%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP217-1 : 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 : n016.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 10:17:12 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 72
% Syntax : Number of formulae : 462 ( 21 unt; 31 def)
% Number of atoms : 1420 ( 439 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1814 ( 856 ~; 927 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 32 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 82 !; 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_c1) = sk_c11
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c1) = sk_c11
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c1) = sk_c11
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c1) = sk_c11
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( inverse(sk_c1) = sk_c11
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f21]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c3 = inverse(sk_c2)
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = inverse(sk_c2)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = inverse(sk_c2)
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = inverse(sk_c2)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f55]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c11,sk_c5) = sk_c10
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c5
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c6,sk_c7) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
( sk_c11 = inverse(sk_c4)
| sk_c11 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f92,plain,
( sk_c11 = inverse(sk_c4)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c7,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f94,plain,
( sk_c11 = inverse(sk_c4)
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f96,plain,
( sk_c11 = inverse(sk_c4)
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f98,plain,
( sk_c11 = inverse(sk_c4)
| sk_c9 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f100,plain,
( sk_c11 = inverse(sk_c4)
| sk_c11 = inverse(sk_c8) ),
inference(reorient_equations,[],[f99]) ).
fof(f101,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c11) != sk_c10
| multiply(sk_c11,X3) != sk_c10
| multiply(X4,sk_c11) != X3
| inverse(X4) != sk_c11
| multiply(X5,X6) != sk_c11
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c11
| multiply(sk_c11,X7) != sk_c10
| multiply(X8,sk_c11) != X7
| inverse(X8) != sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| sk_c10 != multiply(X2,sk_c11)
| sk_c10 != multiply(sk_c11,X3)
| multiply(X4,sk_c11) != X3
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c11 != multiply(X6,sk_c10)
| sk_c10 != multiply(sk_c11,X7)
| multiply(X8,sk_c11) != X7
| sk_c11 != inverse(X8) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,plain,
! [X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(sk_c11,X3)
| multiply(X4,sk_c11) != X3
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c11 != multiply(X6,sk_c10)
| sk_c10 != multiply(sk_c11,X7)
| multiply(X8,sk_c11) != X7
| sk_c11 != inverse(X8) ),
inference(equality_resolution,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X8,X6,X7,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(sk_c11,multiply(X4,sk_c11))
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c11 != multiply(X6,sk_c10)
| sk_c10 != multiply(sk_c11,X7)
| multiply(X8,sk_c11) != X7
| sk_c11 != inverse(X8) ),
inference(equality_resolution,[],[f103]) ).
fof(f105,plain,
! [X0,X1,X8,X7,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(sk_c11,multiply(X4,sk_c11))
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,inverse(X5))
| sk_c11 != multiply(inverse(X5),sk_c10)
| sk_c10 != multiply(sk_c11,X7)
| multiply(X8,sk_c11) != X7
| sk_c11 != inverse(X8) ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X8,X4,X5] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(sk_c11,multiply(X4,sk_c11))
| sk_c11 != inverse(X4)
| sk_c11 != multiply(X5,inverse(X5))
| sk_c11 != multiply(inverse(X5),sk_c10)
| sk_c10 != multiply(sk_c11,multiply(X8,sk_c11))
| sk_c11 != inverse(X8) ),
inference(equality_resolution,[],[f105]) ).
fof(f108,definition,
( spl0_1
<=> ! [X8] :
( sk_c10 != multiply(sk_c11,multiply(X8,sk_c11))
| sk_c11 != inverse(X8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f109,plain,
( ! [X8] :
( sk_c10 != multiply(sk_c11,multiply(X8,sk_c11))
| sk_c11 != inverse(X8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_2
<=> ! [X5] :
( sk_c11 != multiply(X5,inverse(X5))
| sk_c11 != multiply(inverse(X5),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f112,plain,
( ! [X5] :
( sk_c11 != multiply(inverse(X5),sk_c10)
| sk_c11 != multiply(X5,inverse(X5)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_3
<=> ! [X1] :
( sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f115,plain,
( ! [X1] :
( sk_c10 != multiply(inverse(X1),sk_c11)
| sk_c10 != multiply(X1,inverse(X1)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_4
<=> ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f106,f117,f114,f108,f111,f108]) ).
fof(f121,definition,
( spl0_5
<=> sk_c11 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f123,plain,
( sk_c11 = inverse(sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl0_6
<=> sk_c11 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f127,plain,
( sk_c11 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f100,f125,f121]) ).
fof(f130,definition,
( spl0_7
<=> sk_c9 = multiply(sk_c8,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f132,plain,
( sk_c9 = multiply(sk_c8,sk_c11)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f98,f125,f130]) ).
fof(f135,definition,
( spl0_8
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f137,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f96,f125,f135]) ).
fof(f140,definition,
( spl0_9
<=> sk_c11 = multiply(sk_c7,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f142,plain,
( sk_c11 = multiply(sk_c7,sk_c10)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f94,f125,f140]) ).
