%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP370-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 10:13:46 AM UTC 2026
% Result : Unsatisfiable 2.95s 1.31s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 44
% Syntax : Number of formulae : 304 ( 19 unt; 17 def)
% Number of atoms : 1027 ( 289 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1389 ( 666 ~; 706 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| sk_c7 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c7 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c2 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c2 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c9,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c2 = inverse(sk_c1)
| sk_c7 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c2 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c2 = inverse(sk_c1)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c7,sk_c8) != sk_c9
| multiply(X0,X1) != sk_c8
| inverse(X0) != X1
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c7
| multiply(sk_c9,X4) != sk_c7
| multiply(X5,sk_c9) != X4
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c7,sk_c8) != sk_c9
| multiply(X0,X1) != sk_c8
| inverse(X0) != X1
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(sk_c9,X4)
| multiply(X5,sk_c9) != X4
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,plain,
! [X2,X3,X0,X4,X5] :
( multiply(sk_c7,sk_c8) != sk_c9
| sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(sk_c9,X4)
| multiply(X5,sk_c9) != X4
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f62]) ).
fof(f64,plain,
! [X2,X3,X0,X5] :
( multiply(sk_c7,sk_c8) != sk_c9
| sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f63]) ).
fof(f66,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f67,plain,
( ! [X5] :
( sk_c7 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f70,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_3
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f73,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_4
<=> ! [X0] :
( sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f76,plain,
( ! [X0] :
( sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,definition,
( spl0_5
<=> multiply(sk_c7,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f79,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( multiply(sk_c7,sk_c8) != sk_c9
| spl0_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f64,f78,f75,f72,f69,f66]) ).
fof(f83,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f85,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f87,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f89,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f60,f87,f83]) ).
fof(f92,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f94,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f87,f92]) ).
fof(f97,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c9,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c7 = multiply(sk_c9,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f56,f87,f97]) ).
fof(f102,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f54,f87,f102]) ).
fof(f112,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f50,f87,f112]) ).
fof(f117,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f118,plain,
( sk_c8 != multiply(sk_c3,sk_c9)
| spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f48,f87,f117]) ).
fof(f122,definition,
( spl0_14
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f124,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f122,f83]) ).
fof(f126,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f122,f92]) ).
fof(f127,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f122,f97]) ).
fof(f128,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f122,f102]) ).
fof(f130,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f122,f112]) ).
fof(f131,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f122,f117]) ).
fof(f133,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f135,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f133,f83]) ).
fof(f137,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f133,f92]) ).
fof(f138,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f133,f97]) ).
fof(f139,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f133,f102]) ).
fof(f141,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f133,f112]) ).
fof(f142,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f133,f117]) ).
fof(f143,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f78,f83]) ).
fof(f144,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f78,f92]) ).
fof(f145,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f78,f97]) ).
fof(f148,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f78,f112]) ).
fof(f149,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f78,f117]) ).
fof(f150,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f85]) ).
fof(f151,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f104]) ).
fof(f152,plain,
( identity = multiply(sk_c9,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f114]) ).
fof(f155,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f157,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f150]) ).
fof(f161,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f157,f1]) ).
fof(f162,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f155,f1]) ).
fof(f169,plain,
( sk_c9 = multiply(sk_c9,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f161,f94]) ).
fof(f175,plain,
( sk_c7 = sk_c9
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f169,f99]) ).
fof(f190,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f80,f175]) ).
fof(f227,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f162,f3]) ).
fof(f228,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f162,f162]) ).
fof(f229,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_10 ),
inference(superposition,[],[f162,f151]) ).
fof(f233,plain,
( sk_c3 = multiply(inverse(sk_c9),identity)
| ~ spl0_12 ),
inference(superposition,[],[f162,f152]) ).
fof(f235,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f162,f99]) ).
fof(f236,plain,
( sk_c5 = multiply(inverse(sk_c9),identity)
| ~ spl0_6 ),
inference(superposition,[],[f162,f150]) ).
fof(f237,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f162,f119]) ).
fof(f252,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f237,f114]) ).
fof(f253,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f235,f175]) ).
fof(f257,plain,
( sk_c4 = multiply(inverse(sk_c9),identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f229,f175]) ).
fof(f261,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f253,f3]) ).
fof(f267,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f162,f252]) ).
fof(f269,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f267,f3]) ).
