%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP282-1 : 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 : n001.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 10:17:22 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 58
% Syntax : Number of formulae : 334 ( 24 unt; 22 def)
% Number of atoms : 1032 ( 330 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1292 ( 594 ~; 676 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 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,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c9) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c9 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = inverse(sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = inverse(sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f63,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = inverse(sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f79,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f81]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = inverse(sk_c9) ),
inference(reorient_equations,[],[f89]) ).
fof(f95,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f96,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f98,plain,
( sk_c9 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f97]) ).
fof(f101,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(sk_c9,X1) != sk_c8
| multiply(X2,sk_c9) != X1
| inverse(X2) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| inverse(sk_c9) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c7) != sk_c9
| multiply(X4,X5) != sk_c7
| inverse(X4) != X5
| multiply(X5,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,X1)
| multiply(X2,sk_c9) != X1
| sk_c9 != inverse(X2)
| sk_c7 != multiply(sk_c8,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c7)
| sk_c7 != inverse(sk_c9)
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c7)
| sk_c7 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c7 != multiply(X5,sk_c9) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,plain,
! [X2,X3,X0,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c7 != multiply(sk_c8,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c7)
| sk_c7 != inverse(sk_c9)
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c7)
| sk_c7 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c7 != multiply(X5,sk_c9) ),
inference(equality_resolution,[],[f102]) ).
fof(f104,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c9,sk_c8) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c7 != multiply(sk_c8,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c7)
| sk_c7 != inverse(sk_c9)
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c7)
| sk_c7 != multiply(X4,inverse(X4))
| sk_c7 != multiply(inverse(X4),sk_c9) ),
inference(equality_resolution,[],[f103]) ).
fof(f106,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(X4,inverse(X4))
| sk_c7 != multiply(inverse(X4),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f107,plain,
( ! [X4] :
( sk_c7 != multiply(inverse(X4),sk_c9)
| sk_c7 != multiply(X4,inverse(X4)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f110,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl0_3
<=> sk_c7 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f113,plain,
( sk_c7 = inverse(sk_c9)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( sk_c7 != inverse(sk_c9)
| spl0_3 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f116,definition,
( spl0_4
<=> sk_c9 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f117,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f118,plain,
( sk_c9 != multiply(sk_c8,sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f120,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c8,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f121,plain,
( sk_c7 = multiply(sk_c8,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( sk_c7 != multiply(sk_c8,sk_c9)
| spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f124,definition,
( spl0_6
<=> ! [X2] :
( sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f125,plain,
( ! [X2] :
( sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,definition,
( spl0_7
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f128,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,definition,
( spl0_8
<=> multiply(sk_c9,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f131,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f132,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| spl0_8 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f104,f130,f127,f124,f120,f116,f112,f109,f106]) ).
fof(f139,definition,
( spl0_10
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f141,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f144,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f146,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl0_11
| spl0_10 ),
inference(avatar_split_clause,[],[f98,f139,f144]) ).
fof(f149,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f151,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_12
| spl0_10 ),
inference(avatar_split_clause,[],[f96,f139,f149]) ).
fof(f154,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f156,plain,
( sk_c9 = multiply(sk_c4,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f159,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f161,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f163,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f90,f139,f112]) ).
fof(f164,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f88,f139,f116]) ).
fof(f165,plain,
( spl0_5
| spl0_10 ),
inference(avatar_split_clause,[],[f86,f139,f120]) ).
fof(f167,definition,
( spl0_15
<=> sk_c3 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f169,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f171,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f82,f167,f144]) ).
fof(f172,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f80,f167,f149]) ).
fof(f175,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f74,f167,f112]) ).
fof(f176,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f72,f167,f116]) ).
fof(f177,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f70,f167,f120]) ).
fof(f179,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c9,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f181,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f183,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f66,f179,f144]) ).
fof(f184,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f64,f179,f149]) ).
fof(f187,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f58,f179,f112]) ).