fof(f145,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f147,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f92,f125,f145]) ).
fof(f150,definition,
( spl0_11
<=> sk_c11 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f152,plain,
( sk_c11 = multiply(sk_c6,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f90,f125,f150]) ).
fof(f155,definition,
( spl0_12
<=> sk_c5 = multiply(sk_c4,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f156,plain,
( sk_c5 != multiply(sk_c4,sk_c11)
| spl0_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( sk_c5 = multiply(sk_c4,sk_c11)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( spl0_5
| spl0_12 ),
inference(avatar_split_clause,[],[f88,f155,f121]) ).
fof(f159,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f86,f155,f130]) ).
fof(f160,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f84,f155,f135]) ).
fof(f161,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f82,f155,f140]) ).
fof(f162,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f80,f155,f145]) ).
fof(f163,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f78,f155,f150]) ).
fof(f165,definition,
( spl0_13
<=> sk_c10 = multiply(sk_c11,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f167,plain,
( sk_c10 = multiply(sk_c11,sk_c5)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f76,f165,f121]) ).
fof(f169,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f74,f165,f130]) ).
fof(f170,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f72,f165,f135]) ).
fof(f171,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f70,f165,f140]) ).
fof(f172,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f68,f165,f145]) ).
fof(f173,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f66,f165,f150]) ).
fof(f175,definition,
( spl0_14
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f177,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f175,f121]) ).
fof(f182,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f56,f175,f145]) ).
fof(f183,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f54,f175,f150]) ).
fof(f185,definition,
( spl0_15
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f187,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f52,f185,f121]) ).
fof(f189,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f50,f185,f130]) ).
fof(f190,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f48,f185,f135]) ).
fof(f191,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f46,f185,f140]) ).
fof(f192,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f44,f185,f145]) ).
fof(f193,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f42,f185,f150]) ).
fof(f195,definition,
( spl0_16
<=> sk_c10 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f197,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f40,f195,f121]) ).
fof(f201,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f34,f195,f140]) ).
fof(f202,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f32,f195,f145]) ).
fof(f203,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f30,f195,f150]) ).
fof(f205,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f207,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f208,plain,
( spl0_5
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f205,f121]) ).
fof(f211,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f22,f205,f140]) ).
fof(f215,definition,
( spl0_18
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f217,plain,
( inverse(sk_c1) = sk_c11
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( spl0_5
| spl0_18 ),
inference(avatar_split_clause,[],[f16,f215,f121]) ).
fof(f221,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f215,f140]) ).
fof(f222,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f215,f145]) ).
fof(f223,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f215,f150]) ).
fof(f225,plain,
( sk_c11 != multiply(sk_c7,sk_c10)
| sk_c11 != multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f112,f147]) ).
fof(f231,definition,
( spl0_19
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f232,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f233,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| spl0_19 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f235,definition,
( spl0_20
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f239,plain,
( sk_c11 != multiply(sk_c7,sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f225,f152]) ).
fof(f240,plain,
( ~ spl0_9
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f239,f150,f145,f111,f140]) ).
fof(f247,plain,
( sk_c11 != multiply(sk_c3,sk_c10)
| sk_c11 != multiply(sk_c2,sk_c3)
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f112,f187]) ).
fof(f249,definition,
( spl0_22
<=> sk_c11 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f250,plain,
( sk_c11 = multiply(sk_c2,sk_c3)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( sk_c11 != multiply(sk_c2,sk_c3)
| spl0_22 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f253,definition,
( spl0_23
<=> sk_c11 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f255,plain,
( sk_c11 != multiply(sk_c3,sk_c10)
| spl0_23 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( ~ spl0_22
| ~ spl0_23
| ~ spl0_2
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f247,f185,f111,f253,f249]) ).
fof(f257,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[],[f112,f217]) ).
fof(f259,definition,
( spl0_24
<=> sk_c11 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f260,plain,
( sk_c11 = multiply(sk_c1,sk_c11)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f263,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f217]) ).
fof(f264,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f3,f147]) ).
fof(f265,plain,
( identity = multiply(sk_c11,sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f3,f123]) ).
fof(f266,plain,
( identity = multiply(sk_c3,sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f3,f187]) ).
fof(f267,plain,
( identity = multiply(sk_c11,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f127]) ).
fof(f274,definition,
( spl0_26
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f275,plain,
( identity = sk_c11
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f278,plain,
( sk_c11 != sk_c10
| ~ spl0_16
| spl0_22 ),
inference(forward_demodulation,[],[f251,f197]) ).
fof(f281,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f285,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f152]) ).
fof(f289,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c11,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f157]) ).
fof(f290,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f281,f1]) ).
fof(f293,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c1,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f263]) ).
fof(f294,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c1,X0)) = X0
| ~ spl0_18 ),
inference(forward_demodulation,[],[f293,f1]) ).
fof(f295,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f264]) ).
fof(f296,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f295,f1]) ).
fof(f297,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c8,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f265]) ).
