%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP377-1 : 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 : n004.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 0.43s 0.47s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 41
% Syntax : Number of formulae : 281 ( 24 unt; 19 def)
% Number of atoms : 967 ( 328 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1332 ( 646 ~; 667 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 71 !; 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(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(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_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| 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_c9) != sk_c10
| 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_c10 != multiply(sk_c8,sk_c9)
| 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_c10 != multiply(sk_c8,sk_c9)
| 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_c10 != multiply(sk_c8,sk_c9)
| 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_c10 = multiply(sk_c8,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f98,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( sk_c10 != multiply(sk_c8,sk_c9)
| 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(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(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(f273,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f206,f223]) ).
fof(f278,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f206,f143]) ).
fof(f281,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c10)
| ~ spl0_11 ),
inference(superposition,[],[f206,f133]) ).
fof(f298,plain,
( sk_c7 = multiply(sk_c7,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f281,f128]) ).
fof(f301,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f278,f138]) ).
fof(f305,plain,
( identity = sk_c9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f273,f3]) ).
fof(f339,plain,
( sk_c10 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f206,f298]) ).
fof(f341,plain,
( identity = sk_c10
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f339,f3]) ).
fof(f345,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f193,f341]) ).
fof(f354,plain,
( identity = sk_c2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f345,f1]) ).
fof(f358,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f301,f305]) ).
fof(f359,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f358,f1]) ).
fof(f361,plain,
( sk_c10 != multiply(identity,sk_c9)
| 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,f305]) ).
fof(f365,plain,
( $false
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f364,f341]) ).
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,f305]) ).
fof(f370,plain,
( identity != inverse(identity)
| spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f368,f341]) ).
fof(f376,plain,
( sk_c10 = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f148,f354]) ).
fof(f377,plain,
( identity = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f376,f341]) ).
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,f341]) ).
fof(f388,plain,
( identity = inverse(sk_c10)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f102,f305]) ).
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,f305]) ).
fof(f390,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f388,f341]) ).
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,f341]) ).
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,f341]) ).
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,f305]) ).
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,f341]) ).
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(f504,plain,
( sk_c9 != multiply(sk_c2,identity)
| ~ spl0_10
| ~ spl0_11
| spl0_15 ),
inference(forward_demodulation,[],[f152,f341]) ).
fof(f505,plain,
( identity = inverse(sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f158,f341]) ).
fof(f509,plain,
( sk_c9 = inverse(identity)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f102,f341]) ).
fof(f511,plain,
( sk_c9 != multiply(identity,identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f504,f354]) ).
fof(f513,plain,
( identity != sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f511,f1]) ).
fof(f515,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f3,f505]) ).
fof(f516,plain,
( identity = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f515,f1]) ).
fof(f518,plain,
( identity = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f505,f516]) ).
fof(f522,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f518,f509]) ).
fof(f529,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f522,f513]) ).
fof(f530,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f529]) ).
fof(f532,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_5 ),
inference(superposition,[],[f3,f102]) ).
fof(f535,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c10)
| ~ spl0_4 ),
inference(superposition,[],[f206,f98]) ).
fof(f537,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f206,f172]) ).
fof(f539,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f537,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(f545,plain,
( $false
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f544,f158]) ).
fof(f546,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f545]) ).
fof(f553,definition,
( spl0_27
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f554,plain,
( sk_c10 = sk_c9
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f555,plain,
( sk_c10 != sk_c9
| spl0_27 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f558,definition,
( spl0_28
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f559,plain,
( identity = sk_c9
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f578,plain,
( ! [X0] :
( inverse(X0) != inverse(identity)
| sk_c10 != multiply(X0,inverse(X0))
| inverse(X0) != inverse(inverse(identity))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_1 ),
inference(superposition,[],[f89,f1]) ).
fof(f594,definition,
( spl0_32
<=> sk_c10 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f595,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f677,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_27
| ~ spl0_32 ),
inference(forward_demodulation,[],[f595,f554]) ).