fof(f188,plain,
( spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f56,f179,f116]) ).
fof(f189,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f54,f179,f120]) ).
fof(f191,definition,
( spl0_17
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f193,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f195,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f50,f191,f144]) ).
fof(f196,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f48,f191,f149]) ).
fof(f199,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f42,f191,f112]) ).
fof(f200,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f40,f191,f116]) ).
fof(f201,plain,
( spl0_5
| spl0_17 ),
inference(avatar_split_clause,[],[f38,f191,f120]) ).
fof(f203,definition,
( spl0_18
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f207,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f34,f203,f144]) ).
fof(f208,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f203,f149]) ).
fof(f211,plain,
( spl0_3
| spl0_18 ),
inference(avatar_split_clause,[],[f26,f203,f112]) ).
fof(f212,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f24,f203,f116]) ).
fof(f213,plain,
( spl0_5
| spl0_18 ),
inference(avatar_split_clause,[],[f22,f203,f120]) ).
fof(f215,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f18,f130,f144]) ).
fof(f216,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f16,f130,f149]) ).
fof(f217,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f14,f130,f154]) ).
fof(f218,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f12,f130,f159]) ).
fof(f219,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f10,f130,f112]) ).
fof(f220,plain,
( spl0_4
| spl0_8 ),
inference(avatar_split_clause,[],[f8,f130,f116]) ).
fof(f221,plain,
( spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f6,f130,f120]) ).
fof(f222,plain,
( identity = multiply(sk_c7,sk_c9)
| ~ spl0_3 ),
inference(superposition,[],[f3,f113]) ).
fof(f227,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f228,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(sk_c9,X0)
| ~ spl0_4 ),
inference(superposition,[],[f4,f117]) ).
fof(f229,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c9,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f121]) ).
fof(f231,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f151]) ).
fof(f233,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f227,f1]) ).
fof(f275,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c8),multiply(sk_c9,X0))
| ~ spl0_4 ),
inference(superposition,[],[f233,f228]) ).
fof(f278,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_13 ),
inference(superposition,[],[f233,f156]) ).
fof(f280,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f233,f151]) ).
fof(f288,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f280,f146]) ).
fof(f290,plain,
( sk_c7 = multiply(sk_c9,sk_c9)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f278,f161]) ).
fof(f296,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c7,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f231,f288]) ).
fof(f299,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f296,f151]) ).
fof(f301,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c7,sk_c9)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f229,f290]) ).
fof(f302,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f233,f290]) ).
fof(f304,plain,
( sk_c9 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f302,f113]) ).
fof(f305,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f301,f222]) ).
fof(f307,plain,
( identity = sk_c9
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f305,f117]) ).
fof(f316,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f1,f307]) ).
fof(f327,plain,
( sk_c9 = sk_c7
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f304,f299]) ).
fof(f442,plain,
( sk_c8 != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f132,f316]) ).
fof(f448,plain,
( sk_c9 != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f442,f327]) ).
fof(f490,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c8),X0)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f275,f316]) ).
fof(f491,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c8),X0)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f490,f327]) ).
fof(f492,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = X0
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f491,f316]) ).
fof(f495,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f492,f3]) ).
fof(f504,plain,
( sk_c9 = sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f495,f307]) ).
fof(f507,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f504,f448]) ).
fof(f508,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f507]) ).
fof(f598,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_10 ),
inference(superposition,[],[f3,f141]) ).
fof(f603,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c7)
| ~ spl0_8 ),
inference(superposition,[],[f233,f131]) ).
fof(f605,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f603,f113]) ).
fof(f608,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f605,f299]) ).
fof(f611,plain,
( sk_c7 = multiply(sk_c9,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f131,f608]) ).
fof(f616,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_15 ),
inference(superposition,[],[f233,f169]) ).
fof(f618,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f616,f141]) ).
fof(f632,plain,
( ! [X2] :
( sk_c7 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f125,f608]) ).
fof(f637,plain,
( sk_c7 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f632,f121]) ).
