%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP328-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 10:13:39 AM UTC 2026
% Result : Unsatisfiable 1.98s 1.30s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 47
% Syntax : Number of formulae : 294 ( 20 unt; 15 def)
% Number of atoms : 939 ( 297 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1187 ( 542 ~; 630 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X2,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c6 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f67]) ).
fof(f70,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f71,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_2
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f74,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( sk_c6 != inverse(sk_c8)
| spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl0_3
<=> sk_c8 = multiply(sk_c7,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f78,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( sk_c8 != multiply(sk_c7,sk_c6)
| spl0_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl0_4
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f82,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_5
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f85,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_1
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f68,f84,f81,f70,f77,f73,f70]) ).
fof(f89,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f91,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f93,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f95,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f64,f93,f89]) ).
fof(f98,definition,
( spl0_8
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f99,plain,
( sk_c5 != multiply(sk_c4,sk_c8)
| spl0_8 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f100,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f62,f93,f98]) ).
fof(f103,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f60,f93,f103]) ).
fof(f107,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f93,f73]) ).
fof(f108,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f56,f93,f77]) ).
fof(f110,definition,
( spl0_10
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f112,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f54,f110,f89]) ).
fof(f114,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f52,f110,f98]) ).
fof(f115,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f50,f110,f103]) ).
fof(f116,plain,
( spl0_2
| spl0_10 ),
inference(avatar_split_clause,[],[f48,f110,f73]) ).
fof(f117,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f46,f110,f77]) ).
fof(f119,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f121,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f44,f119,f89]) ).
fof(f123,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f42,f119,f98]) ).
fof(f124,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f40,f119,f103]) ).
fof(f125,plain,
( spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f38,f119,f73]) ).
fof(f126,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f36,f119,f77]) ).
fof(f128,definition,
( spl0_12
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f130,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f34,f128,f89]) ).
fof(f133,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f30,f128,f103]) ).
fof(f134,plain,
( spl0_2
| spl0_12 ),
inference(avatar_split_clause,[],[f28,f128,f73]) ).
fof(f135,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f26,f128,f77]) ).
fof(f137,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f139,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f24,f137,f89]) ).
fof(f142,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f20,f137,f103]) ).
fof(f143,plain,
( spl0_2
| spl0_13 ),
inference(avatar_split_clause,[],[f18,f137,f73]) ).
fof(f144,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f16,f137,f77]) ).
fof(f145,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f84,f89]) ).
fof(f146,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f84,f98]) ).
fof(f147,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f84,f103]) ).
fof(f148,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f84,f73]) ).
fof(f149,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f84,f77]) ).
fof(f150,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_2 ),
inference(superposition,[],[f3,f74]) ).
fof(f151,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f91]) ).
fof(f154,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f155,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(sk_c8,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f78]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = multiply(sk_c7,X0)
| ~ spl0_9 ),
inference(superposition,[],[f4,f105]) ).
fof(f157,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c8,X0))
| ~ spl0_2 ),
inference(superposition,[],[f4,f150]) ).
fof(f159,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c8,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f157,f1]) ).
fof(f160,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f154,f1]) ).
fof(f165,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c7,identity)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f155,f150]) ).
fof(f169,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f159,f105]) ).
fof(f170,plain,
( sk_c4 = multiply(sk_c6,identity)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f159,f151]) ).
fof(f193,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f160,f3]) ).
fof(f194,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f160,f160]) ).
fof(f195,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f160,f78]) ).
fof(f199,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c7,X0))
| ~ spl0_9 ),
inference(superposition,[],[f160,f156]) ).
fof(f204,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f160,f100]) ).
fof(f209,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f204,f91]) ).
fof(f210,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f199,f74]) ).
fof(f213,plain,
( sk_c7 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f209,f105]) ).
fof(f217,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f160,f209]) ).
fof(f219,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f217,f3]) ).
fof(f223,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f195,f213]) ).
fof(f228,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f223,f3]) ).
fof(f243,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c7,sk_c5)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f165,f219]) ).
fof(f244,plain,
( multiply(sk_c8,sk_c5) = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f243,f213]) ).
fof(f245,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f244,f105]) ).
fof(f246,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f245,f213]) ).
fof(f255,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f160,f246]) ).
fof(f257,plain,
( identity = sk_c8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f255,f3]) ).