fof(f298,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c8,X0)) = X0
| ~ spl0_5 ),
inference(forward_demodulation,[],[f297,f1]) ).
fof(f299,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c3,multiply(sk_c2,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f266]) ).
fof(f300,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c2,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f299,f1]) ).
fof(f306,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f294,f207]) ).
fof(f317,plain,
( sk_c7 = multiply(sk_c7,sk_c11)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f296,f152]) ).
fof(f326,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c11,sk_c11)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f285,f317]) ).
fof(f328,plain,
( multiply(sk_c6,sk_c7) = sk_c10
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f326,f306]) ).
fof(f329,plain,
( sk_c11 = sk_c10
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f328,f152]) ).
fof(f332,plain,
( sk_c11 = sk_c10
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f250,f197]) ).
fof(f338,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_16
| spl0_19
| ~ spl0_22 ),
inference(superposition,[],[f233,f332]) ).
fof(f341,plain,
( sk_c11 != sk_c10
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_22 ),
inference(forward_demodulation,[],[f338,f306]) ).
fof(f344,plain,
( $false
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f341,f332]) ).
fof(f345,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f344]) ).
fof(f346,plain,
( ! [X8] :
( sk_c11 != multiply(sk_c11,multiply(X8,sk_c11))
| sk_c11 != inverse(X8) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f109,f332]) ).
fof(f356,plain,
( sk_c11 != sk_c11
| inverse(sk_c1) != sk_c11
| ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| ~ spl0_22 ),
inference(superposition,[],[f346,f294]) ).
fof(f359,plain,
( inverse(sk_c1) != sk_c11
| ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f356]) ).
fof(f362,plain,
( $false
| ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f359,f217]) ).
fof(f363,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f430,plain,
( ! [X0] :
( sk_c11 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11 )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f118,f332]) ).
fof(f436,plain,
( sk_c11 != sk_c9
| sk_c11 != inverse(sk_c8)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f430,f132]) ).
fof(f438,plain,
( sk_c11 != sk_c5
| sk_c11 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_12
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f430,f157]) ).
fof(f440,plain,
( sk_c11 != sk_c5
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f438,f127]) ).
fof(f444,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_16
| ~ spl0_22
| spl0_23 ),
inference(forward_demodulation,[],[f255,f332]) ).
fof(f445,plain,
( sk_c11 != sk_c10
| ~ spl0_14
| ~ spl0_16
| ~ spl0_22
| spl0_23 ),
inference(forward_demodulation,[],[f444,f177]) ).
fof(f446,plain,
( $false
| ~ spl0_14
| ~ spl0_16
| ~ spl0_22
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f445,f332]) ).
fof(f447,plain,
( ~ spl0_14
| ~ spl0_16
| ~ spl0_22
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f446]) ).
fof(f459,plain,
( sk_c10 != multiply(sk_c3,sk_c11)
| sk_c10 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f115,f187]) ).
fof(f461,plain,
( identity != sk_c10
| sk_c10 != multiply(sk_c11,inverse(sk_c11))
| ~ spl0_3 ),
inference(superposition,[],[f115,f3]) ).
fof(f467,definition,
( spl0_33
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f468,plain,
( identity = sk_c10
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f479,definition,
( spl0_35
<=> sk_c10 = multiply(sk_c7,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f480,plain,
( sk_c10 = multiply(sk_c7,sk_c11)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f481,plain,
( sk_c10 != multiply(sk_c7,sk_c11)
| spl0_35 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f489,plain,
( ~ spl0_16
| ~ spl0_14
| ~ spl0_3
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f459,f185,f114,f175,f195]) ).
fof(f497,plain,
( sk_c11 = multiply(sk_c1,sk_c11)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f207,f329]) ).
fof(f503,plain,
( spl0_24
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f497,f215,f205,f150,f145,f259]) ).
fof(f504,plain,
( ! [X8] :
( sk_c11 != multiply(sk_c11,multiply(X8,sk_c11))
| sk_c11 != inverse(X8) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f109,f329]) ).
fof(f511,plain,
( sk_c11 != sk_c11
| inverse(sk_c1) != sk_c11
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f504,f294]) ).
fof(f514,plain,
( inverse(sk_c1) != sk_c11
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f511]) ).
fof(f517,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f514,f217]) ).
fof(f518,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f517]) ).
fof(f554,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| ~ spl0_2
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f257,f260]) ).
fof(f560,plain,
( ~ spl0_19
| ~ spl0_2
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f554,f259,f215,f111,f231]) ).
fof(f590,plain,
( sk_c11 = multiply(sk_c11,sk_c9)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f298,f132]) ).
fof(f608,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f590,f137]) ).
fof(f619,plain,
( sk_c3 = multiply(sk_c3,sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f300,f197]) ).
fof(f705,plain,
( sk_c10 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f290,f619]) ).
fof(f707,plain,
( sk_c11 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f290,f157]) ).
fof(f712,plain,
( sk_c11 = multiply(sk_c11,sk_c5)
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f707,f127]) ).