fof(f275,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f269,f261]) ).
fof(f278,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f233,f261]) ).
fof(f279,plain,
( sk_c5 = multiply(inverse(sk_c9),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f236,f261]) ).
fof(f288,plain,
( sk_c4 = multiply(inverse(sk_c9),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f257,f261]) ).
fof(f289,plain,
( sk_c4 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f288,f275]) ).
fof(f290,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f278,f275]) ).
fof(f291,plain,
( sk_c5 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f279,f275]) ).
fof(f298,plain,
( sk_c3 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f290,f289]) ).
fof(f309,plain,
( sk_c4 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f291,f289]) ).
fof(f310,plain,
( sk_c3 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f309,f298]) ).
fof(f380,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f190,f252]) ).
fof(f381,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f382,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f79,f175]) ).
fof(f383,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c5,sk_c9)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f73,f85]) ).
fof(f385,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f73,f114]) ).
fof(f386,plain,
( sk_c8 != multiply(sk_c3,sk_c9)
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f385]) ).
fof(f387,plain,
( sk_c8 != multiply(sk_c5,sk_c9)
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f383]) ).
fof(f391,plain,
( sk_c8 != sk_c6
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f387,f94]) ).
fof(f401,plain,
( ~ spl0_13
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f386,f112,f72,f117]) ).
fof(f415,plain,
( sk_c2 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f162,f135]) ).
fof(f417,plain,
( sk_c2 = multiply(sk_c2,sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f415,f124]) ).
fof(f420,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f162,f382]) ).
fof(f422,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f420,f3]) ).
fof(f426,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f422,f261]) ).
fof(f431,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f426,f391]) ).
fof(f432,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f431]) ).
fof(f433,plain,
( ! [X0] :
( sk_c8 != multiply(inverse(X0),sk_c9)
| sk_c8 != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f76,f175]) ).
fof(f438,plain,
( identity != sk_c8
| sk_c8 != multiply(sk_c9,inverse(sk_c9))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f433,f3]) ).
fof(f439,plain,
( sk_c8 != multiply(sk_c9,inverse(sk_c9))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f438,f422]) ).
fof(f480,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c7,multiply(sk_c8,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f79]) ).
fof(f481,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_7 ),
inference(superposition,[],[f162,f89]) ).
fof(f482,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c2,multiply(sk_c7,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f89]) ).
fof(f487,plain,
( sk_c8 != multiply(sk_c2,sk_c7)
| sk_c8 != multiply(sk_c1,sk_c2)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f76,f124]) ).
fof(f494,definition,
( spl0_22
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f495,plain,
( identity = sk_c8
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f498,plain,
( sk_c8 != multiply(sk_c1,sk_c2)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f487,f89]) ).
fof(f500,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f498,f135]) ).
fof(f501,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f500]) ).
fof(f521,definition,
( spl0_26
<=> sk_c7 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f522,plain,
( sk_c7 = sk_c9
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f546,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f162,f417]) ).
fof(f548,plain,
( identity = sk_c8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f546,f3]) ).
fof(f550,plain,
( spl0_22
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f548,f133,f122,f494]) ).
fof(f551,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_22 ),
inference(superposition,[],[f1,f495]) ).
fof(f554,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c9,X0)
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[],[f480,f551]) ).
fof(f556,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_5
| ~ spl0_22 ),
inference(superposition,[],[f554,f79]) ).
fof(f587,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c2,multiply(sk_c9,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22 ),
inference(forward_demodulation,[],[f482,f554]) ).
fof(f588,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c9,X0)) = X0
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22 ),
inference(forward_demodulation,[],[f587,f551]) ).
fof(f595,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22 ),
inference(superposition,[],[f588,f556]) ).
fof(f597,plain,
( sk_c3 = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_22 ),
inference(superposition,[],[f588,f152]) ).
fof(f600,plain,
( sk_c5 = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_22 ),
inference(superposition,[],[f588,f150]) ).
fof(f606,plain,
( sk_c5 = multiply(sk_c2,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_22 ),
inference(forward_demodulation,[],[f600,f495]) ).
fof(f609,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f597,f495]) ).
fof(f611,plain,
( sk_c5 = sk_c2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f606,f417]) ).
fof(f612,plain,
( sk_c3 = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f609,f417]) ).
fof(f634,plain,
( sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f118,f612]) ).
