%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP267-1 : 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 10:17:20 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 33
% Syntax : Number of formulae : 264 ( 20 unt; 14 def)
% Number of atoms : 974 ( 291 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1403 ( 693 ~; 696 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 92 !; 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_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| 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
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(sk_c6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| 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)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != inverse(sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f50,definition,
( spl0_1
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f51,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f52,plain,
( sk_c7 != inverse(sk_c6)
| spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f54,definition,
( spl0_2
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f55,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,definition,
( spl0_3
<=> ! [X2,X3] :
( sk_c6 != multiply(sk_c7,X2)
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f58,plain,
( ! [X2,X3] :
( sk_c6 != multiply(sk_c7,X2)
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f61,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f48,f54,f60,f57,f54,f50]) ).
fof(f64,definition,
( spl0_5
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f66,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f64,f50]) ).
fof(f69,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f71,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f74,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f76,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f79,definition,
( spl0_8
<=> sk_c4 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f81,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f40,f79,f50]) ).
fof(f86,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c7,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f88,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_1
| spl0_9 ),
inference(avatar_split_clause,[],[f34,f86,f50]) ).
fof(f93,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_1
| spl0_10 ),
inference(avatar_split_clause,[],[f28,f93,f50]) ).
fof(f97,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f26,f93,f69]) ).
fof(f98,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f24,f93,f74]) ).
fof(f100,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f102,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_1
| spl0_11 ),
inference(avatar_split_clause,[],[f22,f100,f50]) ).
fof(f104,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f20,f100,f69]) ).
fof(f105,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f18,f100,f74]) ).
fof(f107,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f109,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_1
| spl0_12 ),
inference(avatar_split_clause,[],[f16,f107,f50]) ).
fof(f111,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f14,f107,f69]) ).
fof(f112,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f12,f107,f74]) ).
fof(f114,definition,
( spl0_13
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f115,plain,
( multiply(sk_c1,sk_c8) != sk_c7
| spl0_13 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f116,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_1
| spl0_13 ),
inference(avatar_split_clause,[],[f10,f114,f50]) ).
fof(f118,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f8,f114,f69]) ).
fof(f119,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f6,f114,f74]) ).
fof(f120,plain,
( sk_c7 = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f116,f109]) ).
fof(f121,plain,
( sk_c6 = multiply(multiply(sk_c1,inverse(sk_c1)),sk_c4)
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f88,f120]) ).
fof(f122,plain,
( sk_c4 = multiply(sk_c3,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f81,f120]) ).
fof(f123,plain,
( sk_c6 = multiply(sk_c1,multiply(inverse(sk_c1),sk_c4))
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f121,f4]) ).
fof(f124,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f3,f3]) ).
fof(f126,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_10 ),
inference(superposition,[],[f3,f95]) ).
fof(f127,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f128,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f127,f4]) ).
fof(f136,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c2,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f126]) ).
fof(f137,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(sk_c7,X0)
| ~ spl0_11 ),
inference(superposition,[],[f4,f102]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(multiply(sk_c1,inverse(sk_c1)),X0)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f137,f120]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c2,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f136,f1]) ).
fof(f149,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(sk_c1,multiply(inverse(sk_c1),X0))
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f142,f4]) ).
fof(f152,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f143,f102]) ).
fof(f155,plain,
( sk_c6 = multiply(sk_c6,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f152,f120]) ).
fof(f163,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c1,multiply(inverse(sk_c1),multiply(sk_c1,inverse(sk_c1))))
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f149,f155]) ).
fof(f167,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f163,f128]) ).
fof(f177,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f128,f1]) ).
fof(f179,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f128,f3]) ).
fof(f180,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f128,f128]) ).
fof(f181,plain,
( multiply(inverse(sk_c1),sk_c4) = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f128,f123]) ).
fof(f183,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f128,f88]) ).
fof(f185,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(inverse(sk_c6),X0)
| ~ spl0_10 ),
inference(superposition,[],[f128,f143]) ).
fof(f186,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f128,f155]) ).
fof(f191,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(inverse(sk_c3),sk_c4)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f128,f122]) ).
fof(f194,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f191,f66]) ).
fof(f199,plain,
( identity = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f186,f3]) ).
fof(f200,plain,
( sk_c4 = multiply(inverse(multiply(sk_c1,inverse(sk_c1))),sk_c6)
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f183,f120]) ).
fof(f201,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f179,f180]) ).
fof(f203,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(multiply(sk_c1,inverse(sk_c1)),sk_c4)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f194,f120]) ).
fof(f206,plain,
( sk_c4 = multiply(inverse(identity),sk_c6)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f200,f199]) ).
fof(f208,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(sk_c1,multiply(inverse(sk_c1),sk_c4))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f203,f4]) ).
fof(f210,plain,
( sk_c6 = sk_c4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f206,f177]) ).