fof(f713,plain,
( identity = sk_c10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f705,f3]) ).
fof(f720,plain,
( spl0_33
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f713,f195,f185,f467]) ).
fof(f758,plain,
( sk_c11 = sk_c10
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f712,f167]) ).
fof(f759,plain,
( sk_c11 = sk_c10
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f167,f712]) ).
fof(f771,plain,
( $false
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f758,f278]) ).
fof(f772,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f771]) ).
fof(f777,definition,
( spl0_37
<=> sk_c11 = multiply(sk_c11,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f778,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f794,plain,
( identity = sk_c11
| ~ spl0_16
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f332,f468]) ).
fof(f797,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_33 ),
inference(forward_demodulation,[],[f759,f468]) ).
fof(f835,definition,
( spl0_41
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f836,plain,
( identity = sk_c5
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f840,plain,
( spl0_26
| ~ spl0_16
| ~ spl0_22
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f794,f467,f249,f195,f274]) ).
fof(f842,plain,
( spl0_26
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f797,f467,f165,f155,f125,f274]) ).
fof(f852,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_8
| ~ spl0_26 ),
inference(superposition,[],[f137,f275]) ).
fof(f854,plain,
( sk_c10 = multiply(identity,sk_c5)
| ~ spl0_13
| ~ spl0_26 ),
inference(superposition,[],[f167,f275]) ).
fof(f856,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f267,f275]) ).
fof(f864,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_26 ),
inference(superposition,[],[f712,f275]) ).
fof(f865,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_26 ),
inference(forward_demodulation,[],[f864,f1]) ).
fof(f874,plain,
( identity = sk_c4
| ~ spl0_6
| ~ spl0_26 ),
inference(forward_demodulation,[],[f856,f1]) ).
fof(f876,plain,
( sk_c10 = sk_c5
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f854,f1]) ).
fof(f877,plain,
( sk_c10 = sk_c9
| ~ spl0_8
| ~ spl0_26 ),
inference(forward_demodulation,[],[f852,f1]) ).
fof(f878,plain,
( spl0_41
| ~ spl0_6
| ~ spl0_12
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f865,f274,f155,f125,f835]) ).
fof(f881,plain,
( identity = sk_c5
| ~ spl0_13
| ~ spl0_26
| ~ spl0_33 ),
inference(forward_demodulation,[],[f876,f468]) ).
fof(f885,plain,
( spl0_41
| ~ spl0_13
| ~ spl0_26
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f881,f467,f274,f165,f835]) ).
fof(f891,plain,
( identity = inverse(sk_c8)
| ~ spl0_5
| ~ spl0_26 ),
inference(forward_demodulation,[],[f123,f275]) ).
fof(f917,plain,
( sk_c10 != multiply(identity,inverse(identity))
| identity != sk_c10
| ~ spl0_3
| ~ spl0_26 ),
inference(forward_demodulation,[],[f461,f275]) ).
fof(f924,plain,
( identity = sk_c10
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_26 ),
inference(forward_demodulation,[],[f759,f275]) ).
fof(f928,plain,
( identity = multiply(identity,sk_c10)
| ~ spl0_19
| ~ spl0_26 ),
inference(forward_demodulation,[],[f232,f275]) ).
fof(f935,plain,
( sk_c10 != inverse(identity)
| identity != sk_c10
| ~ spl0_3
| ~ spl0_26 ),
inference(forward_demodulation,[],[f917,f1]) ).
fof(f939,plain,
( spl0_33
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f924,f274,f165,f155,f125,f467]) ).
fof(f941,plain,
( identity = sk_c10
| ~ spl0_19
| ~ spl0_26 ),
inference(forward_demodulation,[],[f928,f1]) ).
fof(f948,definition,
( spl0_43
<=> sk_c10 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f949,plain,
( sk_c10 = inverse(identity)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f950,plain,
( sk_c10 != inverse(identity)
| spl0_43 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f951,plain,
( ~ spl0_33
| ~ spl0_43
| ~ spl0_3
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f935,f274,f114,f948,f467]) ).
fof(f954,plain,
( spl0_33
| ~ spl0_19
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f941,f274,f231,f467]) ).
fof(f992,definition,
( spl0_50
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f993,plain,
( sk_c11 = sk_c10
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f1000,plain,
( identity = multiply(sk_c11,sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f3,f123]) ).
fof(f1007,plain,
( sk_c10 != multiply(sk_c7,sk_c11)
| multiply(sk_c6,sk_c7) != sk_c10
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f115,f147]) ).
fof(f1013,plain,
( sk_c11 != sk_c10
| sk_c10 != multiply(sk_c7,sk_c11)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1007,f152]) ).
fof(f1017,plain,
( ~ spl0_35
| ~ spl0_50
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f1013,f150,f145,f114,f992,f479]) ).
fof(f1047,plain,
( sk_c11 = multiply(sk_c7,sk_c11)
| ~ spl0_9
| ~ spl0_50 ),
inference(superposition,[],[f142,f993]) ).