fof(f259,plain,
( sk_c8 = sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f257,f228]) ).
fof(f260,plain,
( sk_c8 = sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f257,f219]) ).
fof(f281,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c8,X0))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f210,f213]) ).
fof(f282,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f281,f159]) ).
fof(f283,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f282,f260]) ).
fof(f313,plain,
( identity = sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f151,f283]) ).
fof(f317,plain,
( sk_c5 = sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f313,f219]) ).
fof(f326,plain,
( sk_c8 = sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f317,f260]) ).
fof(f333,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f91,f326]) ).
fof(f349,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c5) = X0
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f193,f219]) ).
fof(f350,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c8) = X0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f349,f260]) ).
fof(f371,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f194,f350]) ).
fof(f638,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f86,f371]) ).
fof(f652,plain,
( sk_c7 != sk_c8
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f638,f259]) ).
fof(f662,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f652,f213]) ).
fof(f663,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f662]) ).
fof(f664,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f71,f283]) ).
fof(f666,plain,
( ! [X4] :
( sk_c7 != X4
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f664,f371]) ).
fof(f668,plain,
( ! [X4] :
( sk_c8 != X4
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f666,f213]) ).
fof(f669,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(equality_resolution,[],[f668]) ).
fof(f670,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f669,f333]) ).
fof(f671,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f670]) ).
fof(f672,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c8)
| inverse(X0) != sk_c7 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f82,f213]) ).
fof(f673,plain,
( ! [X0] :
( sk_c8 != X0
| inverse(X0) != sk_c7 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f672,f371]) ).
fof(f674,plain,
( ! [X0] :
( sk_c8 != X0
| inverse(X0) != sk_c8 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f673,f213]) ).
fof(f675,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(equality_resolution,[],[f674]) ).
fof(f676,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f675,f333]) ).
fof(f677,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f676]) ).
fof(f689,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f95]) ).
fof(f693,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_12 ),
inference(superposition,[],[f3,f130]) ).
fof(f697,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f85]) ).
fof(f700,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f160,f112]) ).
fof(f702,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f700,f95]) ).
fof(f706,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f160,f121]) ).
fof(f708,plain,
( sk_c3 = multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_11 ),
inference(forward_demodulation,[],[f706,f74]) ).
fof(f710,plain,
( sk_c5 = sk_c3
| ~ spl0_2
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f708,f169]) ).
fof(f720,plain,
( sk_c7 != sk_c7
| sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f82,f130]) ).
fof(f722,plain,
( sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f720]) ).
fof(f728,definition,
( spl0_15
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f729,plain,
( sk_c7 = sk_c8
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f728]) ).
fof(f732,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f722,f139]) ).
fof(f733,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f732]) ).
fof(f751,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_7 ),
inference(superposition,[],[f160,f689]) ).
fof(f754,plain,
( sk_c2 = multiply(sk_c6,identity)
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f751,f74]) ).
fof(f756,plain,
( sk_c4 = sk_c2
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f754,f170]) ).
fof(f760,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f71,f95]) ).
fof(f761,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f760]) ).
fof(f763,plain,
( sk_c7 != multiply(sk_c8,sk_c3)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f761,f112]) ).
fof(f775,definition,
( spl0_21
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f776,plain,
( sk_c8 = sk_c6
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f779,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f763,f121]) ).
fof(f780,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f779]) ).
fof(f783,plain,
( multiply(sk_c4,sk_c8) = sk_c3
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f112,f756]) ).
fof(f785,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f783,f710]) ).
fof(f786,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f785,f99]) ).
fof(f787,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f786]) ).
fof(f794,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f121,f702]) ).
fof(f797,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f160,f702]) ).
fof(f799,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f797,f3]) ).
fof(f802,plain,
( spl0_15
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f794,f119,f110,f93,f728]) ).
fof(f803,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f693,f729]) ).
fof(f805,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f139,f729]) ).
fof(f806,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[],[f85,f729]) ).
fof(f810,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f160,f805]) ).
fof(f812,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f810,f130]) ).
fof(f813,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f812,f729]) ).
fof(f818,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f697,f729]) ).
fof(f848,plain,
( sk_c3 = multiply(sk_c8,sk_c1)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f803,f799]) ).
