%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP241-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 10:17:16 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 55
% Syntax : Number of formulae : 279 ( 16 unt; 16 def)
% Number of atoms : 781 ( 287 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 879 ( 377 ~; 486 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c8) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = inverse(sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = inverse(sk_c7)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = inverse(sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| sk_c8 != inverse(sk_c7)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,X4)
| multiply(X5,sk_c8) != X4
| sk_c8 != inverse(X5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,plain,
! [X2,X3,X0,X4,X5] :
( inverse(sk_c8) != sk_c7
| sk_c8 != inverse(sk_c7)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,X4)
| multiply(X5,sk_c8) != X4
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f76]) ).
fof(f78,plain,
! [X2,X3,X0,X5] :
( inverse(sk_c8) != sk_c7
| sk_c8 != inverse(sk_c7)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f77]) ).
fof(f80,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f81,plain,
( ! [X5] :
( sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f84,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl0_3
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f87,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,definition,
( spl0_4
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( sk_c8 != inverse(sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f93,definition,
( spl0_5
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f95,plain,
( inverse(sk_c8) != sk_c7
| spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f78,f93,f89,f86,f80,f83,f80]) ).
fof(f98,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f100,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f102,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f104,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f74,f102,f98]) ).
fof(f107,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f109,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f72,f102,f107]) ).
fof(f112,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f114,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f70,f102,f112]) ).
fof(f117,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f119,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f68,f102,f117]) ).
fof(f122,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f124,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f66,f102,f122]) ).
fof(f127,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f129,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f64,f127,f98]) ).
fof(f131,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f62,f127,f107]) ).
fof(f132,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f60,f127,f112]) ).
fof(f133,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f58,f127,f117]) ).
fof(f134,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f56,f127,f122]) ).
fof(f136,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f138,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f54,f136,f98]) ).
fof(f140,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f136,f107]) ).
fof(f141,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f136,f112]) ).
fof(f142,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f136,f117]) ).
fof(f143,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f136,f122]) ).
fof(f145,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f147,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f145,f98]) ).
fof(f149,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f145,f107]) ).
fof(f150,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f145,f112]) ).
fof(f151,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f145,f117]) ).
fof(f152,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f145,f122]) ).
fof(f154,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f156,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f154,f98]) ).
fof(f158,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f154,f107]) ).
fof(f159,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f154,f112]) ).
fof(f160,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f154,f117]) ).
fof(f161,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f154,f122]) ).
fof(f162,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f24,f89,f98]) ).
fof(f163,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f22,f89,f107]) ).
fof(f164,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f20,f89,f112]) ).
fof(f165,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f18,f89,f117]) ).
fof(f166,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f16,f89,f122]) ).
fof(f167,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f93,f98]) ).
fof(f168,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f93,f107]) ).
fof(f169,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f93,f112]) ).
fof(f170,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f93,f117]) ).
fof(f171,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f93,f122]) ).
fof(f172,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f100]) ).
fof(f173,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f124]) ).
fof(f176,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f177,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c6,X0)) = multiply(sk_c7,X0)
| ~ spl0_9 ),
inference(superposition,[],[f4,f114]) ).
fof(f179,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f109]) ).
fof(f180,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f176,f1]) ).
fof(f183,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f172]) ).
fof(f184,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f183,f1]) ).
fof(f187,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f184,f109]) ).
fof(f190,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f187,f114]) ).
fof(f193,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f119,f190]) ).
fof(f194,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c6,X0)) = multiply(sk_c8,X0)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f177,f190]) ).
fof(f206,plain,
( multiply(sk_c6,sk_c4) = multiply(sk_c5,identity)
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f179,f173]) ).
fof(f243,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f180,f194]) ).
fof(f245,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f180,f173]) ).
fof(f247,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f180,f114]) ).
fof(f248,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_6 ),
inference(superposition,[],[f180,f172]) ).
fof(f261,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f247,f190]) ).
fof(f262,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f243,f180]) ).
fof(f276,plain,
( sk_c4 = sk_c5
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_demodulation,[],[f248,f245]) ).
fof(f280,plain,
( sk_c6 = multiply(sk_c4,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f109,f276]) ).
fof(f282,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f280,f193]) ).
fof(f291,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f261,f282]) ).
fof(f292,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f291,f3]) ).
fof(f301,plain,
( multiply(sk_c5,sk_c8) = multiply(sk_c6,sk_c4)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f206,f292]) ).
fof(f302,plain,
( sk_c4 = multiply(sk_c5,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f301,f262]) ).
fof(f303,plain,
( sk_c4 = multiply(sk_c4,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f302,f276]) ).
fof(f304,plain,
( sk_c8 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f303,f193]) ).
fof(f306,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f124,f304]) ).
fof(f342,plain,
( sk_c8 != sk_c7
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f95,f306]) ).
fof(f346,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f342,f190]) ).
fof(f347,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f346]) ).
fof(f350,plain,
( sk_c8 != inverse(sk_c8)
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f91,f190]) ).
fof(f352,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f350,f306]) ).
fof(f353,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f389,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c8)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f87,f190]) ).
fof(f390,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f389,f190]) ).
fof(f395,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f390,f3]) ).
fof(f413,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f395,f292]) ).
fof(f421,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f413,f306]) ).
fof(f424,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f421,f306]) ).
fof(f425,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f424]) ).
fof(f426,plain,
( ! [X5] :
( sk_c8 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f81,f190]) ).
fof(f435,plain,
( sk_c8 != multiply(sk_c8,sk_c6)
| sk_c8 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f426,f109]) ).