fof(f1067,plain,
( sk_c11 != multiply(sk_c7,sk_c11)
| spl0_35
| ~ spl0_50 ),
inference(forward_demodulation,[],[f481,f993]) ).
fof(f1077,plain,
( multiply(sk_c4,identity) = multiply(sk_c5,sk_c8)
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f289,f1000]) ).
fof(f1082,plain,
( multiply(sk_c4,identity) = multiply(identity,sk_c8)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1077,f836]) ).
fof(f1083,plain,
( sk_c8 = multiply(sk_c4,identity)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1082,f1]) ).
fof(f1091,definition,
( spl0_51
<=> sk_c11 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f1092,plain,
( sk_c11 = sk_c7
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f1096,plain,
( identity != sk_c11
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_16
| ~ spl0_22
| ~ spl0_41 ),
inference(forward_demodulation,[],[f440,f836]) ).
fof(f1106,plain,
( $false
| ~ spl0_9
| spl0_35
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f1047,f1067]) ).
fof(f1107,plain,
( ~ spl0_9
| spl0_35
| ~ spl0_50 ),
inference(avatar_contradiction_clause,[],[f1106]) ).
fof(f1108,plain,
( sk_c11 = multiply(sk_c7,sk_c11)
| ~ spl0_35
| ~ spl0_50 ),
inference(forward_demodulation,[],[f480,f993]) ).
fof(f1157,plain,
( sk_c11 = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_35
| ~ spl0_50 ),
inference(forward_demodulation,[],[f317,f1108]) ).
fof(f1158,plain,
( spl0_51
| ~ spl0_10
| ~ spl0_11
| ~ spl0_35
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1157,f992,f479,f150,f145,f1091]) ).
fof(f1162,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_9
| ~ spl0_51 ),
inference(superposition,[],[f142,f1092]) ).
fof(f1176,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_19
| ~ spl0_50 ),
inference(forward_demodulation,[],[f232,f993]) ).
fof(f1185,plain,
( spl0_37
| ~ spl0_19
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1176,f992,f231,f777]) ).
fof(f1196,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_37 ),
inference(superposition,[],[f290,f778]) ).
fof(f1199,plain,
( identity = sk_c11
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1196,f3]) ).
fof(f1213,plain,
( sk_c11 = sk_c9
| ~ spl0_8
| ~ spl0_26
| ~ spl0_50 ),
inference(forward_demodulation,[],[f877,f993]) ).
fof(f1223,plain,
( ~ spl0_26
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_16
| ~ spl0_22
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f1096,f835,f249,f195,f155,f125,f117,f274]) ).
fof(f1231,plain,
( spl0_26
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1199,f777,f274]) ).
fof(f1232,plain,
( sk_c11 != sk_c9
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f436,f123]) ).
fof(f1237,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_26
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1213,f992,f274,f135,f235]) ).
fof(f1240,plain,
( ~ spl0_20
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1232,f249,f195,f130,f121,f117,f235]) ).
fof(f1255,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_5
| ~ spl0_26 ),
inference(superposition,[],[f3,f891]) ).
fof(f1256,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1255,f1]) ).
fof(f1312,plain,
( identity = sk_c11
| ~ spl0_33
| ~ spl0_50 ),
inference(superposition,[],[f468,f993]) ).
fof(f1327,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_26 ),
inference(superposition,[],[f891,f1256]) ).
fof(f1369,plain,
( spl0_50
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f758,f165,f155,f125,f992]) ).
fof(f1370,plain,
( spl0_50
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f608,f135,f130,f121,f992]) ).
fof(f1374,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_51 ),
inference(forward_demodulation,[],[f317,f1092]) ).
fof(f1375,plain,
( spl0_19
| ~ spl0_9
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f1162,f1091,f140,f231]) ).
fof(f1378,plain,
( spl0_37
| ~ spl0_10
| ~ spl0_11
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f1374,f1091,f150,f145,f777]) ).
fof(f1395,plain,
( spl0_26
| ~ spl0_33
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1312,f992,f467,f274]) ).
fof(f1489,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_4
| ~ spl0_26 ),
inference(forward_demodulation,[],[f118,f275]) ).
fof(f1490,plain,
( ! [X0] :
( sk_c11 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_4
| ~ spl0_26
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1489,f468]) ).
fof(f1491,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_4
| ~ spl0_26
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1490,f275]) ).
fof(f1492,plain,
( identity != inverse(identity)
| ~ spl0_33
| spl0_43 ),
inference(forward_demodulation,[],[f950,f468]) ).
fof(f1496,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_4
| ~ spl0_26
| ~ spl0_33 ),
inference(superposition,[],[f1491,f1]) ).
fof(f1501,plain,
( identity != sk_c8
| identity != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_26
| ~ spl0_33
| ~ spl0_41 ),
inference(superposition,[],[f1491,f1083]) ).
fof(f1503,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_26
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f1496]) ).
fof(f1504,plain,
( identity != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_26
| ~ spl0_33
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1501,f1256]) ).