fof(f851,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f806,f813]) ).
fof(f855,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f160,f813]) ).
fof(f857,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f855,f3]) ).
fof(f861,plain,
( spl0_21
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f851,f728,f137,f128,f84,f775]) ).
fof(f863,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| spl0_3
| ~ spl0_21 ),
inference(superposition,[],[f79,f776]) ).
fof(f864,plain,
( sk_c8 != sk_c6
| spl0_3
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_demodulation,[],[f863,f85]) ).
fof(f867,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f864,f776]) ).
fof(f868,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f867]) ).
fof(f871,plain,
( sk_c8 = sk_c3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f857,f799]) ).
fof(f875,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_5
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f818,f776]) ).
fof(f923,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_5
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f160,f875]) ).
fof(f926,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_5
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f923,f160]) ).
fof(f947,plain,
( sk_c8 = multiply(sk_c8,sk_c1)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f848,f871]) ).
fof(f995,plain,
( sk_c8 = sk_c1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f947,f926]) ).
fof(f1000,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f130,f995]) ).
fof(f1001,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1000,f729]) ).
fof(f1044,plain,
( sk_c8 != sk_c6
| spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f75,f1001]) ).
fof(f1050,plain,
( $false
| spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1044,f776]) ).
fof(f1051,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1050]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f87]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f96]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f101]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f106]) ).
cnf(s6,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f107]) ).
cnf(s7,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f108]) ).
cnf(s8,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s9,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f114]) ).
cnf(s10,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f115]) ).
cnf(s11,plain,
( spl0_2
| spl0_10 ),
inference(sat_conversion,[],[f116]) ).
cnf(s12,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s13,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f122]) ).
cnf(s14,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f123]) ).
cnf(s15,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f124]) ).
cnf(s16,plain,
( spl0_2
| spl0_11 ),
inference(sat_conversion,[],[f125]) ).
cnf(s17,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f126]) ).
cnf(s18,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f131]) ).
cnf(s20,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s21,plain,
( spl0_2
| spl0_12 ),
inference(sat_conversion,[],[f134]) ).
cnf(s22,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s23,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s25,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f142]) ).
cnf(s26,plain,
( spl0_2
| spl0_13 ),
inference(sat_conversion,[],[f143]) ).
cnf(s27,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s28,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f145]) ).
cnf(s29,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f146]) ).
cnf(s30,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f147]) ).
cnf(s31,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f148]) ).
cnf(s32,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f149]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f663]) ).
cnf(s34,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f671]) ).
cnf(s35,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f677]) ).
cnf(s37,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f733]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f780]) ).
cnf(s44,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f787]) ).
cnf(s45,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f802]) ).
cnf(s47,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f861]) ).
cnf(s50,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_21 ),
inference(sat_conversion,[],[f868]) ).
cnf(s52,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f1051]) ).
cnf(s53,plain,
spl0_2,
inference(rat,[],[s52,s47,s45,s6,s11,s16,s21,s26,s31]) ).
cnf(s54,plain,
spl0_3,
inference(rat,[],[s47,s45,s50,s7,s12,s17,s22,s27,s32]) ).
cnf(s55,plain,
spl0_5,
inference(rat,[],[s33,s28,s29,s30,s53,s54]) ).
cnf(s56,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s37,s20,s25]) ).
cnf(s57,plain,
( ~ spl0_9
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s44,s4,s9,s14,s35,s54,s53]) ).
cnf(s58,plain,
( ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s37,s18,s23,s57]) ).
cnf(s59,plain,
~ spl0_4,
inference(rat,[],[s58,s56]) ).
cnf(s60,plain,
spl0_1,
inference(rat,[],[s2,s53,s55,s54,s59]) ).
cnf(s61,plain,
spl0_9,
inference(rat,[],[s42,s5,s10,s15,s60]) ).
cnf(s62,plain,
~ spl0_6,
inference(rat,[],[s44,s4,s9,s14,s34,s53,s61,s60,s54]) ).
cnf(s65,plain,
spl0_11,
inference(rat,[],[s13,s62]) ).
cnf(s66,plain,
spl0_10,
inference(rat,[],[s8,s62]) ).
cnf(s67,plain,
spl0_7,
inference(rat,[],[s3,s62]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s42,s67,s60,s65,s66]) ).
fof(f1053,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP328-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:56:53 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.98/1.30 % (2384596)Input is clausal, will run a generic CNF schedule.