fof(f649,definition,
( spl0_20
<=> sk_c7 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f650,plain,
( sk_c7 = multiply(sk_c9,sk_c7)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f654,definition,
( spl0_21
<=> sk_c9 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f656,plain,
( sk_c9 != inverse(sk_c7)
| spl0_21 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f662,plain,
( sk_c9 != inverse(sk_c7)
| sk_c7 != multiply(sk_c9,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f637,f608]) ).
fof(f677,plain,
( ~ spl0_20
| ~ spl0_21
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f662,f149,f144,f130,f124,f120,f112,f654,f649]) ).
fof(f688,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_18 ),
inference(superposition,[],[f233,f205]) ).
fof(f690,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f688,f193]) ).
fof(f693,plain,
( sk_c2 = multiply(inverse(sk_c9),identity)
| ~ spl0_10 ),
inference(superposition,[],[f233,f598]) ).
fof(f708,plain,
( sk_c8 != multiply(sk_c9,sk_c3)
| sk_c9 != inverse(sk_c2)
| ~ spl0_6
| ~ spl0_15 ),
inference(superposition,[],[f125,f169]) ).
fof(f709,plain,
( sk_c9 != inverse(sk_c2)
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f708,f181]) ).
fof(f740,plain,
( $false
| ~ spl0_6
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f709,f141]) ).
fof(f741,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f740]) ).
fof(f748,plain,
( spl0_20
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f611,f149,f144,f130,f112,f649]) ).
fof(f790,plain,
( sk_c7 != multiply(sk_c7,sk_c9)
| sk_c7 != multiply(sk_c9,sk_c7)
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f107,f113]) ).
fof(f822,definition,
( spl0_35
<=> sk_c9 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f823,plain,
( sk_c9 = sk_c7
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f824,plain,
( sk_c9 != sk_c7
| spl0_35 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f829,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f128,f608]) ).
fof(f834,plain,
( sk_c7 != sk_c7
| sk_c9 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f829,f121]) ).
fof(f841,plain,
( sk_c9 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f834]) ).
fof(f848,plain,
( sk_c9 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f841,f608]) ).
fof(f854,plain,
( ~ spl0_21
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f848,f149,f144,f130,f127,f120,f112,f654]) ).
fof(f858,definition,
( spl0_36
<=> sk_c9 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f859,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f875,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_35 ),
inference(superposition,[],[f299,f823]) ).
fof(f908,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c9) )
| ~ spl0_2
| ~ spl0_35 ),
inference(forward_demodulation,[],[f110,f823]) ).
fof(f909,plain,
( sk_c9 != sk_c7
| sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_35 ),
inference(superposition,[],[f908,f113]) ).
fof(f916,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f909,f823]) ).
fof(f922,definition,
( spl0_38
<=> sk_c9 = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f923,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f926,plain,
( ~ spl0_38
| ~ spl0_2
| ~ spl0_3
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f916,f822,f112,f109,f922]) ).
fof(f948,plain,
( sk_c9 != inverse(sk_c9)
| spl0_3
| ~ spl0_35 ),
inference(forward_demodulation,[],[f114,f823]) ).
fof(f959,plain,
( ~ spl0_36
| spl0_3
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f948,f822,f112,f858]) ).
fof(f999,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_20 ),
inference(superposition,[],[f229,f650]) ).
fof(f1003,plain,
( sk_c7 = multiply(sk_c8,sk_c7)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20 ),
inference(forward_demodulation,[],[f999,f299]) ).
fof(f1005,plain,
( sk_c9 = sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1003,f117]) ).
fof(f1007,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| spl0_35 ),
inference(forward_subsumption_resolution,[],[f1005,f824]) ).
fof(f1008,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| spl0_35 ),
inference(avatar_contradiction_clause,[],[f1007]) ).
fof(f1021,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_38 ),
inference(superposition,[],[f233,f923]) ).
fof(f1102,plain,
( sk_c9 = sk_c8
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f618,f181]) ).
