%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP375-1 : 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 : n020.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 10:17:38 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 47
% Syntax : Number of formulae : 317 ( 19 unt; 21 def)
% Number of atoms : 1079 ( 346 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1478 ( 716 ~; 741 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 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,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c10) = sk_c9
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f7]) ).
fof(f12,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c10) = sk_c9
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = inverse(sk_c1)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| multiply(X0,sk_c10) != sk_c9
| inverse(X0) != sk_c10
| multiply(sk_c8,sk_c10) != sk_c9
| multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| multiply(X3,X4) != sk_c10
| inverse(X3) != X4
| multiply(X4,sk_c9) != sk_c10
| inverse(X5) != X6
| inverse(X6) != X4
| multiply(X5,X4) != X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c10 != multiply(X4,sk_c9)
| inverse(X5) != X6
| inverse(X6) != X4
| multiply(X5,X4) != X6 ),
inference(reorient_equations,[],[f83]) ).
fof(f85,plain,
! [X2,X3,X0,X1,X6,X5] :
( inverse(sk_c10) != sk_c9
| sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,inverse(X3))
| sk_c10 != multiply(inverse(X3),sk_c9)
| inverse(X5) != X6
| inverse(X3) != inverse(X6)
| multiply(X5,inverse(X3)) != X6 ),
inference(equality_resolution,[],[f84]) ).
fof(f86,plain,
! [X2,X3,X0,X1,X5] :
( inverse(sk_c10) != sk_c9
| sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,inverse(X3))
| sk_c10 != multiply(inverse(X3),sk_c9)
| inverse(X3) != inverse(inverse(X5))
| inverse(X5) != multiply(X5,inverse(X3)) ),
inference(equality_resolution,[],[f85]) ).
fof(f88,definition,
( spl0_1
<=> ! [X5,X3] :
( sk_c10 != multiply(X3,inverse(X3))
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5))
| sk_c10 != multiply(inverse(X3),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f89,plain,
( ! [X3,X5] :
( inverse(X5) != multiply(X5,inverse(X3))
| sk_c10 != multiply(X3,inverse(X3))
| inverse(X3) != inverse(inverse(X5))
| sk_c10 != multiply(inverse(X3),sk_c9) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,definition,
( spl0_2
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f92,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,definition,
( spl0_3
<=> ! [X1] :
( sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f95,plain,
( ! [X1] :
( sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl0_4
<=> sk_c9 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f98,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( sk_c9 != multiply(sk_c8,sk_c10)
| spl0_4 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl0_5
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f102,plain,
( inverse(sk_c10) = sk_c9
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( inverse(sk_c10) != sk_c9
| spl0_5 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f86,f101,f94,f97,f94,f91,f88]) ).
fof(f126,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f74,f97,f126]) ).
fof(f131,definition,
( spl0_11
<=> sk_c10 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f133,plain,
( sk_c10 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f72,f97,f131]) ).
fof(f136,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f138,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f70,f97,f136]) ).
fof(f141,definition,
( spl0_13
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f143,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f68,f97,f141]) ).
fof(f146,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f148,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f66,f97,f146]) ).
fof(f151,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f152,plain,
( sk_c9 != multiply(sk_c2,sk_c10)
| spl0_15 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_15
| spl0_4 ),
inference(avatar_split_clause,[],[f64,f97,f151]) ).
fof(f156,definition,
( spl0_16
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f158,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f163,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f54,f156,f126]) ).
fof(f164,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f52,f156,f131]) ).
fof(f165,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f50,f156,f136]) ).
fof(f166,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f48,f156,f141]) ).
fof(f167,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f156,f146]) ).
fof(f168,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f156,f151]) ).
fof(f170,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f172,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f177,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f34,f170,f126]) ).
fof(f178,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f170,f131]) ).
fof(f179,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f170,f136]) ).
fof(f180,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f170,f141]) ).
fof(f181,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f170,f146]) ).
fof(f182,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f170,f151]) ).
fof(f187,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f15,f101,f126]) ).
fof(f188,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f13,f101,f131]) ).
fof(f191,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f101,f146]) ).
fof(f192,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f101,f151]) ).
fof(f193,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f3,f148]) ).
fof(f200,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f206,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f200,f1]) ).
fof(f209,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c2,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f193]) ).
fof(f210,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c2,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f209,f1]) ).
fof(f223,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f210,f153]) ).