fof(f211,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(sk_c1,multiply(inverse(sk_c1),sk_c6))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f208,f181]) ).
fof(f213,plain,
( identity = multiply(sk_c1,multiply(inverse(sk_c1),sk_c6))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f211,f199]) ).
fof(f215,plain,
( sk_c6 = multiply(sk_c1,multiply(inverse(sk_c1),sk_c6))
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f123,f210]) ).
fof(f218,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f215,f213]) ).
fof(f259,plain,
( sk_c7 != inverse(identity)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f52,f218]) ).
fof(f265,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f167,f218]) ).
fof(f266,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(inverse(sk_c6),identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f265,f185]) ).
fof(f272,plain,
( multiply(sk_c1,inverse(sk_c1)) != inverse(identity)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f259,f120]) ).
fof(f273,plain,
( inverse(sk_c6) = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f266,f201]) ).
fof(f277,plain,
( identity != inverse(identity)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f272,f199]) ).
fof(f278,plain,
( identity = inverse(sk_c6)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f273,f199]) ).
fof(f283,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f278,f218]) ).
fof(f286,plain,
( $false
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f283,f277]) ).
fof(f287,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f286]) ).
fof(f325,plain,
( ! [X4] :
( sk_c7 != multiply(X4,inverse(sk_c1))
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_12 ),
inference(forward_demodulation,[],[f55,f109]) ).
fof(f326,plain,
( ! [X4] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(X4,inverse(sk_c1))
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f325,f120]) ).
fof(f327,plain,
( ! [X4] :
( identity != multiply(X4,inverse(sk_c1))
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f326,f199]) ).
fof(f328,plain,
( ! [X4] :
( inverse(sk_c1) != inverse(X4)
| identity != multiply(X4,inverse(sk_c1)) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f327,f109]) ).
fof(f338,plain,
( identity != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(equality_resolution,[],[f328]) ).
fof(f339,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f338,f199]) ).
fof(f340,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f399,plain,
( ! [X1] :
( multiply(X1,sk_c6) != multiply(sk_c1,inverse(sk_c1))
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f61,f120]) ).
fof(f400,plain,
( inverse(sk_c5) = inverse(sk_c1)
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f71,f109]) ).
fof(f401,plain,
( sk_c7 = multiply(sk_c5,inverse(sk_c1))
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f76,f109]) ).
fof(f403,plain,
( inverse(sk_c6) = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f51,f120]) ).
fof(f404,plain,
( ! [X1] :
( identity != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f399,f199]) ).
fof(f407,plain,
( identity = inverse(sk_c6)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f403,f199]) ).
fof(f414,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f3,f407]) ).
fof(f415,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f414,f1]) ).
fof(f426,plain,
( identity = inverse(identity)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f407,f415]) ).
fof(f447,plain,
( identity = multiply(inverse(sk_c1),sk_c5)
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[],[f3,f400]) ).
fof(f476,plain,
( ! [X0] :
( identity != multiply(inverse(X0),X0)
| sk_c6 != inverse(inverse(sk_c6)) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f404,f124]) ).
fof(f486,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f476,f3]) ).
fof(f496,plain,
( sk_c6 != inverse(identity)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f486,f407]) ).
fof(f502,plain,
( identity != sk_c6
| ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f496,f426]) ).
fof(f508,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f502,f415]) ).
fof(f509,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f528,plain,
( sk_c5 = multiply(inverse(inverse(sk_c1)),identity)
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[],[f128,f447]) ).
fof(f531,plain,
( sk_c5 = multiply(sk_c1,identity)
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f528,f180]) ).
fof(f532,plain,
( sk_c1 = sk_c5
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f531,f201]) ).
fof(f556,plain,
( identity = multiply(multiply(sk_c1,inverse(sk_c1)),sk_c6)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f3,f403]) ).
fof(f557,plain,
( identity = multiply(sk_c1,multiply(inverse(sk_c1),sk_c6))
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f556,f4]) ).
fof(f580,definition,
( spl0_16
<=> identity = multiply(sk_c1,inverse(sk_c1)) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f581,plain,
( identity = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f591,plain,
( multiply(inverse(sk_c1),sk_c6) = multiply(inverse(sk_c1),identity)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f128,f557]) ).
fof(f594,plain,
( inverse(sk_c1) = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f591,f201]) ).
fof(f596,plain,
( identity = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f557,f594]) ).
fof(f598,plain,
( sk_c6 = multiply(inverse(inverse(sk_c1)),inverse(sk_c1))
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f128,f594]) ).
fof(f600,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f598,f3]) ).
fof(f610,plain,
( spl0_16
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f596,f114,f107,f50,f580]) ).
fof(f614,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c1,multiply(inverse(sk_c1),X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f581]) ).