fof(f680,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_27
| ~ spl0_32 ),
inference(superposition,[],[f206,f677]) ).
fof(f682,plain,
( identity = sk_c10
| ~ spl0_27
| ~ spl0_32 ),
inference(forward_demodulation,[],[f680,f3]) ).
fof(f733,definition,
( spl0_41
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f734,plain,
( identity = inverse(identity)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f756,plain,
( spl0_28
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f305,f151,f146,f558]) ).
fof(f777,plain,
( identity = multiply(identity,sk_c10)
| ~ spl0_5
| ~ spl0_28 ),
inference(superposition,[],[f532,f559]) ).
fof(f785,plain,
( identity = sk_c10
| ~ spl0_5
| ~ spl0_28 ),
inference(forward_demodulation,[],[f777,f1]) ).
fof(f821,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| inverse(X0) != inverse(identity)
| inverse(X0) != inverse(inverse(identity))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32 ),
inference(forward_demodulation,[],[f578,f682]) ).
fof(f822,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c10)
| identity != multiply(X0,inverse(X0))
| inverse(X0) != inverse(identity)
| inverse(X0) != inverse(inverse(identity)) )
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32 ),
inference(forward_demodulation,[],[f821,f554]) ).
fof(f823,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0))
| inverse(X0) != inverse(identity)
| inverse(X0) != inverse(inverse(identity)) )
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32 ),
inference(forward_demodulation,[],[f822,f682]) ).
fof(f828,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0))
| inverse(X0) != inverse(inverse(identity)) )
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(forward_demodulation,[],[f823,f734]) ).
fof(f829,plain,
( ! [X0] :
( inverse(X0) != inverse(identity)
| identity != inverse(X0)
| identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(forward_demodulation,[],[f828,f734]) ).
fof(f830,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != inverse(X0)
| identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(forward_demodulation,[],[f829,f734]) ).
fof(f831,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != inverse(X0)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(duplicate_literal_removal,[],[f830]) ).
fof(f839,plain,
( identity != identity
| identity != inverse(identity)
| identity != multiply(identity,inverse(identity))
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(superposition,[],[f831,f3]) ).
fof(f840,plain,
( identity != inverse(identity)
| identity != multiply(identity,inverse(identity))
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(trivial_inequality_removal,[],[f839]) ).
fof(f843,plain,
( identity != multiply(identity,inverse(identity))
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f840,f734]) ).
fof(f851,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(forward_demodulation,[],[f843,f1]) ).
fof(f856,plain,
( $false
| ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f851,f734]) ).
fof(f857,plain,
( ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f856]) ).
fof(f906,plain,
( identity != sk_c10
| spl0_27
| ~ spl0_28 ),
inference(forward_demodulation,[],[f555,f559]) ).
fof(f938,definition,
( spl0_43
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f939,plain,
( identity = sk_c10
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f966,plain,
( ~ spl0_43
| spl0_27
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f906,f558,f553,f938]) ).
fof(f1143,plain,
( spl0_32
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f539,f170,f156,f594]) ).
fof(f1158,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_32 ),
inference(superposition,[],[f206,f595]) ).
fof(f1160,plain,
( identity = sk_c9
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1158,f3]) ).
fof(f1162,plain,
( spl0_28
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1160,f594,f558]) ).
fof(f1169,plain,
( spl0_43
| ~ spl0_5
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f785,f558,f101,f938]) ).
fof(f1200,plain,
( sk_c9 = inverse(identity)
| ~ spl0_5
| ~ spl0_43 ),
inference(superposition,[],[f102,f939]) ).
fof(f1214,plain,
( sk_c10 = inverse(identity)
| ~ spl0_5
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1200,f554]) ).
fof(f1218,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1214,f939]) ).
fof(f1220,plain,
( spl0_41
| ~ spl0_5
| ~ spl0_27
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1218,f938,f553,f101,f733]) ).
fof(f1232,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f92,f554]) ).