fof(f272,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f206,f223]) ).
fof(f277,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f206,f143]) ).
fof(f280,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c10)
| ~ spl0_11 ),
inference(superposition,[],[f206,f133]) ).
fof(f297,plain,
( sk_c7 = multiply(sk_c7,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f280,f128]) ).
fof(f300,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f277,f138]) ).
fof(f304,plain,
( identity = sk_c9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f272,f3]) ).
fof(f337,plain,
( sk_c10 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f206,f297]) ).
fof(f339,plain,
( identity = sk_c10
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f337,f3]) ).
fof(f344,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f193,f339]) ).
fof(f353,plain,
( identity = sk_c2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f344,f1]) ).
fof(f358,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f300,f304]) ).
fof(f359,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f358,f1]) ).
fof(f361,plain,
( sk_c9 != multiply(identity,sk_c10)
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f99,f359]) ).
fof(f362,plain,
( sk_c10 != sk_c9
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f361,f1]) ).
fof(f364,plain,
( identity != sk_c10
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f362,f304]) ).
fof(f365,plain,
( $false
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f364,f339]) ).
fof(f366,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f368,plain,
( identity != inverse(sk_c10)
| spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f103,f304]) ).
fof(f370,plain,
( identity != inverse(identity)
| spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f368,f339]) ).
fof(f376,plain,
( sk_c10 = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f148,f353]) ).
fof(f377,plain,
( identity = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f376,f339]) ).
fof(f382,plain,
( $false
| spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f377,f370]) ).
fof(f383,plain,
( spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f382]) ).
fof(f387,plain,
( ! [X3,X5] :
( identity != multiply(X3,inverse(X3))
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5))
| sk_c10 != multiply(inverse(X3),sk_c9) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f89,f339]) ).
fof(f388,plain,
( identity = inverse(sk_c10)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f102,f304]) ).
fof(f389,plain,
( ! [X3,X5] :
( sk_c10 != multiply(inverse(X3),identity)
| identity != multiply(X3,inverse(X3))
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f387,f304]) ).
fof(f390,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f388,f339]) ).
fof(f391,plain,
( ! [X3,X5] :
( inverse(X5) != multiply(X5,inverse(X3))
| identity != multiply(X3,inverse(X3))
| identity != multiply(inverse(X3),identity)
| inverse(X3) != inverse(inverse(X5)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f389,f339]) ).
fof(f395,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f391,f390]) ).
fof(f404,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(duplicate_literal_removal,[],[f395]) ).
fof(f422,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f404,f1]) ).
fof(f453,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f422,f3]) ).
fof(f464,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f453,f390]) ).
fof(f466,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f464,f390]) ).
fof(f468,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f466,f390]) ).
fof(f471,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f468,f390]) ).
fof(f472,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f471,f390]) ).
fof(f473,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f474,plain,
( ! [X1] :
( sk_c9 != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f95,f339]) ).
fof(f475,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f474,f304]) ).
fof(f476,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f475,f339]) ).
fof(f479,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f476,f3]) ).
fof(f481,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f479]) ).
fof(f483,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f481,f390]) ).
fof(f486,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f483,f390]) ).
fof(f487,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f486]) ).
fof(f488,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f92,f304]) ).
fof(f489,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f488,f359]) ).
fof(f490,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f489,f304]) ).
fof(f493,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f490,f3]) ).
fof(f495,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f493]) ).
fof(f497,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f495,f390]) ).
fof(f500,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f497,f390]) ).
fof(f501,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f500]) ).
fof(f504,plain,
( sk_c9 != multiply(sk_c2,identity)
| ~ spl0_10
| ~ spl0_11
| spl0_15 ),
inference(forward_demodulation,[],[f152,f339]) ).
fof(f505,plain,
( identity = inverse(sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f158,f339]) ).
fof(f508,plain,
( sk_c9 = inverse(identity)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f102,f339]) ).
fof(f510,plain,
( sk_c9 != multiply(identity,identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f504,f353]) ).
fof(f512,plain,
( identity != sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f510,f1]) ).
fof(f514,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f3,f505]) ).
fof(f515,plain,
( identity = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f514,f1]) ).
fof(f517,plain,
( identity = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f505,f515]) ).
fof(f521,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f517,f508]) ).
fof(f528,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f521,f512]) ).
fof(f529,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f528]) ).
