%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP306-1 : 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 : n005.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 10:13:35 AM UTC 2026
% Result : Unsatisfiable 2.52s 1.33s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 43
% Syntax : Number of formulae : 289 ( 24 unt; 18 def)
% Number of atoms : 945 ( 270 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1255 ( 599 ~; 638 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 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_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = inverse(sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c2 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c2 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c2 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(X0,X1) != sk_c8
| inverse(X0) != X1
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| multiply(X0,X1) != sk_c8
| inverse(X0) != X1
| sk_c8 != multiply(X1,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f47]) ).
fof(f49,plain,
! [X2,X0,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f48]) ).
fof(f51,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f52,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f55,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,definition,
( spl0_3
<=> ! [X0] :
( sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f58,plain,
( ! [X0] :
( sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_4
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f61,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( sk_c6 != inverse(sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f64,definition,
( spl0_5
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f49,f64,f60,f57,f54,f51]) ).
fof(f69,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f71,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f73,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f75,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f45,f73,f69]) ).
fof(f78,definition,
( spl0_8
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f80,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f43,f73,f78]) ).
fof(f83,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f85,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f41,f73,f83]) ).
fof(f88,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f90,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f39,f73,f88]) ).
fof(f93,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f95,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f37,f73,f93]) ).
fof(f98,definition,
( spl0_12
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f100,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f35,f98,f69]) ).
fof(f102,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f33,f98,f78]) ).
fof(f103,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f31,f98,f83]) ).
fof(f104,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f29,f98,f88]) ).
fof(f105,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f27,f98,f93]) ).
fof(f107,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f109,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f25,f107,f69]) ).
fof(f111,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f23,f107,f78]) ).
fof(f112,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f21,f107,f83]) ).
fof(f113,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f19,f107,f88]) ).
fof(f114,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f17,f107,f93]) ).
fof(f115,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f15,f60,f69]) ).
fof(f116,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f13,f60,f78]) ).
fof(f117,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f11,f60,f83]) ).
fof(f118,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f9,f60,f88]) ).
fof(f119,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f7,f60,f93]) ).
fof(f120,plain,
spl0_5,
inference(avatar_split_clause,[],[f5,f64]) ).
fof(f121,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f71]) ).
fof(f122,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f90]) ).
fof(f125,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f126,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_5 ),
inference(superposition,[],[f4,f65]) ).
fof(f127,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f85]) ).
fof(f128,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f95]) ).
fof(f129,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f80]) ).
fof(f130,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f125,f1]) ).
fof(f133,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f121]) ).
fof(f134,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f133,f1]) ).
fof(f137,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f134,f80]) ).
fof(f143,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f137,f85]) ).
fof(f151,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f128,f143]) ).
fof(f155,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c4,sk_c6)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f129,f65]) ).
fof(f165,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c5,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f155,f143]) ).
fof(f177,plain,
( identity = multiply(sk_c3,identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f151,f122]) ).
fof(f194,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c7,X0))
| ~ spl0_9 ),
inference(superposition,[],[f130,f127]) ).
fof(f196,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f130,f122]) ).
fof(f198,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f130,f85]) ).
fof(f199,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_6 ),
inference(superposition,[],[f130,f121]) ).
fof(f200,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f130,f95]) ).
fof(f213,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f200,f143]) ).
fof(f214,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f198,f143]) ).
fof(f217,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f194,f143]) ).
fof(f219,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f213,f90]) ).
fof(f220,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f214,f3]) ).
fof(f221,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f217,f130]) ).
fof(f223,plain,
( sk_c5 = multiply(sk_c3,sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f177,f220]) ).
fof(f232,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f130,f219]) ).
fof(f234,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f232,f3]) ).
fof(f242,plain,
( sk_c5 = multiply(inverse(sk_c3),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f130,f223]) ).
fof(f245,plain,
( sk_c5 = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f242,f90]) ).
fof(f246,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f245,f85]) ).
fof(f247,plain,
( sk_c8 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f246,f143]) ).
fof(f256,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f196,f220]) ).
fof(f257,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f256,f247]) ).
fof(f258,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f257,f3]) ).
fof(f259,plain,
( sk_c8 = sk_c3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f258,f234]) ).
fof(f260,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f90,f259]) ).
fof(f271,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f199,f220]) ).
fof(f272,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f271,f247]) ).
fof(f273,plain,
( identity = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f272,f3]) ).
fof(f274,plain,
( sk_c5 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f273,f220]) ).
fof(f275,plain,
( sk_c8 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f274,f247]) ).
fof(f288,plain,
( sk_c8 != sk_c6
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f62,f260]) ).
fof(f301,plain,
( sk_c8 = multiply(sk_c4,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f165,f221]) ).