fof(f673,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f634,f595]) ).
fof(f674,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f673]) ).
fof(f703,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c9 != multiply(sk_c9,multiply(X5,sk_c9)) )
| ~ spl0_1
| ~ spl0_26 ),
inference(forward_demodulation,[],[f67,f522]) ).
fof(f704,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c5,sk_c9))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f703,f85]) ).
fof(f708,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c5,sk_c9))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f704]) ).
fof(f711,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f708,f161]) ).
fof(f712,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f711]) ).
fof(f717,plain,
( sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[],[f387,f611]) ).
fof(f720,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f717,f595]) ).
fof(f721,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f720]) ).
fof(f722,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_26 ),
inference(forward_demodulation,[],[f70,f522]) ).
fof(f724,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_demodulation,[],[f481,f522]) ).
fof(f725,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) )
| ~ spl0_2
| ~ spl0_26 ),
inference(forward_demodulation,[],[f722,f522]) ).
fof(f726,plain,
( spl0_3
| ~ spl0_2
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f725,f521,f69,f72]) ).
fof(f849,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c8) = X0
| ~ spl0_22 ),
inference(forward_demodulation,[],[f227,f495]) ).
fof(f859,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_22 ),
inference(superposition,[],[f228,f849]) ).
fof(f1058,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(superposition,[],[f859,f724]) ).
fof(f1078,plain,
( sk_c7 = sk_c9
| ~ spl0_5
| ~ spl0_22 ),
inference(superposition,[],[f79,f859]) ).
fof(f1138,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(superposition,[],[f703,f1058]) ).
fof(f1141,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f1138]) ).
fof(f1143,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1141,f595]) ).
fof(f1146,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1143,f556]) ).
fof(f1147,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1146]) ).
fof(f1162,plain,
( spl0_26
| ~ spl0_5
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1078,f494,f78,f521]) ).
fof(f1212,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(superposition,[],[f73,f1058]) ).
fof(f1218,plain,
( sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f1212]) ).
fof(f1222,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1218,f595]) ).
fof(f1223,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1222]) ).
fof(f1228,plain,
( sk_c8 != multiply(sk_c9,inverse(sk_c9))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f438,f495]) ).
fof(f1246,plain,
( sk_c3 = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f609,f859]) ).
fof(f1272,plain,
( sk_c5 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_6
| ~ spl0_22 ),
inference(superposition,[],[f849,f85]) ).
fof(f1274,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f85]) ).
fof(f1275,plain,
( sk_c8 = multiply(sk_c9,sk_c5)
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1274,f495]) ).
fof(f1276,plain,
( sk_c5 = inverse(sk_c9)
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1272,f859]) ).
fof(f1278,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_12
| ~ spl0_22 ),
inference(superposition,[],[f849,f114]) ).
fof(f1282,plain,
( sk_c3 = inverse(sk_c9)
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1278,f859]) ).
fof(f1320,plain,
( sk_c3 = inverse(sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1276,f310]) ).
fof(f1321,plain,
( sk_c2 = inverse(sk_c9)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1320,f1246]) ).
fof(f1325,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1275,f310]) ).
fof(f1326,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1325,f1246]) ).
fof(f1347,plain,
( sk_c8 != multiply(sk_c9,sk_c2)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f439,f1321]) ).
fof(f1348,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1347,f1326]) ).
fof(f1349,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1348]) ).
fof(f1364,definition,
( spl0_31
<=> sk_c8 = multiply(sk_c9,inverse(sk_c9)) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f1366,plain,
( sk_c8 != multiply(sk_c9,inverse(sk_c9))
| spl0_31 ),
inference(avatar_component_clause,[],[f1364]) ).
fof(f1372,plain,
( spl0_22
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f422,f97,f92,f83,f78,f494]) ).
fof(f1380,plain,
( spl0_22
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f269,f117,f112,f494]) ).
fof(f1403,plain,
( ~ spl0_31
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1228,f494,f97,f92,f83,f75,f1364]) ).
fof(f1459,plain,
( sk_c8 != multiply(sk_c9,sk_c3)
| ~ spl0_12
| ~ spl0_22
| spl0_31 ),
inference(forward_demodulation,[],[f1366,f1282]) ).
fof(f1460,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f1459,f1325]) ).
fof(f1461,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_31 ),
inference(avatar_contradiction_clause,[],[f1460]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f81]) ).