fof(f531,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_5 ),
inference(superposition,[],[f3,f102]) ).
fof(f533,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f158]) ).
fof(f535,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c8,multiply(sk_c10,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f98]) ).
fof(f536,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f206,f172]) ).
fof(f538,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f536,f158]) ).
fof(f543,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f95,f172]) ).
fof(f544,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f543]) ).
fof(f546,plain,
( $false
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f544,f158]) ).
fof(f547,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f554,definition,
( spl0_27
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f555,plain,
( sk_c10 = sk_c9
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f556,plain,
( sk_c10 != sk_c9
| spl0_27 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f559,definition,
( spl0_28
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f560,plain,
( identity = sk_c9
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f561,plain,
( identity != sk_c9
| spl0_28 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f574,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c10 != multiply(sk_c10,sk_c9)
| sk_c9 != inverse(inverse(X0))
| sk_c10 != multiply(sk_c9,sk_c9) )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f89,f102]) ).
fof(f596,definition,
( spl0_32
<=> sk_c10 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f597,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f608,definition,
( spl0_35
<=> sk_c10 = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f610,plain,
( sk_c10 != multiply(sk_c9,sk_c9)
| spl0_35 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f612,definition,
( spl0_36
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f613,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f614,plain,
( ~ spl0_35
| ~ spl0_32
| spl0_36
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f574,f101,f88,f612,f596,f608]) ).
fof(f674,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_27
| ~ spl0_32 ),
inference(forward_demodulation,[],[f597,f555]) ).
fof(f678,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_27
| ~ spl0_32 ),
inference(superposition,[],[f206,f674]) ).
fof(f680,plain,
( identity = sk_c10
| ~ spl0_27
| ~ spl0_32 ),
inference(forward_demodulation,[],[f678,f3]) ).
fof(f724,plain,
( identity = multiply(identity,sk_c10)
| ~ spl0_5
| ~ spl0_28 ),
inference(superposition,[],[f531,f560]) ).
fof(f727,plain,
( sk_c10 != multiply(identity,identity)
| ~ spl0_28
| spl0_35 ),
inference(superposition,[],[f610,f560]) ).
fof(f728,plain,
( identity != sk_c10
| ~ spl0_28
| spl0_35 ),
inference(forward_demodulation,[],[f727,f1]) ).
fof(f730,plain,
( identity = sk_c10
| ~ spl0_5
| ~ spl0_28 ),
inference(forward_demodulation,[],[f724,f1]) ).
fof(f745,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_27
| ~ spl0_36 ),
inference(forward_demodulation,[],[f613,f555]) ).
fof(f746,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36 ),
inference(forward_demodulation,[],[f745,f680]) ).
fof(f747,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,identity) )
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36 ),
inference(forward_demodulation,[],[f746,f555]) ).
fof(f748,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36 ),
inference(forward_demodulation,[],[f747,f680]) ).
fof(f774,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36 ),
inference(superposition,[],[f748,f3]) ).
fof(f787,definition,
( spl0_41
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f788,plain,
( identity = inverse(identity)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f804,plain,
( identity != sk_c10
| spl0_27
| ~ spl0_28 ),
inference(forward_demodulation,[],[f556,f560]) ).
fof(f828,definition,
( spl0_43
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f829,plain,
( identity = sk_c10
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f832,plain,
( ~ spl0_43
| spl0_27
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f804,f559,f554,f828]) ).
fof(f835,plain,
( ~ spl0_43
| ~ spl0_28
| spl0_35 ),
inference(avatar_split_clause,[],[f728,f608,f559,f828]) ).
fof(f847,plain,
( spl0_32
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f538,f170,f156,f596]) ).
fof(f860,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_32 ),
inference(superposition,[],[f206,f597]) ).
fof(f862,plain,
( identity = sk_c9
| ~ spl0_32 ),
inference(forward_demodulation,[],[f860,f3]) ).
fof(f865,plain,
( $false
| spl0_28
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f862,f561]) ).
fof(f866,plain,
( spl0_28
| ~ spl0_32 ),
inference(avatar_contradiction_clause,[],[f865]) ).
fof(f873,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36
| ~ spl0_41 ),
inference(forward_demodulation,[],[f774,f788]) ).
fof(f878,plain,
( spl0_43
| ~ spl0_5
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f730,f559,f101,f828]) ).
fof(f881,plain,
( spl0_28
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f862,f596,f559]) ).