fof(f1117,plain,
( sk_c9 = sk_c7
| ~ spl0_8
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f131,f690]) ).
fof(f1146,plain,
( spl0_35
| ~ spl0_8
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1117,f203,f191,f130,f822]) ).
fof(f1154,plain,
( spl0_38
| ~ spl0_11
| ~ spl0_12
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f875,f822,f149,f144,f922]) ).
fof(f1165,plain,
( sk_c9 != inverse(sk_c9)
| spl0_21
| ~ spl0_35 ),
inference(superposition,[],[f656,f823]) ).
fof(f1166,plain,
( ~ spl0_36
| spl0_21
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1165,f822,f654,f858]) ).
fof(f1353,plain,
( identity = sk_c9
| ~ spl0_38 ),
inference(superposition,[],[f1021,f3]) ).
fof(f1386,plain,
( sk_c2 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_10
| ~ spl0_38 ),
inference(superposition,[],[f693,f1353]) ).
fof(f1391,plain,
( sk_c9 = sk_c2
| ~ spl0_10
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1386,f1021]) ).
fof(f1434,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_10
| ~ spl0_38 ),
inference(superposition,[],[f141,f1391]) ).
fof(f1480,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f690,f1102]) ).
fof(f1509,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| sk_c7 != multiply(sk_c9,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_35 ),
inference(forward_demodulation,[],[f790,f823]) ).
fof(f1517,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_3
| ~ spl0_35 ),
inference(forward_demodulation,[],[f113,f823]) ).
fof(f1566,plain,
( spl0_36
| ~ spl0_10
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1434,f922,f139,f858]) ).
fof(f1572,plain,
( spl0_38
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1480,f203,f191,f179,f167,f139,f922]) ).
fof(f1576,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1509,f823]) ).
fof(f1577,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_35 ),
inference(duplicate_literal_removal,[],[f1576]) ).
fof(f1584,plain,
( spl0_36
| ~ spl0_3
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1517,f822,f112,f858]) ).
fof(f1604,plain,
( ~ spl0_38
| ~ spl0_1
| ~ spl0_3
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1577,f822,f112,f106,f922]) ).
fof(f1636,plain,
( ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c9) )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f128,f1102]) ).
fof(f1647,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_36 ),
inference(superposition,[],[f1636,f859]) ).
fof(f1650,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_36 ),
inference(trivial_inequality_removal,[],[f1647]) ).
fof(f1651,plain,
( ~ spl0_38
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f1650,f858,f179,f167,f139,f127,f922]) ).
fof(f1655,plain,
( sk_c9 != multiply(sk_c8,sk_c9)
| spl0_4
| ~ spl0_35 ),
inference(forward_demodulation,[],[f118,f823]) ).
fof(f1664,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| spl0_4
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1655,f1102]) ).
fof(f1668,plain,
( ~ spl0_38
| spl0_4
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1664,f822,f179,f167,f139,f116,f922]) ).
fof(f1691,plain,
( sk_c7 != multiply(sk_c9,sk_c9)
| spl0_5
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f122,f1102]) ).
fof(f1709,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| spl0_5
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1691,f823]) ).
fof(f1717,plain,
( ~ spl0_38
| spl0_5
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1709,f822,f179,f167,f139,f120,f922]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f133]) ).
cnf(s3,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f147]) ).
cnf(s4,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f152]) ).
cnf(s7,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f163]) ).
cnf(s8,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f164]) ).
cnf(s9,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f165]) ).
cnf(s11,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f171]) ).
cnf(s12,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f172]) ).
cnf(s15,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f175]) ).
cnf(s16,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f176]) ).
cnf(s17,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f177]) ).
cnf(s19,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f183]) ).
cnf(s20,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f184]) ).
cnf(s23,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f187]) ).
cnf(s24,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f188]) ).
cnf(s25,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f189]) ).
cnf(s27,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f195]) ).
cnf(s28,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f196]) ).
