,f391,f364,f83,f78,f67,f63,f60,f451]) ).
fof(f563,plain,
( sk_c6 != multiply(sk_c4,identity)
| spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f79,f365]) ).
fof(f564,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f110,f392]) ).
fof(f573,plain,
( identity != sk_c6
| ~ spl0_20
| spl0_22 ),
inference(forward_demodulation,[],[f375,f365]) ).
fof(f579,plain,
( sk_c7 != multiply(sk_c4,identity)
| spl0_7
| ~ spl0_20
| ~ spl0_23 ),
inference(forward_demodulation,[],[f563,f392]) ).
fof(f580,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f564,f381]) ).
fof(f584,plain,
( identity != sk_c7
| ~ spl0_20
| spl0_22
| ~ spl0_23 ),
inference(forward_demodulation,[],[f573,f392]) ).
fof(f589,plain,
( identity = multiply(sk_c4,sk_c7)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_23 ),
inference(forward_demodulation,[],[f580,f365]) ).
fof(f590,plain,
( ~ spl0_30
| ~ spl0_20
| spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f584,f391,f373,f364,f451]) ).
fof(f597,plain,
( identity = sk_c6
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f374,f365]) ).
fof(f598,plain,
( spl0_25
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f597,f373,f364,f400]) ).
fof(f610,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_11
| ~ spl0_25 ),
inference(superposition,[],[f327,f401]) ).
fof(f615,plain,
( identity = sk_c2
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_demodulation,[],[f610,f1]) ).
fof(f633,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_13
| ~ spl0_30 ),
inference(superposition,[],[f329,f452]) ).
fof(f639,plain,
( identity = sk_c1
| ~ spl0_13
| ~ spl0_30 ),
inference(forward_demodulation,[],[f633,f1]) ).
fof(f652,plain,
( identity = multiply(sk_c4,identity)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_23
| ~ spl0_30 ),
inference(forward_demodulation,[],[f589,f452]) ).
fof(f656,plain,
( sk_c6 = inverse(identity)
| ~ spl0_11
| ~ spl0_25 ),
inference(superposition,[],[f101,f615]) ).
fof(f657,plain,
( sk_c7 = inverse(identity)
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f656,f392]) ).
fof(f660,plain,
( $false
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f657,f431]) ).
fof(f661,plain,
( ~ spl0_11
| ~ spl0_23
| ~ spl0_25
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f660]) ).
fof(f663,plain,
( identity = inverse(identity)
| ~ spl0_28
| ~ spl0_30 ),
inference(forward_demodulation,[],[f430,f452]) ).
fof(f668,plain,
( identity != sk_c7
| spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_23
| ~ spl0_30 ),
inference(superposition,[],[f579,f652]) ).
fof(f675,plain,
( $false
| spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_23
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f668,f452]) ).
fof(f676,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_23
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f675]) ).
fof(f695,plain,
( sk_c7 = inverse(identity)
| ~ spl0_13
| ~ spl0_30 ),
inference(superposition,[],[f119,f639]) ).
fof(f696,plain,
( identity = inverse(identity)
| ~ spl0_13
| ~ spl0_30 ),
inference(forward_demodulation,[],[f695,f452]) ).
fof(f727,plain,
( identity != sk_c5
| sk_c6 != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_30 ),
inference(forward_demodulation,[],[f344,f452]) ).
fof(f743,plain,
( spl0_20
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f275,f93,f88,f83,f78,f63,f364]) ).
fof(f748,plain,
( identity = inverse(sk_c4)
| ~ spl0_8
| ~ spl0_25 ),
inference(forward_demodulation,[],[f85,f401]) ).
fof(f757,plain,
( identity != inverse(inverse(identity))
| spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f362,f401]) ).
fof(f774,plain,
( sk_c7 != sk_c6
| identity != sk_c5
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_30 ),
inference(forward_demodulation,[],[f727,f95]) ).
fof(f798,plain,
( identity != inverse(identity)
| spl0_19
| ~ spl0_25
| ~ spl0_28
| ~ spl0_30 ),
inference(forward_demodulation,[],[f757,f663]) ).
fof(f809,plain,
( identity != sk_c7
| identity != sk_c5
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_demodulation,[],[f774,f401]) ).
fof(f818,plain,
( $false
| spl0_19
| ~ spl0_25
| ~ spl0_28
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f798,f663]) ).
fof(f819,plain,
( spl0_19
| ~ spl0_25
| ~ spl0_28
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f818]) ).
fof(f822,plain,
( identity != sk_c5
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f809,f452]) ).
fof(f824,plain,
( ~ spl0_20
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_25
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f822,f451,f400,f93,f88,f71,f364]) ).