fof(f1233,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1232,f939]) ).
fof(f1234,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c8 != multiply(X2,identity) )
| ~ spl0_2
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1233,f554]) ).
fof(f1235,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1234,f939]) ).
fof(f1250,plain,
( identity != sk_c8
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_27
| ~ spl0_43 ),
inference(superposition,[],[f1235,f1]) ).
fof(f1269,definition,
( spl0_49
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f1271,plain,
( identity != sk_c8
| spl0_49 ),
inference(avatar_component_clause,[],[f1269]) ).
fof(f1274,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_27
| ~ spl0_41
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[],[f1250,f734]) ).
fof(f1276,plain,
( ~ spl0_49
| ~ spl0_2
| ~ spl0_27
| ~ spl0_41
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1274,f938,f733,f553,f91,f1269]) ).
fof(f1413,plain,
( sk_c9 = multiply(inverse(sk_c8),identity)
| ~ spl0_4
| ~ spl0_43 ),
inference(forward_demodulation,[],[f535,f939]) ).
fof(f1414,plain,
( sk_c10 = multiply(inverse(sk_c8),identity)
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1413,f554]) ).
fof(f1415,plain,
( identity = multiply(inverse(sk_c8),identity)
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1414,f939]) ).
fof(f1504,plain,
( ! [X0] : multiply(identity,X0) = multiply(inverse(sk_c8),multiply(identity,X0))
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(superposition,[],[f4,f1415]) ).
fof(f1505,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = X0
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1504,f1]) ).
fof(f1611,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43 ),
inference(superposition,[],[f1505,f3]) ).
fof(f1623,plain,
( $false
| ~ spl0_4
| ~ spl0_27
| ~ spl0_43
| spl0_49 ),
inference(forward_subsumption_resolution,[],[f1611,f1271]) ).
fof(f1624,plain,
( ~ spl0_4
| ~ spl0_27
| ~ spl0_43
| spl0_49 ),
inference(avatar_contradiction_clause,[],[f1623]) ).
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(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(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(s56,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f530]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f546]) ).
cnf(s73,plain,
( ~ spl0_14
| ~ spl0_15
| spl0_28 ),
inference(sat_conversion,[],[f756]) ).
cnf(s81,plain,
( ~ spl0_1
| ~ spl0_27
| ~ spl0_32
| ~ spl0_41 ),
inference(sat_conversion,[],[f857]) ).
cnf(s102,plain,
( spl0_27
| ~ spl0_28
| ~ spl0_43 ),
inference(sat_conversion,[],[f966]) ).
cnf(s136,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_32 ),
inference(sat_conversion,[],[f1143]) ).
cnf(s140,plain,
( spl0_28
| ~ spl0_32 ),
inference(sat_conversion,[],[f1162]) ).
cnf(s163,plain,
( ~ spl0_5
| ~ spl0_28
| spl0_43 ),
inference(sat_conversion,[],[f1169]) ).
cnf(s168,plain,
( ~ spl0_5
| ~ spl0_27
| spl0_41
| ~ spl0_43 ),
inference(sat_conversion,[],[f1220]) ).
cnf(s172,plain,
( ~ spl0_2
| ~ spl0_27
| ~ spl0_41
| ~ spl0_43
| ~ spl0_49 ),
inference(sat_conversion,[],[f1276]) ).
cnf(s185,plain,
( ~ spl0_4
| ~ spl0_27
| ~ spl0_43
| spl0_49 ),
inference(sat_conversion,[],[f1624]) ).
cnf(s186,plain,
spl0_4,
inference(rat,[],[s43,s7,s8,s9,s10,s11,s12]) ).
cnf(s187,plain,
spl0_5,
inference(rat,[],[s44,s37,s38,s41,s42]) ).
cnf(s188,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_3
| ~ spl0_10 ),
inference(rat,[],[s56,s22,s52,s187]) ).
cnf(s189,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s57,s21,s31]) ).