fof(f302,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f301,f275]) ).
fof(f304,plain,
( multiply(sk_c4,sk_c8) = multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f129,f302]) ).
fof(f308,plain,
( sk_c6 = multiply(sk_c4,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f304,f221]) ).
fof(f310,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f308,f275]) ).
fof(f313,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f310,f219]) ).
fof(f314,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f313,f288]) ).
fof(f315,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f316,plain,
( ! [X0] :
( sk_c8 != multiply(inverse(X0),sk_c8)
| sk_c8 != multiply(X0,inverse(X0)) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f58,f143]) ).
fof(f322,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f316,f71]) ).
fof(f331,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f322,f219]) ).
fof(f335,plain,
( sk_c8 != sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f331,f80]) ).
fof(f338,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f335,f247]) ).
fof(f339,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f340,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f52,f143]) ).
fof(f341,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f340,f71]) ).
fof(f343,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f340,f260]) ).
fof(f344,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f343]) ).
fof(f346,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f341]) ).
fof(f347,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f344,f219]) ).
fof(f349,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f346,f134]) ).
fof(f350,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f351,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f347,f219]) ).
fof(f352,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f356,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c8) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f55,f143]) ).
fof(f358,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f356,f71]) ).
fof(f363,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f358]) ).
fof(f368,plain,
( sk_c8 != sk_c5
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f363,f80]) ).
fof(f369,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f368,f247]) ).
fof(f370,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f369]) ).
fof(f371,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f200,f90]) ).
fof(f373,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f61]) ).
fof(f378,plain,
( sk_c2 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f130,f109]) ).
fof(f379,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c2,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f109]) ).
fof(f380,plain,
( sk_c2 = multiply(sk_c2,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f378,f100]) ).
fof(f383,plain,
( sk_c8 != multiply(sk_c2,sk_c7)
| sk_c8 != multiply(sk_c1,sk_c2)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f58,f100]) ).
fof(f390,definition,
( spl0_15
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f391,plain,
( identity = sk_c8
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f394,plain,
( sk_c8 != multiply(sk_c1,sk_c2)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f383,f75]) ).
fof(f405,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f394,f109]) ).
fof(f406,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f413,definition,
( spl0_19
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f414,plain,
( sk_c8 = sk_c7
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f415,plain,
( sk_c8 != sk_c7
| spl0_19 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f422,plain,
( sk_c8 != sk_c2
| sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f52,f100]) ).
fof(f425,definition,
( spl0_20
<=> sk_c7 = multiply(sk_c8,multiply(sk_c1,sk_c8)) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f427,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| spl0_20 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f429,definition,
( spl0_21
<=> sk_c8 = sk_c2 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f432,plain,
( ~ spl0_20
| ~ spl0_21
| ~ spl0_1
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f422,f98,f51,f429,f425]) ).
fof(f446,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f130,f371]) ).
fof(f448,plain,
( identity = sk_c7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f446,f3]) ).
fof(f476,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f130,f380]) ).
fof(f478,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f476,f3]) ).
fof(f479,plain,
( spl0_15
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f478,f107,f98,f390]) ).
fof(f480,plain,
( sk_c8 = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_15 ),
inference(superposition,[],[f391,f448]) ).
fof(f482,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_15 ),
inference(superposition,[],[f1,f391]) ).
fof(f485,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_15
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f480,f415]) ).
fof(f486,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_15
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f494,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c1,sk_c8)
| ~ spl0_7
| ~ spl0_13 ),
inference(superposition,[],[f379,f75]) ).
fof(f501,plain,
( sk_c6 = multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f494,f65]) ).
fof(f517,plain,
( sk_c8 = multiply(sk_c2,sk_c8)
| ~ spl0_7
| ~ spl0_19 ),
inference(superposition,[],[f75,f414]) ).
fof(f523,plain,
( sk_c8 = sk_c2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(superposition,[],[f380,f517]) ).
fof(f527,plain,
( spl0_21
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f523,f413,f107,f98,f73,f429]) ).
fof(f622,plain,
( sk_c8 != sk_c2
| sk_c7 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f55,f100]) ).
fof(f626,definition,
( spl0_23
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f627,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f629,plain,
( ~ spl0_23
| ~ spl0_21
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f622,f98,f54,f429,f626]) ).
fof(f641,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[],[f482,f65]) ).
fof(f671,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_23 ),
inference(superposition,[],[f4,f627]) ).
fof(f672,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,X0)
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f671,f482]) ).
fof(f682,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_15
| ~ spl0_23 ),
inference(superposition,[],[f672,f627]) ).
fof(f697,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_15
| ~ spl0_23 ),
inference(superposition,[],[f126,f682]) ).
fof(f701,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f697,f373]) ).