fof(f1507,plain,
( identity != sk_c11
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_26
| ~ spl0_33
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1504,f127]) ).
fof(f1510,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_26
| ~ spl0_33
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1507,f275]) ).
fof(f1511,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_26
| ~ spl0_33
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f1510]) ).
fof(f1514,plain,
( sk_c5 != multiply(sk_c4,identity)
| spl0_12
| ~ spl0_26 ),
inference(forward_demodulation,[],[f156,f275]) ).
fof(f1515,plain,
( sk_c5 != multiply(identity,identity)
| ~ spl0_6
| spl0_12
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1514,f874]) ).
fof(f1516,plain,
( identity != sk_c5
| ~ spl0_6
| spl0_12
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1515,f1]) ).
fof(f1521,plain,
( ~ spl0_41
| ~ spl0_6
| spl0_12
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f1516,f274,f155,f125,f835]) ).
fof(f1537,plain,
( $false
| ~ spl0_5
| ~ spl0_26
| ~ spl0_33
| spl0_43 ),
inference(forward_subsumption_resolution,[],[f1327,f1492]) ).
fof(f1538,plain,
( ~ spl0_5
| ~ spl0_26
| ~ spl0_33
| spl0_43 ),
inference(avatar_contradiction_clause,[],[f1537]) ).
fof(f1540,plain,
( identity = inverse(identity)
| ~ spl0_33
| ~ spl0_43 ),
inference(forward_demodulation,[],[f949,f468]) ).
fof(f1543,plain,
( $false
| ~ spl0_4
| ~ spl0_26
| ~ spl0_33
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[],[f1540,f1503]) ).
fof(f1544,plain,
( ~ spl0_4
| ~ spl0_26
| ~ spl0_33
| ~ spl0_43 ),
inference(avatar_contradiction_clause,[],[f1543]) ).
fof(f1545,plain,
( ! [X8] :
( sk_c10 != multiply(identity,multiply(X8,identity))
| sk_c11 != inverse(X8) )
| ~ spl0_1
| ~ spl0_26 ),
inference(forward_demodulation,[],[f109,f275]) ).
fof(f1546,plain,
( ! [X8] :
( sk_c10 != multiply(X8,identity)
| sk_c11 != inverse(X8) )
| ~ spl0_1
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1545,f1]) ).
fof(f1547,plain,
( ! [X8] :
( identity != multiply(X8,identity)
| sk_c11 != inverse(X8) )
| ~ spl0_1
| ~ spl0_26
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1546,f468]) ).
fof(f1548,plain,
( ! [X8] :
( identity != multiply(X8,identity)
| identity != inverse(X8) )
| ~ spl0_1
| ~ spl0_26
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1547,f275]) ).
fof(f1549,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_26
| ~ spl0_33 ),
inference(superposition,[],[f1548,f1]) ).
fof(f1555,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_26
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f1549]) ).
fof(f1565,plain,
( $false
| ~ spl0_1
| ~ spl0_26
| ~ spl0_33
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[],[f1555,f1540]) ).
fof(f1566,plain,
( ~ spl0_1
| ~ spl0_26
| ~ spl0_33
| ~ spl0_43 ),
inference(avatar_contradiction_clause,[],[f1565]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f119]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f128]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f133]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f138]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f143]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f148]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f153]) ).
cnf(s9,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f158]) ).
cnf(s10,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f159]) ).
cnf(s11,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f160]) ).
cnf(s12,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f161]) ).
cnf(s13,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f162]) ).
cnf(s14,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f163]) ).
cnf(s15,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f168]) ).
cnf(s16,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f169]) ).
cnf(s17,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f170]) ).
cnf(s18,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f171]) ).
cnf(s19,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f172]) ).
cnf(s20,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f173]) ).
cnf(s21,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f178]) ).
cnf(s25,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f182]) ).
cnf(s26,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f183]) ).
cnf(s27,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f188]) ).
cnf(s28,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f189]) ).
cnf(s29,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f190]) ).
cnf(s30,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f191]) ).
cnf(s31,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f192]) ).
cnf(s32,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f193]) ).
cnf(s33,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f198]) ).
cnf(s36,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f201]) ).
cnf(s37,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f202]) ).
cnf(s38,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f203]) ).
cnf(s39,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s42,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f211]) ).
cnf(s45,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f218]) ).
cnf(s48,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f221]) ).
cnf(s49,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f222]) ).
cnf(s50,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f223]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f240]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f256]) ).
cnf(s60,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f345]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f363]) ).
cnf(s70,plain,
( ~ spl0_14
| ~ spl0_16
| ~ spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f447]) ).
cnf(s75,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f489]) ).
cnf(s78,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18
| spl0_24 ),
inference(sat_conversion,[],[f503]) ).
cnf(s79,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f518]) ).
cnf(s85,plain,
( ~ spl0_2
| ~ spl0_18
| ~ spl0_19
| ~ spl0_24 ),
inference(sat_conversion,[],[f560]) ).
