%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP363-1 : 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 : n007.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 10:13:45 AM UTC 2026
% Result : Unsatisfiable 2.32s 1.03s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 42
% Syntax : Number of formulae : 281 ( 18 unt; 14 def)
% Number of atoms : 1001 ( 275 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1376 ( 656 ~; 706 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 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_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = inverse(sk_c6)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = inverse(sk_c6)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c5 = inverse(sk_c6)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c5 = inverse(sk_c6)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c5 = inverse(sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c6) != sk_c5
| multiply(X0,sk_c6) != sk_c5
| inverse(X0) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(sk_c7,X2) != sk_c6
| multiply(X3,sk_c7) != X2
| inverse(X3) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != inverse(sk_c6)
| sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(sk_c7,X2)
| multiply(X3,sk_c7) != X2
| sk_c7 != inverse(X3) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
! [X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != inverse(sk_c6)
| sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ),
inference(equality_resolution,[],[f54]) ).
fof(f57,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ! [X3] :
( sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_2
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f61,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_4
<=> ! [X0] :
( sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c5 != multiply(X0,sk_c6) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl0_5
<=> sk_c5 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f71,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f72,plain,
( sk_c5 != inverse(sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f74,definition,
( spl0_6
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c5) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f55,f74,f70,f67,f63,f60,f57]) ).
fof(f79,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f81,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f85,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f52,f83,f79]) ).
fof(f88,definition,
( spl0_9
<=> sk_c4 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f50,f83,f88]) ).
fof(f93,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c7,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f48,f83,f93]) ).
fof(f98,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f100,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f46,f83,f98]) ).
fof(f103,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f44,f83,f103]) ).
fof(f107,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f42,f83,f63]) ).
fof(f109,definition,
( spl0_13
<=> sk_c5 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f111,plain,
( sk_c5 = multiply(sk_c1,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f109,f79]) ).
fof(f113,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f109,f88]) ).
fof(f114,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f109,f93]) ).
fof(f115,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f34,f109,f98]) ).
fof(f116,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f32,f109,f103]) ).
fof(f117,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f30,f109,f63]) ).
fof(f118,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f28,f70,f79]) ).
fof(f119,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f26,f70,f88]) ).
fof(f120,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f24,f70,f93]) ).
fof(f121,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f22,f70,f98]) ).
fof(f122,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f20,f70,f103]) ).
fof(f123,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f70,f63]) ).
fof(f124,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f74,f79]) ).
fof(f125,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f74,f88]) ).
fof(f126,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f74,f93]) ).
fof(f127,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f74,f98]) ).
fof(f128,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f74,f103]) ).
fof(f129,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f74,f63]) ).
fof(f130,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_7 ),
inference(superposition,[],[f3,f81]) ).
fof(f131,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_11 ),
inference(superposition,[],[f3,f100]) ).
fof(f133,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f135,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(sk_c7,X0)
| ~ spl0_12 ),
inference(superposition,[],[f4,f105]) ).
fof(f140,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f133,f1]) ).
fof(f142,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f130]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f142,f1]) ).
fof(f146,plain,
( sk_c7 = multiply(sk_c7,sk_c4)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f143,f90]) ).
fof(f149,plain,
( sk_c6 = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f146,f95]) ).
fof(f159,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f64,f149]) ).
fof(f230,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f140,f105]) ).
fof(f235,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f140,f131]) ).
fof(f236,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f140,f95]) ).
fof(f238,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_7 ),
inference(superposition,[],[f140,f130]) ).
fof(f242,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f238,f149]) ).
fof(f244,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f236,f149]) ).
fof(f248,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f230,f149]) ).
fof(f255,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f244,f3]) ).
fof(f257,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f248,f100]) ).
fof(f268,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c7,sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f135,f257]) ).
fof(f269,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f140,f257]) ).
fof(f271,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f269,f3]) ).
fof(f272,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f268,f149]) ).
fof(f275,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f272,f159]) ).
fof(f276,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f275,f105]) ).
fof(f277,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f276,f149]) ).
fof(f278,plain,
( sk_c6 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f271,f255]) ).