cnf(s31,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f199]) ).
cnf(s32,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f200]) ).
cnf(s33,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s35,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f207]) ).
cnf(s36,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f208]) ).
cnf(s39,plain,
( spl0_3
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s40,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s41,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s43,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f215]) ).
cnf(s44,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f216]) ).
cnf(s45,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f217]) ).
cnf(s46,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f218]) ).
cnf(s47,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f219]) ).
cnf(s48,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f220]) ).
cnf(s49,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f221]) ).
cnf(s51,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f508]) ).
cnf(s68,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f677]) ).
cnf(s76,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f741]) ).
cnf(s77,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f748]) ).
cnf(s92,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21 ),
inference(sat_conversion,[],[f854]) ).
cnf(s102,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_35
| ~ spl0_38 ),
inference(sat_conversion,[],[f926]) ).
cnf(s108,plain,
( spl0_3
| ~ spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f959]) ).
cnf(s114,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| spl0_35 ),
inference(sat_conversion,[],[f1008]) ).
cnf(s128,plain,
( ~ spl0_8
| ~ spl0_17
| ~ spl0_18
| spl0_35 ),
inference(sat_conversion,[],[f1146]) ).
cnf(s138,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_35
| spl0_38 ),
inference(sat_conversion,[],[f1154]) ).
cnf(s139,plain,
( spl0_21
| ~ spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f1166]) ).
cnf(s167,plain,
( ~ spl0_10
| spl0_36
| ~ spl0_38 ),
inference(sat_conversion,[],[f1566]) ).
cnf(s170,plain,
( ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_38 ),
inference(sat_conversion,[],[f1572]) ).
cnf(s175,plain,
( ~ spl0_3
| ~ spl0_35
| spl0_36 ),
inference(sat_conversion,[],[f1584]) ).
cnf(s184,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_35
| ~ spl0_38 ),
inference(sat_conversion,[],[f1604]) ).
cnf(s198,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_36
| ~ spl0_38 ),
inference(sat_conversion,[],[f1651]) ).
cnf(s200,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_35
| ~ spl0_38 ),
inference(sat_conversion,[],[f1668]) ).
cnf(s212,plain,
( spl0_5
| ~ spl0_10
| ~ spl0_15
| ~ spl0_16
| ~ spl0_35
| ~ spl0_38 ),
inference(sat_conversion,[],[f1717]) ).
cnf(s215,plain,
spl0_3,
inference(rat,[],[s108,s167,s170,s128,s7,s15,s23,s31,s39,s47]) ).
cnf(s216,plain,
( spl0_8
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s51,s43,s44,s45,s46,s215]) ).
cnf(s217,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_7
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s139,s175,s114,s77,s92,s216,s215]) ).
cnf(s218,plain,
( spl0_12
| ~ spl0_7 ),
inference(rat,[],[s198,s167,s170,s4,s12,s20,s28,s36]) ).
cnf(s219,plain,
( ~ spl0_12
| ~ spl0_7
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s198,s167,s170,s3,s11,s19,s27,s35,s217]) ).
cnf(s220,plain,
( ~ spl0_7
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s219,s218]) ).
cnf(s221,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_6
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s139,s175,s68,s114,s77,s216,s215]) ).
cnf(s222,plain,
( spl0_11
| ~ spl0_6 ),
inference(rat,[],[s76,s3,s11,s19]) ).
cnf(s223,plain,
( ~ spl0_11
| ~ spl0_6
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s76,s4,s12,s20,s221]) ).
cnf(s224,plain,
( spl0_7
| ~ spl0_8
| spl0_1
| ~ spl0_4
| ~ spl0_5
| spl0_2 ),
inference(rat,[],[s223,s222,s1,s215]) ).
cnf(s226,plain,
spl0_5,
inference(rat,[],[s212,s170,s128,s9,s17,s25,s33,s41,s49]) ).
cnf(s227,plain,
spl0_4,
inference(rat,[],[s200,s170,s128,s8,s16,s24,s32,s40,s48]) ).