cnf(s92,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_33 ),
inference(sat_conversion,[],[f720]) ).
cnf(s95,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| spl0_22 ),
inference(sat_conversion,[],[f772]) ).
cnf(s108,plain,
( ~ spl0_16
| ~ spl0_22
| spl0_26
| ~ spl0_33 ),
inference(sat_conversion,[],[f840]) ).
cnf(s110,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| spl0_26
| ~ spl0_33 ),
inference(sat_conversion,[],[f842]) ).
cnf(s115,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_26
| spl0_41 ),
inference(sat_conversion,[],[f878]) ).
cnf(s116,plain,
( ~ spl0_13
| ~ spl0_26
| ~ spl0_33
| spl0_41 ),
inference(sat_conversion,[],[f885]) ).
cnf(s124,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_26
| spl0_33 ),
inference(sat_conversion,[],[f939]) ).
cnf(s126,plain,
( ~ spl0_3
| ~ spl0_26
| ~ spl0_33
| ~ spl0_43 ),
inference(sat_conversion,[],[f951]) ).
cnf(s129,plain,
( ~ spl0_19
| ~ spl0_26
| spl0_33 ),
inference(sat_conversion,[],[f954]) ).
cnf(s147,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_35
| ~ spl0_50 ),
inference(sat_conversion,[],[f1017]) ).
cnf(s167,plain,
( ~ spl0_9
| spl0_35
| ~ spl0_50 ),
inference(sat_conversion,[],[f1107]) ).
cnf(s168,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_35
| ~ spl0_50
| spl0_51 ),
inference(sat_conversion,[],[f1158]) ).
cnf(s175,plain,
( ~ spl0_19
| spl0_37
| ~ spl0_50 ),
inference(sat_conversion,[],[f1185]) ).
cnf(s197,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_16
| ~ spl0_22
| ~ spl0_26
| ~ spl0_41 ),
inference(sat_conversion,[],[f1223]) ).
cnf(s204,plain,
( spl0_26
| ~ spl0_37 ),
inference(sat_conversion,[],[f1231]) ).
cnf(s207,plain,
( ~ spl0_8
| spl0_20
| ~ spl0_26
| ~ spl0_50 ),
inference(sat_conversion,[],[f1237]) ).
cnf(s210,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f1240]) ).
cnf(s223,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| spl0_50 ),
inference(sat_conversion,[],[f1369]) ).
cnf(s225,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_50 ),
inference(sat_conversion,[],[f1370]) ).
cnf(s228,plain,
( ~ spl0_9
| spl0_19
| ~ spl0_51 ),
inference(sat_conversion,[],[f1375]) ).
cnf(s235,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_37
| ~ spl0_51 ),
inference(sat_conversion,[],[f1378]) ).
cnf(s255,plain,
( spl0_26
| ~ spl0_33
| ~ spl0_50 ),
inference(sat_conversion,[],[f1395]) ).
cnf(s284,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_26
| ~ spl0_33
| ~ spl0_41 ),
inference(sat_conversion,[],[f1511]) ).
cnf(s286,plain,
( ~ spl0_6
| spl0_12
| ~ spl0_26
| ~ spl0_41 ),
inference(sat_conversion,[],[f1521]) ).
cnf(s290,plain,
( ~ spl0_5
| ~ spl0_26
| ~ spl0_33
| spl0_43 ),
inference(sat_conversion,[],[f1538]) ).
cnf(s291,plain,
( ~ spl0_4
| ~ spl0_26
| ~ spl0_33
| ~ spl0_43 ),
inference(sat_conversion,[],[f1544]) ).
cnf(s292,plain,
( ~ spl0_1
| ~ spl0_26
| ~ spl0_33
| ~ spl0_43 ),
inference(sat_conversion,[],[f1566]) ).
cnf(s293,plain,
( spl0_5
| ~ spl0_4 ),
inference(rat,[],[s197,s115,s95,s110,s92,s3,s9,s15,s27,s33]) ).
cnf(s294,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_13
| ~ spl0_12
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s291,s290,s108,s92,s95,s293]) ).
cnf(s295,plain,
( spl0_16
| ~ spl0_13
| ~ spl0_12
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s284,s116,s129,s204,s228,s235,s168,s167,s36,s37,s38,s293,s223]) ).
cnf(s296,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s204,s235,s207,s168,s210,s167,s28,s29,s30,s31,s32,s294,s95,s295,s223,s293]) ).
cnf(s297,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s291,s290,s129,s204,s228,s235,s168,s167,s225,s16,s17,s18,s19,s20,s293]) ).
cnf(s298,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s286,s116,s129,s204,s228,s235,s168,s167,s225,s10,s11,s12,s13,s14,s296,s293,s297]) ).
cnf(s299,plain,
~ spl0_4,
inference(rat,[],[s291,s290,s129,s204,s228,s235,s168,s167,s225,s4,s5,s6,s7,s8,s298,s293]) ).