fof(f282,plain,
( sk_c2 = multiply(inverse(sk_c6),sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f235,f255]) ).
fof(f283,plain,
( sk_c3 = multiply(inverse(sk_c6),sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f242,f255]) ).
fof(f291,plain,
( sk_c2 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f282,f278]) ).
fof(f292,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f291,f3]) ).
fof(f293,plain,
( sk_c6 = sk_c2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f292,f271]) ).
fof(f294,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f100,f293]) ).
fof(f306,plain,
( sk_c3 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f283,f278]) ).
fof(f307,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f306,f3]) ).
fof(f308,plain,
( sk_c4 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f307,f255]) ).
fof(f309,plain,
( sk_c6 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f308,f278]) ).
fof(f342,plain,
( sk_c6 != sk_c5
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f72,f294]) ).
fof(f346,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f342,f277]) ).
fof(f347,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f346]) ).
fof(f350,plain,
( sk_c6 != multiply(sk_c6,sk_c5)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f76,f149]) ).
fof(f351,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f350,f277]) ).
fof(f352,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f351,f257]) ).
fof(f353,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f355,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f75,f149]) ).
fof(f367,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f230,f100]) ).
fof(f370,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f3,f71]) ).
fof(f374,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f140,f75]) ).
fof(f376,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f374,f71]) ).
fof(f377,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c5)
| ~ spl0_13 ),
inference(superposition,[],[f140,f111]) ).
fof(f378,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f111]) ).
fof(f379,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f377,f85]) ).
fof(f426,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f140,f376]) ).
fof(f428,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f426,f3]) ).
fof(f430,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f379,f75]) ).
fof(f434,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f140,f379]) ).
fof(f436,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f434,f3]) ).
fof(f481,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f64,f367]) ).
fof(f491,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f68,f481]) ).
fof(f493,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f491,f100]) ).
fof(f497,plain,
( sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f493]) ).
fof(f500,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f497,f105]) ).
fof(f506,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f428,f430]) ).
fof(f508,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f64,f430]) ).
fof(f513,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c1,sk_c5)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f378,f508]) ).
fof(f517,plain,
( identity = multiply(sk_c1,sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f513,f370]) ).
fof(f519,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f506,f436]) ).
fof(f526,plain,
( sk_c6 != sk_c6
| sk_c5 != multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f68,f85]) ).
fof(f527,plain,
( sk_c5 != multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f526]) ).
fof(f529,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f527,f111]) ).
fof(f530,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f529]) ).
fof(f532,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f61,f430]) ).
fof(f539,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f532,f85]) ).
fof(f540,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f539]) ).
fof(f542,plain,
( sk_c6 != sk_c5
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f540,f111]) ).
fof(f576,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f519,f542]) ).
fof(f577,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f576]) ).
fof(f578,plain,
( sk_c5 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f65,f430]) ).
fof(f582,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f370,f519]) ).
fof(f592,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f582,f436]) ).
fof(f593,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f592,f578]) ).
fof(f594,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f593]) ).
fof(f602,definition,
( spl0_15
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f603,plain,
( sk_c6 = sk_c5
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f607,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f481,f103,f98,f63,f602]) ).
fof(f615,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f64,f603]) ).
fof(f626,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f149,f500]) ).
fof(f627,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f626]) ).
fof(f628,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f355,f603]) ).
fof(f652,plain,
( ! [X3] :
( sk_c6 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f58,f149]) ).
fof(f653,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(sk_c6,multiply(X3,sk_c6)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f652,f149]) ).
fof(f656,plain,
( sk_c6 != sk_c7
| sk_c6 != multiply(sk_c6,multiply(sk_c3,sk_c6))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f653,f81]) ).
fof(f658,plain,
( sk_c6 != multiply(sk_c6,multiply(sk_c3,sk_c6))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f656,f149]) ).
fof(f661,plain,
( sk_c6 != multiply(sk_c6,multiply(sk_c6,sk_c6))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f658,f309]) ).
fof(f664,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f661,f628]) ).
fof(f669,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f664,f628]) ).
fof(f670,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f671,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f61,f149]) ).
fof(f674,plain,
( sk_c6 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f671,f81]) ).