fof(f703,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f701,f65]) ).
fof(f704,plain,
( identity = sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f703,f641]) ).
fof(f705,plain,
( sk_c8 = sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f704,f391]) ).
fof(f706,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15
| spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f705,f415]) ).
fof(f707,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_15
| spl0_19
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f706]) ).
fof(f708,plain,
( sk_c7 != multiply(sk_c1,sk_c8)
| ~ spl0_15
| spl0_20 ),
inference(forward_demodulation,[],[f427,f482]) ).
fof(f709,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f501,f641]) ).
fof(f710,plain,
( ~ spl0_23
| ~ spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f708,f425,f390,f626]) ).
fof(f711,plain,
( spl0_23
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f709,f390,f107,f73,f64,f626]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f67]) ).
cnf(s2,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f76]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f81]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f86]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f91]) ).
cnf(s6,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f96]) ).
cnf(s7,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f101]) ).
cnf(s8,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f102]) ).
cnf(s9,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f103]) ).
cnf(s10,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f104]) ).
cnf(s11,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f105]) ).
cnf(s12,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f110]) ).
cnf(s13,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f111]) ).
cnf(s14,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f112]) ).
cnf(s15,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f113]) ).
cnf(s16,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f114]) ).
cnf(s17,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f115]) ).
cnf(s18,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f116]) ).
cnf(s19,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s20,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s21,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f119]) ).
cnf(s22,plain,
spl0_5,
inference(sat_conversion,[],[f120]) ).
cnf(s24,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f315]) ).
cnf(s28,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f339]) ).
cnf(s29,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f350]) ).
cnf(s30,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f352]) ).
cnf(s34,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f370]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f406]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f432]) ).
cnf(s46,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f479]) ).
cnf(s48,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f486]) ).
cnf(s50,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19
| spl0_21 ),
inference(sat_conversion,[],[f527]) ).
cnf(s65,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f629]) ).
cnf(s73,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_15
| spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f707]) ).
cnf(s74,plain,
( ~ spl0_15
| spl0_20
| ~ spl0_23 ),
inference(sat_conversion,[],[f710]) ).
cnf(s75,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_15
| spl0_23 ),
inference(sat_conversion,[],[f711]) ).
cnf(s76,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s1,s22]) ).
cnf(s77,plain,
spl0_4,
inference(rat,[],[s24,s17,s18,s19,s20,s21,s22]) ).
cnf(s78,plain,
( spl0_7
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s28,s3,s4,s5,s6]) ).
cnf(s79,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s37,s11,s16]) ).
cnf(s80,plain,
( spl0_10
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s37,s10,s15]) ).
cnf(s81,plain,
( spl0_9
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s37,s9,s14]) ).
cnf(s82,plain,
( ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s37,s8,s13,s28,s81,s80,s79,s78]) ).
cnf(s83,plain,
~ spl0_3,
inference(rat,[],[s37,s2,s7,s12,s82]) ).
cnf(s84,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s50,s73,s65,s75,s46,s11,s16,s22,s77]) ).
cnf(s85,plain,
( spl0_10
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s50,s73,s65,s75,s46,s10,s15,s22,s77]) ).
cnf(s86,plain,
( spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s50,s65,s48,s75,s46,s9,s14,s84,s85,s22]) ).
cnf(s87,plain,
( ~ spl0_7
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s50,s65,s48,s75,s46,s8,s13,s34,s86,s85,s84,s22]) ).
cnf(s88,plain,
( ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s34,s3,s4,s5,s6,s87]) ).
cnf(s89,plain,
~ spl0_2,
inference(rat,[],[s50,s65,s48,s75,s85,s84,s46,s2,s7,s12,s88,s22]) ).
cnf(s90,plain,
spl0_1,
inference(rat,[],[s76,s77,s83,s89]) ).
cnf(s91,plain,
( spl0_9
| ~ spl0_7 ),
inference(rat,[],[s50,s39,s73,s74,s75,s46,s9,s14,s90,s22,s77]) ).
cnf(s92,plain,
( ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s50,s39,s73,s74,s75,s46,s8,s13,s29,s91,s90,s22,s77]) ).
cnf(s93,plain,
~ spl0_6,
inference(rat,[],[s30,s3,s4,s5,s6,s92,s90]) ).
cnf(s94,plain,
spl0_13,
inference(rat,[],[s12,s93]) ).
cnf(s95,plain,
spl0_12,
inference(rat,[],[s7,s93]) ).
cnf(s96,plain,
spl0_7,
inference(rat,[],[s2,s93]) ).
cnf(s97,plain,
spl0_15,
inference(rat,[],[s46,s94,s95]) ).
cnf(s99,plain,
spl0_23,
inference(rat,[],[s75,s94,s96,s22,s97]) ).
cnf(s100,plain,
spl0_20,
inference(rat,[],[s74,s97,s99]) ).
cnf(s101,plain,
spl0_19,
inference(rat,[],[s73,s97,s77,s22,s99]) ).
cnf(s102,plain,
~ spl0_21,
inference(rat,[],[s39,s95,s90,s100]) ).
cnf(s103,plain,
$false,
inference(rat,[],[s50,s94,s95,s96,s101,s102]) ).
fof(f712,plain,
$false,
inference(avatar_sat_refutation,[],[s103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP306-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:49:02 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.52/1.33 % (3746135)Input is clausal, will run a generic CNF schedule.