fof(f615,plain,
( ! [X0] : multiply(sk_c1,multiply(inverse(sk_c1),X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f614,f1]) ).
fof(f692,plain,
( multiply(sk_c1,inverse(sk_c1)) = inverse(identity)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f403,f600]) ).
fof(f704,plain,
( identity = inverse(identity)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f692,f581]) ).
fof(f714,plain,
( ! [X2,X3] :
( sk_c6 != multiply(multiply(sk_c1,inverse(sk_c1)),X2)
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2 )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f58,f120]) ).
fof(f717,plain,
( ! [X2,X3] :
( sk_c6 != multiply(sk_c1,multiply(inverse(sk_c1),X2))
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2 )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f714,f4]) ).
fof(f719,plain,
( ! [X2,X3] :
( sk_c6 != X2
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2 )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f717,f615]) ).
fof(f720,plain,
( ! [X2,X3] :
( identity != X2
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f719,f600]) ).
fof(f721,plain,
( ! [X2,X3] :
( inverse(X3) != multiply(sk_c1,inverse(sk_c1))
| identity != X2
| multiply(X3,sk_c7) != X2 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f720,f120]) ).
fof(f722,plain,
( ! [X2,X3] :
( identity != inverse(X3)
| identity != X2
| multiply(X3,sk_c7) != X2 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f721,f581]) ).
fof(f723,plain,
( ! [X2,X3] :
( multiply(X3,multiply(sk_c1,inverse(sk_c1))) != X2
| identity != inverse(X3)
| identity != X2 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f722,f120]) ).
fof(f724,plain,
( ! [X2,X3] :
( multiply(X3,identity) != X2
| identity != inverse(X3)
| identity != X2 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f723,f581]) ).
fof(f725,plain,
( ! [X2,X3] :
( X2 != X3
| identity != inverse(X3)
| identity != X2 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f724,f201]) ).
fof(f726,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(equality_resolution,[],[f725]) ).
fof(f738,plain,
( sk_c7 != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_12
| spl0_13 ),
inference(forward_demodulation,[],[f115,f109]) ).
fof(f740,plain,
( sk_c7 = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f401,f532]) ).
fof(f750,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f740,f738]) ).
fof(f751,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| spl0_13 ),
inference(avatar_contradiction_clause,[],[f750]) ).
fof(f772,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(sk_c7,sk_c6)
| ~ spl0_1 ),
inference(superposition,[],[f124,f51]) ).
fof(f774,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_1 ),
inference(superposition,[],[f3,f51]) ).
fof(f907,plain,
( identity != identity
| identity != identity
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f726,f704]) ).
fof(f911,plain,
( identity != identity
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(duplicate_literal_removal,[],[f907]) ).
fof(f912,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f911]) ).
fof(f913,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f912]) ).
fof(f979,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f71]) ).
fof(f1054,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_6 ),
inference(superposition,[],[f128,f979]) ).
fof(f1057,plain,
( sk_c5 = inverse(sk_c8)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1054,f201]) ).
fof(f1060,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f76,f1057]) ).
fof(f1061,plain,
( sk_c8 = inverse(inverse(sk_c8))
| ~ spl0_6 ),
inference(superposition,[],[f71,f1057]) ).
fof(f1088,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1060,f3]) ).
fof(f1205,plain,
( ! [X2,X3] :
( sk_c6 != multiply(identity,X2)
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f58,f1088]) ).
fof(f1207,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f774,f1088]) ).
fof(f1209,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(identity,sk_c6)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f772,f1088]) ).
fof(f1220,plain,
( ! [X2,X3] :
( sk_c6 != X2
| sk_c7 != inverse(X3)
| multiply(X3,sk_c7) != X2 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1205,f1]) ).
fof(f1222,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1207,f1]) ).
fof(f1224,plain,
( ! [X0] : multiply(inverse(X0),X0) = sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1209,f1]) ).
fof(f1259,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c6) = X0
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f128,f1224]) ).
fof(f1266,plain,
( ! [X0] : multiply(X0,sk_c6) = X0
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1259,f180]) ).
fof(f1298,plain,
( ! [X2,X3] :
( identity != inverse(X3)
| sk_c6 != X2
| multiply(X3,sk_c7) != X2 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1220,f1088]) ).
fof(f1309,plain,
( ! [X2,X3] :
( multiply(X3,identity) != X2
| identity != inverse(X3)
| sk_c6 != X2 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1298,f1088]) ).
fof(f1310,plain,
( ! [X2,X3] :
( X2 != X3
| identity != inverse(X3)
| sk_c6 != X2 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1309,f201]) ).
fof(f1322,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c6 != X0 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(equality_resolution,[],[f1310]) ).
fof(f1323,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1322,f1222]) ).
fof(f1335,plain,
( identity != sk_c7
| identity != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f1323,f51]) ).
fof(f1336,plain,
( identity != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1335,f1088]) ).