fof(f676,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f674,f149]) ).
fof(f679,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f676,f309]) ).
fof(f684,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f679,f628]) ).
fof(f685,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f684]) ).
fof(f686,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f508,f603]) ).
fof(f690,plain,
( identity = multiply(sk_c1,sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f517,f603]) ).
fof(f703,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f690,f111]) ).
fof(f705,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f703,f603]) ).
fof(f719,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f140,f615]) ).
fof(f721,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f719,f3]) ).
fof(f723,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f721,f705]) ).
fof(f739,plain,
( ! [X3] :
( sk_c6 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f58,f723]) ).
fof(f740,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(sk_c6,multiply(X3,sk_c6)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f739,f723]) ).
fof(f741,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c6,multiply(sk_c6,sk_c6))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f740,f71]) ).
fof(f750,plain,
( sk_c6 != multiply(sk_c6,multiply(sk_c6,sk_c6))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f741,f603]) ).
fof(f753,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f750,f686]) ).
fof(f758,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f753,f686]) ).
fof(f759,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f758]) ).
fof(f761,plain,
( spl0_15
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f519,f109,f83,f74,f70,f602]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s7,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f112]) ).
cnf(s9,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f113]) ).
cnf(s10,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f114]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f115]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s13,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f117]) ).
cnf(s14,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f118]) ).
cnf(s15,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s16,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f120]) ).
cnf(s17,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f121]) ).
cnf(s18,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s19,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f123]) ).
cnf(s20,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f124]) ).
cnf(s21,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f125]) ).
cnf(s22,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f126]) ).
cnf(s23,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f127]) ).
cnf(s24,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f128]) ).
cnf(s25,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f129]) ).
cnf(s26,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f347]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f353]) ).
cnf(s32,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f530]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f577]) ).
cnf(s35,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f594]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f607]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f627]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(sat_conversion,[],[f670]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(sat_conversion,[],[f685]) ).
cnf(s48,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f759]) ).
cnf(s50,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f761]) ).
cnf(s53,plain,
spl0_3,
inference(rat,[],[s35,s7,s13,s19,s25]) ).
cnf(s54,plain,
spl0_6,
inference(rat,[],[s27,s20,s21,s22,s23,s24,s53]) ).
cnf(s55,plain,
spl0_5,
inference(rat,[],[s26,s14,s15,s16,s17,s18,s53]) ).
cnf(s56,plain,
( spl0_13
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s39,s9,s10,s11,s12,s53]) ).
cnf(s57,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s39,s3,s4,s5,s6,s32,s56,s53]) ).
cnf(s58,plain,
~ spl0_4,
inference(rat,[],[s32,s2,s8,s57]) ).
cnf(s59,plain,
( spl0_13
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s45,s38,s9,s10,s11,s12,s54,s53]) ).
cnf(s60,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s45,s38,s3,s4,s5,s6,s33,s59,s55,s53,s54]) ).
cnf(s61,plain,
~ spl0_2,
inference(rat,[],[s33,s2,s8,s60,s54,s55]) ).
cnf(s62,plain,
spl0_1,
inference(rat,[],[s1,s54,s53,s55,s58,s61]) ).
cnf(s63,plain,
( spl0_15
| ~ spl0_8 ),
inference(rat,[],[s38,s11,s12,s50,s54,s55,s53]) ).
cnf(s64,plain,
( ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s42,s9,s10,s11,s12,s48,s63,s54,s62,s55,s53]) ).
cnf(s65,plain,
~ spl0_7,
inference(rat,[],[s42,s38,s3,s4,s5,s6,s64,s54,s62,s53]) ).
cnf(s66,plain,
spl0_13,
inference(rat,[],[s8,s65]) ).
cnf(s67,plain,
spl0_8,
inference(rat,[],[s2,s65]) ).
cnf(s68,plain,
~ spl0_15,
inference(rat,[],[s48,s62,s53,s55,s54,s67,s66]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s63,s67,s68]) ).
fof(f763,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP363-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:54:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.32/1.03 % (1168527)Input is clausal, will run a generic CNF schedule.