fof(f830,plain,
( identity != sk_c5
| sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_25 ),
inference(forward_demodulation,[],[f412,f401]) ).
fof(f871,plain,
( sk_c7 != inverse(identity)
| identity != sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_25 ),
inference(forward_demodulation,[],[f830,f401]) ).
fof(f883,plain,
( identity != inverse(identity)
| identity != sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_demodulation,[],[f871,f452]) ).
fof(f887,definition,
( spl0_32
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f890,plain,
( ~ spl0_20
| ~ spl0_32
| ~ spl0_3
| ~ spl0_6
| ~ spl0_25
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f883,f451,f400,f74,f63,f887,f364]) ).
fof(f904,plain,
( identity = inverse(identity)
| ~ spl0_8
| ~ spl0_15
| ~ spl0_25 ),
inference(superposition,[],[f748,f316]) ).
fof(f905,plain,
( spl0_32
| ~ spl0_8
| ~ spl0_15
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f904,f400,f315,f83,f887]) ).
fof(f906,plain,
( identity != multiply(sk_c6,sk_c7)
| spl0_3
| ~ spl0_20 ),
inference(forward_demodulation,[],[f65,f365]) ).
fof(f938,plain,
( spl0_32
| ~ spl0_13
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f696,f451,f117,f887]) ).
fof(f945,plain,
( identity != multiply(sk_c6,identity)
| spl0_3
| ~ spl0_20
| ~ spl0_30 ),
inference(forward_demodulation,[],[f906,f452]) ).
fof(f964,plain,
( identity != multiply(identity,identity)
| spl0_3
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_demodulation,[],[f945,f401]) ).
fof(f971,plain,
( $false
| spl0_3
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f964,f1]) ).
fof(f972,plain,
( spl0_3
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f971]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s2,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f81]) ).
cnf(s3,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s6,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f97]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s8,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f103]) ).
cnf(s9,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s10,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f105]) ).
cnf(s11,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f106]) ).
cnf(s12,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s13,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s14,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s15,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f114]) ).
cnf(s16,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s17,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s18,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s19,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s20,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s21,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s22,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s23,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s24,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f131]) ).
cnf(s25,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s26,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s28,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f298]) ).
cnf(s31,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f325]) ).
cnf(s32,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f349]) ).
cnf(s36,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f389]) ).
cnf(s37,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f394]) ).
cnf(s41,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f422]) ).
cnf(s47,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_23 ),
inference(sat_conversion,[],[f456]) ).
cnf(s48,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f475]) ).
cnf(s49,plain,
( spl0_18
| ~ spl0_20
| ~ spl0_30 ),
inference(sat_conversion,[],[f483]) ).
cnf(s51,plain,
( ~ spl0_4
| ~ spl0_20
| spl0_23 ),
inference(sat_conversion,[],[f489]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_25 ),
inference(sat_conversion,[],[f535]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_30 ),
inference(sat_conversion,[],[f540]) ).
cnf(s58,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| spl0_30 ),
inference(sat_conversion,[],[f546]) ).
cnf(s59,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f548]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_23
| ~ spl0_30 ),
inference(sat_conversion,[],[f558]) ).
cnf(s63,plain,
( ~ spl0_20
| spl0_22
| ~ spl0_23
| ~ spl0_30 ),
inference(sat_conversion,[],[f590]) ).
cnf(s65,plain,
( ~ spl0_20
| ~ spl0_22
| spl0_25 ),
inference(sat_conversion,[],[f598]) ).
cnf(s76,plain,
( ~ spl0_11
| ~ spl0_23
| ~ spl0_25
| spl0_28 ),
inference(sat_conversion,[],[f661]) ).
cnf(s77,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_23
| ~ spl0_30 ),
inference(sat_conversion,[],[f676]) ).
cnf(s83,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_20 ),
inference(sat_conversion,[],[f743]) ).
cnf(s107,plain,
( spl0_19
| ~ spl0_25
| ~ spl0_28
| ~ spl0_30 ),
inference(sat_conversion,[],[f819]) ).
cnf(s112,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f824]) ).
cnf(s122,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30
| ~ spl0_32 ),
inference(sat_conversion,[],[f890]) ).
cnf(s124,plain,
( ~ spl0_8
| ~ spl0_15
| ~ spl0_25
| spl0_32 ),
inference(sat_conversion,[],[f905]) ).
cnf(s126,plain,
( ~ spl0_13
| ~ spl0_30
| spl0_32 ),
inference(sat_conversion,[],[f938]) ).
cnf(s134,plain,
( spl0_3
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f972]) ).
cnf(s135,plain,
spl0_3,
inference(rat,[],[s65,s63,s134,s58,s51,s48,s6,s11,s16,s21,s26]) ).