cnf(s2,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f90]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f95]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f100]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s9,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f125]) ).
cnf(s10,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f126]) ).
cnf(s11,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s12,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s15,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f131]) ).
cnf(s16,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f136]) ).
cnf(s17,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f137]) ).
cnf(s18,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f138]) ).
cnf(s19,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f139]) ).
cnf(s21,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f141]) ).
cnf(s22,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f142]) ).
cnf(s23,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f143]) ).
cnf(s24,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f144]) ).
cnf(s25,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f145]) ).
cnf(s28,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f148]) ).
cnf(s29,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f149]) ).
cnf(s30,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f381]) ).
cnf(s34,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f401]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f432]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f501]) ).
cnf(s53,plain,
( ~ spl0_14
| ~ spl0_15
| spl0_22 ),
inference(sat_conversion,[],[f550]) ).
cnf(s66,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(sat_conversion,[],[f674]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_26 ),
inference(sat_conversion,[],[f712]) ).
cnf(s74,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(sat_conversion,[],[f721]) ).
cnf(s75,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_26 ),
inference(sat_conversion,[],[f726]) ).
cnf(s90,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(sat_conversion,[],[f1147]) ).
cnf(s91,plain,
( ~ spl0_5
| ~ spl0_22
| spl0_26 ),
inference(sat_conversion,[],[f1162]) ).
cnf(s100,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22
| ~ spl0_26 ),
inference(sat_conversion,[],[f1223]) ).
cnf(s121,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f1349]) ).
cnf(s126,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_22 ),
inference(sat_conversion,[],[f1372]) ).
cnf(s127,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_22 ),
inference(sat_conversion,[],[f1380]) ).
cnf(s136,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22
| ~ spl0_31 ),
inference(sat_conversion,[],[f1403]) ).
cnf(s149,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| spl0_31 ),
inference(sat_conversion,[],[f1461]) ).
cnf(s150,plain,
spl0_5,
inference(rat,[],[s30,s23,s24,s25,s28,s29]) ).
cnf(s151,plain,
( spl0_7
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s136,s149,s127,s3,s4,s5,s7,s8]) ).
cnf(s152,plain,
( ~ spl0_12
| ~ spl0_10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_22 ),
inference(rat,[],[s66,s15,s22,s121,s150]) ).
cnf(s153,plain,
( spl0_12
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s47,s14,s21]) ).
cnf(s154,plain,
( spl0_10
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s47,s12,s19]) ).
cnf(s155,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s152,s126,s153,s154,s151,s150]) ).
cnf(s156,plain,
( spl0_9
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s47,s11,s18]) ).
cnf(s157,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s47,s10,s17,s155,s156,s151]) ).
cnf(s158,plain,
~ spl0_4,
inference(rat,[],[s47,s2,s9,s16,s157]) ).
cnf(s159,plain,
( spl0_9
| ~ spl0_7
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s74,s53,s11,s18,s150]) ).
cnf(s160,plain,
( ~ spl0_7
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s74,s53,s10,s17,s37,s159,s150]) ).
cnf(s161,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s34,s7,s8]) ).
cnf(s162,plain,
( ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s100,s91,s53,s9,s16,s160,s150]) ).
cnf(s163,plain,
~ spl0_3,
inference(rat,[],[s162,s161]) ).
cnf(s164,plain,
( spl0_9
| spl0_22 ),
inference(rat,[],[s53,s11,s18]) ).
cnf(s165,plain,
( spl0_8
| spl0_22 ),
inference(rat,[],[s53,s10,s17]) ).
cnf(s166,plain,
( ~ spl0_8
| spl0_22
| ~ spl0_9 ),
inference(rat,[],[s53,s9,s16,s126,s150]) ).
cnf(s167,plain,
spl0_22,
inference(rat,[],[s166,s165,s164]) ).
cnf(s168,plain,
spl0_26,
inference(rat,[],[s91,s150,s167]) ).
cnf(s169,plain,
~ spl0_2,
inference(rat,[],[s75,s163,s168]) ).
cnf(s170,plain,
spl0_1,
inference(rat,[],[s1,s150,s158,s163,s169]) ).
cnf(s171,plain,
~ spl0_6,
inference(rat,[],[s71,s168,s170]) ).
cnf(s172,plain,
~ spl0_7,
inference(rat,[],[s90,s168,s167,s150,s170]) ).
cnf(s175,plain,
$false,
inference(rat,[],[s2,s172,s171]) ).
fof(f1462,plain,
$false,
inference(avatar_sat_refutation,[],[s175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP370-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 % Computer : n004.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 27 09:56:52 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.43 Running first-order theorem proving
% 0.09/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.95/1.31 % (3264300)Input is clausal, will run a generic CNF schedule.