cnf(s228,plain,
spl0_8,
inference(rat,[],[s216,s226,s227]) ).
cnf(s229,plain,
~ spl0_7,
inference(rat,[],[s220,s226,s227]) ).
cnf(s230,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s102,s138,s114,s77,s215,s227,s226,s228]) ).
cnf(s231,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s102,s170,s128,s4,s12,s20,s28,s36,s215,s228]) ).
cnf(s232,plain,
( ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s102,s170,s128,s3,s11,s19,s27,s35,s230,s228,s215]) ).
cnf(s233,plain,
~ spl0_2,
inference(rat,[],[s232,s231]) ).
cnf(s234,plain,
spl0_1,
inference(rat,[],[s224,s233,s226,s227,s228,s229]) ).
cnf(s235,plain,
( ~ spl0_12
| ~ spl0_35
| ~ spl0_11 ),
inference(rat,[],[s184,s138,s234,s215]) ).
cnf(s236,plain,
( ~ spl0_12
| ~ spl0_20
| ~ spl0_11 ),
inference(rat,[],[s235,s114,s226,s227]) ).
cnf(s237,plain,
( ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s236,s77,s228,s215]) ).
cnf(s238,plain,
spl0_12,
inference(rat,[],[s184,s170,s128,s4,s12,s20,s28,s36,s215,s234,s228]) ).
cnf(s239,plain,
~ spl0_11,
inference(rat,[],[s237,s238]) ).
cnf(s240,plain,
spl0_18,
inference(rat,[],[s35,s239]) ).
cnf(s241,plain,
spl0_17,
inference(rat,[],[s27,s239]) ).
cnf(s242,plain,
spl0_16,
inference(rat,[],[s19,s239]) ).
cnf(s243,plain,
spl0_15,
inference(rat,[],[s11,s239]) ).
cnf(s244,plain,
spl0_10,
inference(rat,[],[s3,s239]) ).
cnf(s246,plain,
spl0_35,
inference(rat,[],[s128,s240,s228,s241]) ).
cnf(s247,plain,
spl0_38,
inference(rat,[],[s170,s242,s240,s241,s244,s243]) ).
cnf(s253,plain,
$false,
inference(rat,[],[s184,s234,s215,s247,s246]) ).
fof(f1719,plain,
$false,
inference(avatar_sat_refutation,[],[s253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP282-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n001.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 09:50:45 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.19/0.47 % (3310295)Will run a generic schedule for satisfiability detection.
% 0.19/0.47 % (3310304)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=668975224:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.47 % (3310300)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=583844750_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.47 % (3310302)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3298433030:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.47 % (3310303)dis+10_1_sil=32000:sp=arity:random_seed=82771003:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.47 % (3310305)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3568644720:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.47 % (3310306)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=184575168:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.47 % (3310301)% WARNING: option uhcvi not known.
% 0.19/0.47 % (3310301)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3307174004:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.47 % TRYING [1]
% 0.19/0.47 % TRYING [2]
% 0.19/0.47 % TRYING [3]
% 0.19/0.47 % TRYING [4]
% 0.19/0.47 % TRYING [5]
% 0.19/0.47 % (3310301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3310295-3310301"...
% 0.19/0.47 % (3310301)...printing done.
% 0.19/0.47 % (3310301)Refutation found. Thanks to Tanya!
% 0.19/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47 % (3310301)------------------------------
% 0.19/0.47 % (3310301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.47 % (3310301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.47 % (3310301)CaDiCaL version: 2.1.3
% 0.19/0.47 % (3310301)Termination reason: Refutation
% 0.19/0.47 % (3310301)Time elapsed: 0.019 s
% 0.19/0.47 % (3310301)Peak memory usage: 13 MB
% 0.19/0.47 % (3310301)Instructions burned: 57 (million)
% 0.19/0.47 % (3310295)Success in time 0.058 s
% 0.19/0.47 % Vampire exiting
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