cnf(s300,plain,
( ~ spl0_26
| ~ spl0_13
| ~ spl0_12
| ~ spl0_6
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s126,s290,s124]) ).
cnf(s301,plain,
( spl0_9
| spl0_19
| ~ spl0_13
| ~ spl0_12
| ~ spl0_6 ),
inference(rat,[],[s95,s60,s36,s42,s48]) ).
cnf(s302,plain,
( spl0_15
| ~ spl0_35
| ~ spl0_50
| ~ spl0_3 ),
inference(rat,[],[s147,s31,s32]) ).
cnf(s303,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_6
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s147,s37,s38,s92,s302,s167,s301,s175,s204,s255,s300,s223]) ).
cnf(s304,plain,
( spl0_13
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s167,s147,s225,s16,s17,s18,s19,s20]) ).
cnf(s305,plain,
( spl0_12
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s167,s147,s225,s10,s11,s12,s13,s14]) ).
cnf(s306,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_3
| ~ spl0_5 ),
inference(rat,[],[s167,s147,s225,s4,s5,s6,s7,s8,s303]) ).
cnf(s307,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s306,s305,s304]) ).
cnf(s308,plain,
~ spl0_3,
inference(rat,[],[s75,s21,s27,s33,s307]) ).
cnf(s309,plain,
( spl0_11
| ~ spl0_6
| ~ spl0_13
| ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s55,s70,s95,s26,s32,s38]) ).
cnf(s310,plain,
( spl0_10
| ~ spl0_6
| ~ spl0_13
| ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s55,s70,s95,s25,s31,s37]) ).
cnf(s311,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_2
| ~ spl0_12 ),
inference(rat,[],[s85,s78,s301,s42,s48,s53,s310,s309]) ).
cnf(s312,plain,
( spl0_6
| ~ spl0_2 ),
inference(rat,[],[s53,s6,s7,s8]) ).
cnf(s313,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s53,s18,s19,s20]) ).
cnf(s314,plain,
( ~ spl0_13
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s53,s12,s13,s14,s311]) ).
cnf(s315,plain,
~ spl0_2,
inference(rat,[],[s314,s313,s312]) ).
cnf(s316,plain,
spl0_1,
inference(rat,[],[s2,s299,s308,s315]) ).
cnf(s317,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_50 ),
inference(rat,[],[s79,s39,s45,s290,s292,s129,s204,s228,s235,s168,s167,s316]) ).
cnf(s318,plain,
( spl0_11
| ~ spl0_6
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s95,s61,s38,s50,s316]) ).
cnf(s319,plain,
( spl0_10
| ~ spl0_6
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s95,s61,s37,s49,s316]) ).
cnf(s320,plain,
( ~ spl0_10
| ~ spl0_50
| ~ spl0_11 ),
inference(rat,[],[s79,s42,s48,s317,s316]) ).
cnf(s321,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s320,s319,s318,s223]) ).
cnf(s322,plain,
spl0_6,
inference(rat,[],[s225,s320,s3,s4,s5,s7,s8]) ).
cnf(s323,plain,
spl0_13,
inference(rat,[],[s225,s320,s15,s16,s17,s19,s20]) ).
cnf(s324,plain,
~ spl0_12,
inference(rat,[],[s321,s322,s323]) ).
cnf(s325,plain,
spl0_11,
inference(rat,[],[s14,s324]) ).
cnf(s326,plain,
spl0_10,
inference(rat,[],[s13,s324]) ).
cnf(s328,plain,
spl0_8,
inference(rat,[],[s11,s324]) ).
cnf(s329,plain,
spl0_7,
inference(rat,[],[s10,s324]) ).
cnf(s330,plain,
spl0_5,
inference(rat,[],[s9,s324]) ).
cnf(s331,plain,
~ spl0_50,
inference(rat,[],[s320,s325,s326]) ).
cnf(s332,plain,
$false,
inference(rat,[],[s225,s328,s330,s331,s329]) ).
fof(f1567,plain,
$false,
inference(avatar_sat_refutation,[],[s332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP217-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:42:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.48 % (2375869)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (2375889)dis+10_1_sil=32000:sp=arity:random_seed=524307622:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (2375887)% WARNING: option uhcvi not known.
% 0.16/0.48 % (2375887)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2903069218:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (2375886)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=566587782_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (2375888)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4072619380:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (2375890)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3114963208:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (2375892)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3050299154:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (2375891)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1920131708:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (2375889) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2375869-2375889"...
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (2375889)...printing done.
% 0.16/0.48 % (2375889)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (2375889)------------------------------
% 0.16/0.48 % (2375889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (2375889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (2375889)CaDiCaL version: 2.1.3
% 0.16/0.48 % (2375889)Termination reason: Refutation
% 0.16/0.48 % (2375889)Time elapsed: 0.019 s
% 0.16/0.48 % (2375889)Peak memory usage: 13 MB
% 0.16/0.48 % (2375889)Instructions burned: 55 (million)
% 0.16/0.48 % (2375869)Success in time 0.052 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------