% 2.95/1.31 % (3264309)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2325262134:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.95/1.31 % (3264308)lrs+10_1_sil=8000:sp=occurrence:random_seed=3888108501:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.95/1.31 % (3264309)Instruction limit reached!
% 2.95/1.31 % (3264309)------------------------------
% 2.95/1.31 % (3264309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.31 % (3264309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.31 % (3264309)CaDiCaL version: 2.1.3
% 2.95/1.31 % (3264309)Termination reason: Instruction limit
% 2.95/1.31 % (3264309)Termination phase: Saturation
% 2.95/1.31 % (3264309)Time elapsed: 0.037 s
% 2.95/1.31 % (3264309)Peak memory usage: 89 MB
% 2.95/1.31 % (3264309)Instructions burned: 117 (million)
% 2.95/1.31 % (3264311)dis-21_1_sil=8000:lcm=predicate:random_seed=2483038701:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.95/1.31 % (3264306)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3612506829:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.95/1.31 % (3264305)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=47788320:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.95/1.31 % (3264307)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=966154333:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.95/1.31 % (3264308)Refutation not found, incomplete strategy
% 2.95/1.31 % (3264308)------------------------------
% 2.95/1.31 % (3264308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.31 % (3264308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.31 % (3264308)CaDiCaL version: 2.1.3
% 2.95/1.31 % (3264308)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.31 % (3264308)Time elapsed: 0.003 s
% 2.95/1.31 % (3264308)Peak memory usage: 88 MB
% 2.95/1.31 % (3264308)Instructions burned: 4 (million)
% 2.95/1.31 % (3264311)Refutation not found, incomplete strategy
% 2.95/1.31 % (3264311)------------------------------
% 2.95/1.31 % (3264311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.31 % (3264311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.31 % (3264311)CaDiCaL version: 2.1.3
% 2.95/1.31 % (3264311)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.31 % (3264311)Time elapsed: 0.002 s
% 2.95/1.31 % (3264311)Peak memory usage: 88 MB
% 2.95/1.31 % (3264311)Instructions burned: 1 (million)
% 2.95/1.31 % (3264310)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1552514927:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.95/1.31 % (3264310)First to succeed.
% 2.95/1.31 % (3264310)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3264300"
% 2.95/1.31 % (3264318)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1983900572:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.95/1.31 % (3264318)Refutation not found, incomplete strategy
% 2.95/1.31 % (3264318)------------------------------
% 2.95/1.31 % (3264318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.31 % (3264318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.31 % (3264318)CaDiCaL version: 2.1.3
% 2.95/1.31 % (3264318)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.31 % (3264318)Time elapsed: 0.002 s
% 2.95/1.31 % (3264318)Peak memory usage: 88 MB
% 2.95/1.31 % (3264318)Instructions burned: 4 (million)
% 2.95/1.31 % (3264318)------------------------------
% 2.95/1.31 % (3264318)------------------------------
% 2.95/1.31 % (3264311)------------------------------
% 2.95/1.31 % (3264311)------------------------------
% 2.95/1.31 % (3264308)------------------------------
% 2.95/1.31 % (3264308)------------------------------
% 2.95/1.31 % (3264310)Refutation found. Thanks to Tanya!
% 2.95/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.95/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.41 % (3264310)------------------------------
% 3.66/1.41 % (3264310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.41 % (3264310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.41 % (3264310)CaDiCaL version: 2.1.3
% 3.66/1.41 % (3264310)Termination reason: Refutation
% 3.66/1.41 % (3264310)Time elapsed: 0.032 s
% 3.66/1.41 % (3264310)Peak memory usage: 90 MB
% 3.66/1.41 % (3264310)Instructions burned: 50 (million)
% 3.66/1.41 % (3264310)------------------------------
% 3.66/1.41 % (3264310)------------------------------
% 3.66/1.41 % (3264300)Success in time 0.443 s
% 3.66/1.41 % Vampire exiting
%------------------------------------------------------------------------------