cnf(s190,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s57,s18,s28]) ).
cnf(s191,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_3 ),
inference(rat,[],[s57,s17,s27,s188]) ).
cnf(s192,plain,
~ spl0_3,
inference(rat,[],[s191,s190,s189]) ).
cnf(s195,plain,
( ~ spl0_28
| ~ spl0_2 ),
inference(rat,[],[s172,s168,s185,s102,s163,s187,s186]) ).
cnf(s196,plain,
( spl0_17
| spl0_28 ),
inference(rat,[],[s73,s31,s32]) ).
cnf(s197,plain,
spl0_28,
inference(rat,[],[s73,s21,s22,s136,s196,s140]) ).
cnf(s198,plain,
spl0_43,
inference(rat,[],[s163,s187,s197]) ).
cnf(s199,plain,
spl0_27,
inference(rat,[],[s102,s198,s197]) ).
cnf(s200,plain,
~ spl0_2,
inference(rat,[],[s195,s197]) ).
cnf(s202,plain,
spl0_41,
inference(rat,[],[s168,s199,s187,s198]) ).
cnf(s203,plain,
spl0_1,
inference(rat,[],[s2,s186,s187,s192,s200]) ).
cnf(s205,plain,
~ spl0_32,
inference(rat,[],[s81,s199,s203,s202]) ).
cnf(s208,plain,
spl0_17,
inference(rat,[],[s50,s27,s28,s31,s32,s203,s187]) ).
cnf(s209,plain,
~ spl0_16,
inference(rat,[],[s136,s205,s208]) ).
cnf(s210,plain,
spl0_15,
inference(rat,[],[s22,s209]) ).
cnf(s211,plain,
spl0_14,
inference(rat,[],[s21,s209]) ).
cnf(s214,plain,
spl0_11,
inference(rat,[],[s18,s209]) ).
cnf(s215,plain,
spl0_10,
inference(rat,[],[s17,s209]) ).
cnf(s220,plain,
$false,
inference(rat,[],[s50,s214,s215,s187,s203,s210,s211]) ).
fof(f1625,plain,
$false,
inference(avatar_sat_refutation,[],[s220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP377-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:59:06 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
% 0.43/0.47 % (3265998)Will run a generic schedule for satisfiability detection.
% 0.43/0.47 % (3266004)% WARNING: option uhcvi not known.
% 0.43/0.47 % (3266005)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3933555175:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.43/0.47 % (3266003)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4293754360_2999 on theBenchmark for (2999ds/0Mi)
% 0.43/0.47 % (3266004)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3141266238:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.43/0.47 % (3266006)dis+10_1_sil=32000:sp=arity:random_seed=2604147443:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.43/0.47 % (3266007)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=429260678:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.43/0.47 % (3266008)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3101750826:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.43/0.47 % (3266009)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3085232061:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.43/0.47 % TRYING [1]
% 0.43/0.47 % TRYING [2]
% 0.43/0.47 % TRYING [3]
% 0.43/0.47 % TRYING [4]
% 0.43/0.47 % TRYING [5]
% 0.43/0.47 % (3266006) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3265998-3266006"...
% 0.43/0.47 % (3266007) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3265998-3266007"...
% 0.43/0.47 % (3266006)...printing done.
% 0.43/0.47 % (3266006)Refutation found. Thanks to Tanya!
% 0.43/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.43/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.43/0.47 % (3266006)------------------------------
% 0.43/0.47 % (3266006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.47 % (3266006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.47 % (3266006)CaDiCaL version: 2.1.3
% 0.43/0.47 % (3266006)Termination reason: Refutation
% 0.43/0.47 % (3266006)Time elapsed: 0.033 s
% 0.43/0.47 % (3266006)Peak memory usage: 13 MB
% 0.43/0.47 % (3266006)Instructions burned: 54 (million)
% 0.43/0.47 % (3265998)Success in time 0.065 s
% 0.43/0.47 % Vampire exiting
%------------------------------------------------------------------------------