% 2.32/1.03 % (1168537)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=433202278:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.32/1.03 % (1168534)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4210260824:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.32/1.03 % (1168532)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=2015119881:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.32/1.03 % (1168535)lrs+10_1_sil=8000:sp=occurrence:random_seed=2254992499:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.32/1.03 % (1168533)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4244823588:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.32/1.03 % (1168536)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=641132891:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.32/1.03 % (1168538)dis-21_1_sil=8000:lcm=predicate:random_seed=3720275968: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)
% 2.32/1.03 % (1168538)Refutation not found, incomplete strategy
% 2.32/1.03 % (1168538)------------------------------
% 2.32/1.03 % (1168538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.03 % (1168538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.03 % (1168538)CaDiCaL version: 2.1.3
% 2.32/1.03 % (1168538)Termination reason: Refutation not found, incomplete strategy
% 2.32/1.03 % (1168538)Time elapsed: 0.002 s
% 2.32/1.03 % (1168538)Peak memory usage: 88 MB
% 2.32/1.03 % (1168538)Instructions burned: 1 (million)
% 2.32/1.03 % (1168537)First to succeed.
% 2.32/1.03 % (1168537)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1168527"
% 2.32/1.03 % (1168535)Instruction limit reached!
% 2.32/1.03 % (1168535)------------------------------
% 2.32/1.03 % (1168535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.03 % (1168535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.03 % (1168535)CaDiCaL version: 2.1.3
% 2.32/1.03 % (1168535)Termination reason: Instruction limit
% 2.32/1.03 % (1168535)Termination phase: Saturation
% 2.32/1.03 % (1168535)Time elapsed: 0.050 s
% 2.32/1.03 % (1168535)Peak memory usage: 88 MB
% 2.32/1.03 % (1168535)Instructions burned: 108 (million)
% 2.32/1.03 % (1168536)Instruction limit reached!
% 2.32/1.03 % (1168536)------------------------------
% 2.32/1.03 % (1168536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.03 % (1168536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.03 % (1168536)CaDiCaL version: 2.1.3
% 2.32/1.03 % (1168536)Termination reason: Instruction limit
% 2.32/1.03 % (1168536)Termination phase: Saturation
% 2.32/1.03 % (1168536)Time elapsed: 0.065 s
% 2.32/1.03 % (1168536)Peak memory usage: 89 MB
% 2.32/1.03 % (1168536)Instructions burned: 114 (million)
% 2.32/1.03 % (1168546)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=3002969786:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.32/1.03 % (1168547)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=939690672:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.32/1.03 % (1168547)Refutation not found, incomplete strategy
% 2.32/1.03 % (1168547)------------------------------
% 2.32/1.03 % (1168547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.03 % (1168547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.03 % (1168547)CaDiCaL version: 2.1.3
% 2.32/1.03 % (1168547)Termination reason: Refutation not found, incomplete strategy
% 2.32/1.03 % (1168547)Time elapsed: 0.004 s
% 2.32/1.03 % (1168547)Peak memory usage: 88 MB
% 2.32/1.03 % (1168547)Instructions burned: 4 (million)
% 2.32/1.03 % (1168538)------------------------------
% 2.32/1.03 % (1168538)------------------------------
% 2.32/1.03 % (1168537)Refutation found. Thanks to Tanya!
% 2.32/1.03 % SZS status Unsatisfiable for theBenchmark
% 2.32/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 2.32/1.13 % (1168537)------------------------------
% 2.32/1.13 % (1168537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.13 % (1168537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.13 % (1168537)CaDiCaL version: 2.1.3
% 2.32/1.13 % (1168537)Termination reason: Refutation
% 2.32/1.13 % (1168537)Time elapsed: 0.020 s
% 2.32/1.13 % (1168537)Peak memory usage: 89 MB
% 2.32/1.13 % (1168537)Instructions burned: 29 (million)
% 2.32/1.13 % (1168537)------------------------------
% 2.32/1.13 % (1168537)------------------------------
% 2.32/1.13 % (1168527)Success in time 0.422 s
% 2.32/1.13 % Vampire exiting
%------------------------------------------------------------------------------