cnf(s136,plain,
( spl0_7
| ~ spl0_6 ),
inference(rat,[],[s41,s17,s22]) ).
cnf(s137,plain,
( ~ spl0_13
| ~ spl0_6 ),
inference(rat,[],[s122,s126,s55,s57,s83,s23,s24,s25,s41,s136,s135]) ).
cnf(s138,plain,
~ spl0_6,
inference(rat,[],[s124,s122,s31,s55,s57,s83,s18,s19,s20,s137,s136,s135]) ).
cnf(s140,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s112,s55,s57,s83,s135]) ).
cnf(s141,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s32,s10,s15]) ).
cnf(s142,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s32,s9,s14]) ).
cnf(s143,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s32,s8,s13]) ).
cnf(s144,plain,
( ~ spl0_8
| ~ spl0_5
| ~ spl0_10
| ~ spl0_9 ),
inference(rat,[],[s32,s7,s12,s140]) ).
cnf(s145,plain,
~ spl0_5,
inference(rat,[],[s144,s143,s142,s141]) ).
cnf(s146,plain,
spl0_4,
inference(rat,[],[s28,s2,s3,s4,s5,s135]) ).
cnf(s147,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s62,s58,s51,s48,s10,s15,s20,s25,s135,s146]) ).
cnf(s148,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s62,s58,s51,s48,s9,s14,s19,s24,s59,s147,s146,s135]) ).
cnf(s149,plain,
( spl0_8
| ~ spl0_2 ),
inference(rat,[],[s49,s47,s58,s51,s48,s8,s13,s18,s23,s146]) ).
cnf(s150,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s77,s58,s51,s48,s7,s12,s17,s22,s148,s146]) ).
cnf(s151,plain,
~ spl0_2,
inference(rat,[],[s150,s149]) ).
cnf(s152,plain,
spl0_1,
inference(rat,[],[s1,s138,s145,s135,s146,s151]) ).
cnf(s153,plain,
spl0_8,
inference(rat,[],[s107,s76,s65,s63,s37,s58,s51,s48,s8,s13,s18,s23,s135,s152,s146]) ).
cnf(s154,plain,
~ spl0_7,
inference(rat,[],[s36,s152,s153]) ).
cnf(s155,plain,
spl0_14,
inference(rat,[],[s22,s154]) ).
cnf(s156,plain,
spl0_13,
inference(rat,[],[s17,s154]) ).
cnf(s157,plain,
spl0_12,
inference(rat,[],[s12,s154]) ).
cnf(s158,plain,
spl0_11,
inference(rat,[],[s7,s154]) ).
cnf(s159,plain,
spl0_20,
inference(rat,[],[s48,s157,s158]) ).
cnf(s160,plain,
spl0_23,
inference(rat,[],[s51,s146,s159]) ).
cnf(s161,plain,
spl0_30,
inference(rat,[],[s58,s156,s155,s160]) ).
cnf(s163,plain,
$false,
inference(rat,[],[s77,s159,s158,s154,s157,s153,s161,s160]) ).
fof(f973,plain,
$false,
inference(avatar_sat_refutation,[],[s163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP262-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n003.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 09:45:11 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.44 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
% 0.18/0.51 % (257007)Will run a generic schedule for satisfiability detection.
% 0.18/0.51 % (257012)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3379658040_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.51 % TRYING [1]
% 0.18/0.51 % TRYING [2]
% 0.18/0.51 % TRYING [3]
% 0.18/0.51 % TRYING [4]
% 0.18/0.51 % (257013)% WARNING: option uhcvi not known.
% 0.18/0.51 % (257013)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2905148107:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.51 % (257014)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2158214261:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.51 % (257015)dis+10_1_sil=32000:sp=arity:random_seed=1666421093:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.51 % (257018)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=992116082:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.51 % (257016)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4128510904:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.51 % (257017)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=959188373:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.51 % TRYING [5]
% 0.18/0.51 % (257015) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-257007-257015"...
% 0.18/0.51 % TRYING [6]
% 0.18/0.51 % (257016) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-257007-257016"...
% 0.18/0.51 % (257017) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-257007-257017"...
% 0.18/0.51 % (257015)...printing done.
% 0.18/0.51 % (257015)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (257015)------------------------------
% 0.18/0.51 % (257015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.51 % (257015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.51 % (257015)CaDiCaL version: 2.1.3
% 0.18/0.51 % (257015)Termination reason: Refutation
% 0.18/0.51 % (257015)Time elapsed: 0.019 s
% 0.18/0.51 % (257015)Peak memory usage: 12 MB
% 0.18/0.51 % (257015)Instructions burned: 30 (million)
% 0.18/0.51 % (257007)Success in time 0.065 s
% 0.18/0.51 % Vampire exiting
%------------------------------------------------------------------------------