% 1.98/1.30 % (2384602)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1762675380:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.98/1.30 % (2384605)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=744925860:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.98/1.30 % (2384604)lrs+10_1_sil=8000:sp=occurrence:random_seed=496924926:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.98/1.30 % (2384601)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3368294281:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.98/1.30 % (2384603)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3732341130:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.98/1.30 % (2384604)Refutation not found, incomplete strategy
% 1.98/1.30 % (2384604)------------------------------
% 1.98/1.30 % (2384604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/1.30 % (2384604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/1.30 % (2384604)CaDiCaL version: 2.1.3
% 1.98/1.30 % (2384604)Termination reason: Refutation not found, incomplete strategy
% 1.98/1.30 % (2384604)Time elapsed: 0.003 s
% 1.98/1.30 % (2384604)Peak memory usage: 88 MB
% 1.98/1.30 % (2384604)Instructions burned: 4 (million)
% 1.98/1.30 % (2384606)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1581957812:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.98/1.30 % (2384607)dis-21_1_sil=8000:lcm=predicate:random_seed=1578303749:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.98/1.30 % (2384607)Refutation not found, incomplete strategy
% 1.98/1.30 % (2384607)------------------------------
% 1.98/1.30 % (2384607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/1.30 % (2384607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/1.30 % (2384607)CaDiCaL version: 2.1.3
% 1.98/1.30 % (2384607)Termination reason: Refutation not found, incomplete strategy
% 1.98/1.30 % (2384607)Time elapsed: 0.002 s
% 1.98/1.30 % (2384607)Peak memory usage: 88 MB
% 1.98/1.30 % (2384607)Instructions burned: 2 (million)
% 1.98/1.30 % (2384606)First to succeed.
% 1.98/1.30 % (2384606)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2384596"
% 1.98/1.30 % (2384605)Instruction limit reached!
% 1.98/1.30 % (2384605)------------------------------
% 1.98/1.30 % (2384605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/1.30 % (2384605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/1.30 % (2384605)CaDiCaL version: 2.1.3
% 1.98/1.30 % (2384605)Termination reason: Instruction limit
% 1.98/1.30 % (2384605)Termination phase: Saturation
% 1.98/1.30 % (2384605)Time elapsed: 0.067 s
% 1.98/1.30 % (2384605)Peak memory usage: 89 MB
% 1.98/1.30 % (2384605)Instructions burned: 115 (million)
% 1.98/1.30 % (2384615)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3880114161:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.98/1.30 % (2384615)Refutation not found, incomplete strategy
% 1.98/1.30 % (2384615)------------------------------
% 1.98/1.30 % (2384615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/1.30 % (2384615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/1.30 % (2384615)CaDiCaL version: 2.1.3
% 1.98/1.30 % (2384615)Termination reason: Refutation not found, incomplete strategy
% 1.98/1.30 % (2384615)Time elapsed: 0.003 s
% 1.98/1.30 % (2384615)Peak memory usage: 88 MB
% 1.98/1.30 % (2384615)Instructions burned: 4 (million)
% 1.98/1.30 % (2384604)------------------------------
% 1.98/1.30 % (2384604)------------------------------
% 1.98/1.30 % (2384607)------------------------------
% 1.98/1.30 % (2384607)------------------------------
% 1.98/1.30 % (2384606)Refutation found. Thanks to Tanya!
% 1.98/1.30 % SZS status Unsatisfiable for theBenchmark
% 1.98/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.49 % (2384606)------------------------------
% 3.59/1.49 % (2384606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.49 % (2384606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.49 % (2384606)CaDiCaL version: 2.1.3
% 3.59/1.49 % (2384606)Termination reason: Refutation
% 3.59/1.49 % (2384606)Time elapsed: 0.021 s
% 3.59/1.49 % (2384606)Peak memory usage: 90 MB
% 3.59/1.49 % (2384606)Instructions burned: 32 (million)
% 3.59/1.49 % (2384606)------------------------------
% 3.59/1.49 % (2384606)------------------------------
% 3.59/1.49 % (2384596)Success in time 0.434 s
% 3.59/1.49 % Vampire exiting
%------------------------------------------------------------------------------