fof(f448,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f435,f187]) ).
fof(f458,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f448,f100]) ).
fof(f459,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f489,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f180,f129]) ).
fof(f491,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f489,f104]) ).
fof(f501,plain,
( sk_c7 != multiply(sk_c8,sk_c3)
| sk_c8 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f81,f129]) ).
fof(f506,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f501,f138]) ).
fof(f517,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f506,f104]) ).
fof(f518,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f517]) ).
fof(f524,plain,
( sk_c8 != sk_c8
| sk_c7 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f87,f156]) ).
fof(f525,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f524]) ).
fof(f527,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f525,f147]) ).
fof(f528,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f527]) ).
fof(f536,definition,
( spl0_19
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f538,plain,
( sk_c8 != sk_c7
| spl0_19 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f545,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f84,f119]) ).
fof(f546,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f84,f156]) ).
fof(f547,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f546]) ).
fof(f548,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f545]) ).
fof(f549,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f548,f124]) ).
fof(f550,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f549]) ).
fof(f562,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f547,f147]) ).
fof(f563,plain,
( ~ spl0_19
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f562,f154,f145,f83,f536]) ).
fof(f620,plain,
( sk_c8 = sk_c7
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f491,f138]) ).
fof(f629,plain,
( $false
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f620,f538]) ).
fof(f630,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f629]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f96]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f105]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f110]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f115]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f120]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f125]) ).
cnf(s8,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f130]) ).
cnf(s9,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f131]) ).
cnf(s10,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f132]) ).
cnf(s11,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s12,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f134]) ).
cnf(s13,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s14,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s15,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f141]) ).
cnf(s16,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f142]) ).
cnf(s17,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f143]) ).
cnf(s18,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f148]) ).
cnf(s19,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s20,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s21,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s22,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s23,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s24,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f158]) ).
cnf(s25,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f159]) ).
cnf(s26,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f160]) ).
cnf(s27,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s28,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f162]) ).
cnf(s29,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f163]) ).
cnf(s30,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f164]) ).
cnf(s31,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f165]) ).
cnf(s32,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f166]) ).
cnf(s33,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f167]) ).
cnf(s34,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s35,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f169]) ).
cnf(s36,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f170]) ).
cnf(s37,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f171]) ).
cnf(s38,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f347]) ).
cnf(s39,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f353]) ).
cnf(s53,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f425]) ).
cnf(s57,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f459]) ).
cnf(s66,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f518]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f528]) ).
cnf(s70,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f550]) ).
cnf(s73,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f563]) ).
cnf(s75,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f630]) ).
cnf(s76,plain,
spl0_4,
inference(rat,[],[s39,s28,s29,s30,s31,s32]) ).
cnf(s77,plain,
spl0_5,
inference(rat,[],[s38,s33,s34,s35,s36,s37]) ).
cnf(s79,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s67,s22,s27]) ).
cnf(s80,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s67,s21,s26]) ).
cnf(s81,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s67,s20,s25]) ).
cnf(s82,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s67,s19,s24]) ).
cnf(s83,plain,
( ~ spl0_8
| ~ spl0_11
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(rat,[],[s67,s18,s23,s53]) ).
cnf(s84,plain,
~ spl0_3,
inference(rat,[],[s83,s82,s81,s80,s79]) ).
cnf(s86,plain,
( spl0_11
| spl0_19 ),
inference(rat,[],[s75,s7,s12,s17]) ).
cnf(s87,plain,
( spl0_19
| ~ spl0_2 ),
inference(rat,[],[s75,s6,s11,s16,s70,s86]) ).
cnf(s88,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s70,s26,s27]) ).
cnf(s89,plain,
( ~ spl0_15
| ~ spl0_19
| ~ spl0_2 ),
inference(rat,[],[s70,s21,s22,s73]) ).
cnf(s90,plain,
~ spl0_2,
inference(rat,[],[s89,s88,s87]) ).
cnf(s91,plain,
spl0_1,
inference(rat,[],[s2,s76,s77,s84,s90]) ).
cnf(s95,plain,
spl0_8,
inference(rat,[],[s66,s4,s9,s14,s91]) ).
cnf(s96,plain,
spl0_6,
inference(rat,[],[s66,s3,s8,s13,s91]) ).
cnf(s97,plain,
spl0_9,
inference(rat,[],[s66,s5,s10,s15,s91]) ).
cnf(s98,plain,
$false,
inference(rat,[],[s57,s95,s91,s97,s96]) ).
fof(f631,plain,
$false,
inference(avatar_sat_refutation,[],[s98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP241-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n019.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:38:49 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.46 % (2840177)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (2840189)% WARNING: option uhcvi not known.
% 0.16/0.46 % (2840189)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2302185754:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (2840189) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2840177-2840189"...
% 0.16/0.46 % (2840191)dis+10_1_sil=32000:sp=arity:random_seed=2857639637:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (2840188)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2087455078_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (2840190)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=382674690:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (2840192)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=710533423:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (2840194)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1148166138:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (2840193)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3101654075:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (2840189)...printing done.
% 0.16/0.46 % (2840189)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (2840189)------------------------------
% 0.16/0.46 % (2840189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (2840189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (2840189)CaDiCaL version: 2.1.3
% 0.16/0.46 % (2840189)Termination reason: Refutation
% 0.16/0.46 % (2840189)Time elapsed: 0.008 s
% 0.16/0.46 % (2840189)Peak memory usage: 12 MB
% 0.16/0.46 % (2840189)Instructions burned: 21 (million)
% 0.16/0.46 % (2840177)Success in time 0.037 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------