% 2.52/1.33 % (3746141)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1735281777:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.52/1.33 % (3746144)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2278946287:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.52/1.33 % (3746140)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=2871618093:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.52/1.33 % (3746142)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=100799505:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.52/1.33 % (3746145)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1431285685:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.52/1.33 % (3746143)lrs+10_1_sil=8000:sp=occurrence:random_seed=3461598079:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.52/1.33 % (3746146)dis-21_1_sil=8000:lcm=predicate:random_seed=1809122146: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)
% 2.52/1.33 % (3746146)Refutation not found, incomplete strategy
% 2.52/1.33 % (3746146)------------------------------
% 2.52/1.33 % (3746146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.33 % (3746146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.33 % (3746146)CaDiCaL version: 2.1.3
% 2.52/1.33 % (3746146)Termination reason: Refutation not found, incomplete strategy
% 2.52/1.33 % (3746146)Time elapsed: 0.002 s
% 2.52/1.33 % (3746146)Peak memory usage: 88 MB
% 2.52/1.33 % (3746146)Instructions burned: 1 (million)
% 2.52/1.33 % (3746143)Refutation not found, incomplete strategy
% 2.52/1.33 % (3746143)------------------------------
% 2.52/1.33 % (3746143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.33 % (3746143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.33 % (3746143)CaDiCaL version: 2.1.3
% 2.52/1.33 % (3746143)Termination reason: Refutation not found, incomplete strategy
% 2.52/1.33 % (3746143)Time elapsed: 0.003 s
% 2.52/1.33 % (3746143)Peak memory usage: 88 MB
% 2.52/1.33 % (3746143)Instructions burned: 4 (million)
% 2.52/1.33 % (3746145)First to succeed.
% 2.52/1.33 % (3746145)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3746135"
% 2.52/1.33 % (3746144)Instruction limit reached!
% 2.52/1.33 % (3746144)------------------------------
% 2.52/1.33 % (3746144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.33 % (3746144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.33 % (3746144)CaDiCaL version: 2.1.3
% 2.52/1.33 % (3746144)Termination reason: Instruction limit
% 2.52/1.33 % (3746144)Termination phase: Saturation
% 2.52/1.33 % (3746144)Time elapsed: 0.067 s
% 2.52/1.33 % (3746144)Peak memory usage: 89 MB
% 2.52/1.33 % (3746144)Instructions burned: 116 (million)
% 2.52/1.33 % (3746143)------------------------------
% 2.52/1.33 % (3746143)------------------------------
% 2.52/1.33 % (3746146)------------------------------
% 2.52/1.33 % (3746146)------------------------------
% 2.52/1.33 % (3746154)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=2790894576:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.52/1.33 % (3746154)Refutation not found, incomplete strategy
% 2.52/1.33 % (3746154)------------------------------
% 2.52/1.33 % (3746154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.33 % (3746154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.33 % (3746154)CaDiCaL version: 2.1.3
% 2.52/1.33 % (3746154)Termination reason: Refutation not found, incomplete strategy
% 2.52/1.33 % (3746154)Time elapsed: 0.006 s
% 2.52/1.33 % (3746154)Peak memory usage: 88 MB
% 2.52/1.33 % (3746154)Instructions burned: 9 (million)
% 2.52/1.33 % (3746145)Refutation found. Thanks to Tanya!
% 2.52/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.52/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.53 % (3746145)------------------------------
% 3.89/1.53 % (3746145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.53 % (3746145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.53 % (3746145)CaDiCaL version: 2.1.3
% 3.89/1.53 % (3746145)Termination reason: Refutation
% 3.89/1.53 % (3746145)Time elapsed: 0.018 s
% 3.89/1.53 % (3746145)Peak memory usage: 89 MB
% 3.89/1.53 % (3746145)Instructions burned: 26 (million)
% 3.89/1.53 % (3746145)------------------------------
% 3.89/1.53 % (3746145)------------------------------
% 3.89/1.53 % (3746135)Success in time 0.459 s
% 3.89/1.53 % Vampire exiting
%------------------------------------------------------------------------------