fof(f884,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f873,f788]) ).
fof(f888,plain,
( identity != inverse(inverse(identity))
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36
| ~ spl0_41 ),
inference(forward_demodulation,[],[f884,f788]) ).
fof(f889,plain,
( identity != inverse(identity)
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36
| ~ spl0_41 ),
inference(forward_demodulation,[],[f888,f788]) ).
fof(f890,plain,
( $false
| ~ spl0_27
| ~ spl0_32
| ~ spl0_36
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f889,f788]) ).
fof(f891,plain,
( ~ spl0_27
| ~ spl0_32
| ~ spl0_36
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f890]) ).
fof(f911,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f92,f555]) ).
fof(f912,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c8 != multiply(X2,sk_c10) )
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f911,f555]) ).
fof(f918,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_16
| ~ spl0_43 ),
inference(superposition,[],[f533,f829]) ).
fof(f919,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c8,multiply(identity,X0))
| ~ spl0_4
| ~ spl0_43 ),
inference(superposition,[],[f535,f829]) ).
fof(f924,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c8,X0)
| ~ spl0_4
| ~ spl0_43 ),
inference(forward_demodulation,[],[f919,f1]) ).
fof(f925,plain,
( identity = sk_c1
| ~ spl0_16
| ~ spl0_43 ),
inference(forward_demodulation,[],[f918,f1]) ).
fof(f932,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c8,X0)
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f924,f555]) ).
fof(f938,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,X0)
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f932,f829]) ).
fof(f940,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f938,f1]) ).
fof(f941,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c8 != multiply(X2,sk_c10) )
| ~ spl0_2
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f912,f829]) ).
fof(f942,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f941,f829]) ).
fof(f954,plain,
( identity != sk_c8
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_27
| ~ spl0_43 ),
inference(superposition,[],[f942,f1]) ).
fof(f972,plain,
( sk_c10 = inverse(identity)
| ~ spl0_16
| ~ spl0_43 ),
inference(superposition,[],[f158,f925]) ).
fof(f1094,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = X0
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(superposition,[],[f206,f940]) ).
fof(f1306,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(superposition,[],[f3,f1094]) ).
fof(f1330,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_27
| ~ spl0_41
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[],[f954,f788]) ).
fof(f1335,definition,
( spl0_53
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_53])],[avatar_definition]) ).
fof(f1366,plain,
( spl0_53
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1306,f828,f554,f97,f1335]) ).
fof(f1376,plain,
( ~ spl0_53
| ~ spl0_2
| ~ spl0_27
| ~ spl0_41
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1330,f828,f787,f554,f91,f1335]) ).
fof(f1423,plain,
( identity = inverse(identity)
| ~ spl0_16
| ~ spl0_43 ),
inference(forward_demodulation,[],[f972,f829]) ).
fof(f1437,plain,
( spl0_41
| ~ spl0_16
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1423,f828,f156,f787]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f129]) ).
cnf(s8,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f134]) ).
cnf(s9,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f139]) ).
cnf(s10,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s11,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s12,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s17,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f163]) ).
cnf(s18,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f164]) ).
cnf(s19,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s20,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s21,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s22,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s27,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f177]) ).
cnf(s28,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f178]) ).
cnf(s29,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f179]) ).
cnf(s30,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f180]) ).
cnf(s31,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f181]) ).
cnf(s32,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f182]) ).
cnf(s37,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f187]) ).
cnf(s38,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f188]) ).
cnf(s41,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f191]) ).
cnf(s42,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f192]) ).
cnf(s43,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f366]) ).
cnf(s44,plain,
( spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f383]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f473]) ).
cnf(s52,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f487]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f501]) ).
cnf(s56,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f529]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f547]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_32
| ~ spl0_35
| spl0_36 ),
inference(sat_conversion,[],[f614]) ).
cnf(s78,plain,
( spl0_27
| ~ spl0_28
| ~ spl0_43 ),
inference(sat_conversion,[],[f832]) ).
cnf(s80,plain,
( ~ spl0_28
| spl0_35
| ~ spl0_43 ),
inference(sat_conversion,[],[f835]) ).
cnf(s83,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_32 ),
inference(sat_conversion,[],[f847]) ).
cnf(s85,plain,
( spl0_28
| ~ spl0_32 ),
inference(sat_conversion,[],[f866]) ).