fof(f1338,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1336,f1222]) ).
fof(f1339,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1338]) ).
fof(f1340,plain,
( ! [X1] :
( sk_c7 != X1
| sk_c6 != inverse(X1) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f61,f1266]) ).
fof(f1341,plain,
( ! [X1] :
( identity != X1
| sk_c6 != inverse(X1) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1340,f1088]) ).
fof(f1342,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1341,f1222]) ).
fof(f1355,plain,
( identity != sk_c7
| identity != sk_c6
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f1342,f51]) ).
fof(f1359,plain,
( identity != sk_c6
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1355,f1088]) ).
fof(f1361,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1359,f1222]) ).
fof(f1362,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1361]) ).
fof(f1363,plain,
( ! [X4] :
( identity != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f55,f1088]) ).
fof(f1373,plain,
( ! [X0] :
( identity != multiply(inverse(X0),X0)
| sk_c8 != inverse(inverse(sk_c8)) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f1363,f124]) ).
fof(f1384,plain,
( ! [X0] : identity != multiply(inverse(X0),X0)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1373,f1061]) ).
fof(f1393,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1384,f3]) ).
fof(f1394,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1393]) ).
cnf(s1,plain,
( spl0_2
| ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f62]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f67]) ).
cnf(s6,plain,
( spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f82]) ).
cnf(s9,plain,
( spl0_1
| spl0_9 ),
inference(sat_conversion,[],[f89]) ).
cnf(s12,plain,
( spl0_1
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s13,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f97]) ).
cnf(s14,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f98]) ).
cnf(s15,plain,
( spl0_1
| spl0_11 ),
inference(sat_conversion,[],[f103]) ).
cnf(s16,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s17,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f105]) ).
cnf(s18,plain,
( spl0_1
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s19,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s20,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s21,plain,
( spl0_1
| spl0_13 ),
inference(sat_conversion,[],[f117]) ).
cnf(s22,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s23,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s25,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f287]) ).
cnf(s28,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f340]) ).
cnf(s37,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f509]) ).
cnf(s46,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f610]) ).
cnf(s51,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f751]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(sat_conversion,[],[f913]) ).
cnf(s78,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f1339]) ).
cnf(s80,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f1362]) ).
cnf(s84,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f1394]) ).
cnf(s85,plain,
spl0_1,
inference(rat,[],[s25,s3,s6,s9,s12,s15,s18,s21]) ).
cnf(s86,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s37,s13,s16,s19,s22,s85]) ).
cnf(s87,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s37,s14,s17,s20,s23,s80,s85]) ).
cnf(s88,plain,
~ spl0_4,
inference(rat,[],[s87,s86]) ).
cnf(s89,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_3 ),
inference(rat,[],[s46,s54,s85]) ).
cnf(s90,plain,
( spl0_6
| ~ spl0_3 ),
inference(rat,[],[s89,s19,s22]) ).
cnf(s91,plain,
( ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s89,s20,s23,s78,s85]) ).
cnf(s92,plain,
~ spl0_3,
inference(rat,[],[s91,s90]) ).
cnf(s93,plain,
spl0_2,
inference(rat,[],[s2,s88,s85,s92]) ).
cnf(s94,plain,
( spl0_6
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s28,s13,s16,s93]) ).
cnf(s95,plain,
( ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s28,s14,s17,s84,s94,s93]) ).
cnf(s96,plain,
~ spl0_12,
inference(rat,[],[s51,s22,s23,s95]) ).
cnf(s97,plain,
spl0_7,
inference(rat,[],[s20,s96]) ).
cnf(s98,plain,
spl0_6,
inference(rat,[],[s19,s96]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s84,s93,s97,s98]) ).
fof(f1395,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:45:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (258254)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (258264)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4583966:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (258259)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3675279035_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (258265)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1272753031:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (258261)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2088540783:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (258262)dis+10_1_sil=32000:sp=arity:random_seed=2570114795:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (258263)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2554622915:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % TRYING [2]
% 0.10/0.45 % (258260)% WARNING: option uhcvi not known.
% 0.10/0.45 % TRYING [3]
% 0.10/0.45 % (258264) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-258254-258264"...
% 0.10/0.45 % TRYING [4]
% 0.10/0.45 % (258260)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1749048969:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (258264)...printing done.
% 0.10/0.45 % (258264)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (258264)------------------------------
% 0.10/0.46 % (258264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (258264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (258264)CaDiCaL version: 2.1.3
% 0.10/0.46 % (258264)Termination reason: Refutation
% 0.10/0.46 % (258264)Time elapsed: 0.015 s
% 0.10/0.46 % (258264)Peak memory usage: 12 MB
% 0.10/0.46 % (258264)Instructions burned: 42 (million)
% 0.10/0.46 % (258254)Success in time 0.039 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------