cnf(s95,plain,
( ~ spl0_5
| ~ spl0_28
| spl0_43 ),
inference(sat_conversion,[],[f878]) ).
cnf(s97,plain,
( spl0_28
| ~ spl0_32 ),
inference(sat_conversion,[],[f881]) ).
cnf(s101,plain,
( ~ spl0_27
| ~ spl0_32
| ~ spl0_36
| ~ spl0_41 ),
inference(sat_conversion,[],[f891]) ).
cnf(s126,plain,
( ~ spl0_4
| ~ spl0_27
| ~ spl0_43
| spl0_53 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s128,plain,
( ~ spl0_2
| ~ spl0_27
| ~ spl0_41
| ~ spl0_43
| ~ spl0_53 ),
inference(sat_conversion,[],[f1376]) ).
cnf(s156,plain,
( ~ spl0_16
| spl0_41
| ~ spl0_43 ),
inference(sat_conversion,[],[f1437]) ).
cnf(s164,plain,
spl0_4,
inference(rat,[],[s43,s7,s8,s9,s10,s11,s12]) ).
cnf(s165,plain,
spl0_5,
inference(rat,[],[s44,s37,s38,s41,s42]) ).
cnf(s166,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_10
| ~ spl0_3 ),
inference(rat,[],[s56,s22,s52,s165]) ).
cnf(s167,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s57,s21,s31]) ).
cnf(s168,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s57,s18,s28]) ).
cnf(s169,plain,
( ~ spl0_11
| ~ spl0_3
| ~ spl0_14 ),
inference(rat,[],[s57,s17,s27,s166]) ).
cnf(s170,plain,
~ spl0_3,
inference(rat,[],[s169,s168,s167]) ).
cnf(s171,plain,
( ~ spl0_28
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s128,s156,s126,s78,s95,s164,s165]) ).
cnf(s172,plain,
( ~ spl0_16
| ~ spl0_14
| ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s54,s29,s30,s83,s97,s171,s56,s165]) ).
cnf(s173,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_2
| ~ spl0_10 ),
inference(rat,[],[s54,s19,s20,s22,s172,s165]) ).
cnf(s174,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s85,s171,s83,s21,s31]) ).
cnf(s175,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s85,s171,s83,s18,s28]) ).
cnf(s176,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s85,s171,s83,s17,s27,s173]) ).
cnf(s177,plain,
~ spl0_2,
inference(rat,[],[s176,s175,s174]) ).
cnf(s178,plain,
spl0_1,
inference(rat,[],[s2,s164,s165,s170,s177]) ).
cnf(s180,plain,
( ~ spl0_32
| ~ spl0_16 ),
inference(rat,[],[s101,s62,s156,s78,s80,s95,s97,s178,s165]) ).
cnf(s181,plain,
spl0_17,
inference(rat,[],[s27,s50,s28,s31,s32,s165,s178]) ).
cnf(s182,plain,
~ spl0_16,
inference(rat,[],[s83,s180,s181]) ).
cnf(s183,plain,
spl0_15,
inference(rat,[],[s22,s182]) ).
cnf(s184,plain,
spl0_14,
inference(rat,[],[s21,s182]) ).
cnf(s187,plain,
spl0_11,
inference(rat,[],[s18,s182]) ).
cnf(s188,plain,
spl0_10,
inference(rat,[],[s17,s182]) ).
cnf(s193,plain,
$false,
inference(rat,[],[s50,s184,s178,s165,s187,s183,s188]) ).
fof(f1459,plain,
$false,
inference(avatar_sat_refutation,[],[s193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP375-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:00:20 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (3147973)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3147981)dis+10_1_sil=32000:sp=arity:random_seed=2783886531:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3147979)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3147978)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1221837860_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3147979)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3508959329:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3147980)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1527783477:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3147983)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=188538576:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3147982)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2568485524:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3147984)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3121150581:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % (3147981) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3147973-3147981"...
% 0.17/0.48 % (3147981)...printing done.
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (3147981)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3147981)------------------------------
% 0.17/0.48 % (3147981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3147981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3147981)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3147981)Termination reason: Refutation
% 0.17/0.48 % (3147981)Time elapsed: 0.016 s
% 0.17/0.48 % (3147981)Peak memory usage: 13 MB
% 0.17/0.48 % (3147981)Instructions burned: 46 (million)
% 0.17/0.48 % (3147973)Success in time 0.046 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------