%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP223-1 : 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 : n010.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 10:17:13 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.59s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 55
% Syntax : Number of formulae : 282 ( 22 unt; 21 def)
% Number of atoms : 765 ( 282 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 862 ( 379 ~; 462 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 53 !; 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_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c1) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c1) = sk_c9
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c1) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c1) = sk_c9
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c1) = sk_c9
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( inverse(sk_c1) = sk_c9
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(X0) != sk_c9
| multiply(X0,sk_c8) != sk_c9
| multiply(sk_c9,X1) != sk_c8
| multiply(X2,sk_c9) != X1
| inverse(X2) != sk_c9
| multiply(X3,X4) != sk_c9
| inverse(X3) != X4
| multiply(X4,sk_c8) != sk_c9
| multiply(sk_c9,X5) != sk_c8
| multiply(X6,sk_c9) != X5
| inverse(X6) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,X1)
| multiply(X2,sk_c9) != X1
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X6,X4,X5] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X2,X3,X0,X6,X5] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(equality_resolution,[],[f67]) ).
fof(f69,plain,
! [X2,X3,X0,X6] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) ),
inference(equality_resolution,[],[f68]) ).
fof(f71,definition,
( spl0_1
<=> ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f72,plain,
( ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f75,plain,
( ! [X3] :
( sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c9 != multiply(X3,inverse(X3)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,definition,
( spl0_3
<=> ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f78,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f69,f77,f71,f74,f71]) ).
fof(f81,definition,
( spl0_4
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f83,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f85,definition,
( spl0_5
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f87,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f64,f85,f81]) ).
fof(f90,definition,
( spl0_6
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f92,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f62,f85,f90]) ).
fof(f95,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f97,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f60,f85,f95]) ).
fof(f100,definition,
( spl0_8
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f102,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f58,f85,f100]) ).
fof(f105,definition,
( spl0_9
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f107,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f56,f85,f105]) ).
fof(f110,definition,
( spl0_10
<=> sk_c9 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f112,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f54,f85,f110]) ).
fof(f115,definition,
( spl0_11
<=> sk_c3 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f117,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_4
| spl0_11 ),
inference(avatar_split_clause,[],[f52,f115,f81]) ).
fof(f119,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f50,f115,f90]) ).
fof(f120,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f48,f115,f95]) ).
fof(f121,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f46,f115,f100]) ).
fof(f122,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f44,f115,f105]) ).
fof(f123,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f42,f115,f110]) ).
fof(f125,definition,
( spl0_12
<=> sk_c8 = multiply(sk_c9,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f127,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_4
| spl0_12 ),
inference(avatar_split_clause,[],[f40,f125,f81]) ).
fof(f129,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f38,f125,f90]) ).
fof(f130,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f125,f95]) ).
fof(f131,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f34,f125,f100]) ).
fof(f132,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f32,f125,f105]) ).
fof(f133,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f30,f125,f110]) ).
fof(f135,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f137,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f28,f135,f81]) ).
fof(f139,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f26,f135,f90]) ).
fof(f140,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f24,f135,f95]) ).
fof(f141,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f22,f135,f100]) ).
fof(f142,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f20,f135,f105]) ).
fof(f143,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f18,f135,f110]) ).
fof(f145,definition,
( spl0_14
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f147,plain,
( inverse(sk_c1) = sk_c9
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f16,f145,f81]) ).
fof(f149,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f14,f145,f90]) ).
fof(f150,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f12,f145,f95]) ).
fof(f151,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f10,f145,f100]) ).
fof(f152,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f8,f145,f105]) ).
fof(f153,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f6,f145,f110]) ).
fof(f155,plain,
( sk_c9 != multiply(sk_c5,sk_c8)
| sk_c9 != multiply(sk_c4,sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f75,f107]) ).
fof(f156,plain,
( sk_c9 != multiply(sk_c4,sk_c5)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f155,f102]) ).
fof(f158,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f162,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f164,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| spl0_16 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f168,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f156,f105,f100,f74,f110]) ).
fof(f175,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f75,f147]) ).
fof(f177,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f178,plain,
( sk_c9 = multiply(sk_c1,sk_c9)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f180,plain,
( ~ spl0_18
| ~ spl0_16
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f175,f145,f74,f162,f177]) ).
fof(f181,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f147]) ).
fof(f191,definition,
( spl0_20
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f192,plain,
( identity = sk_c9
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f197,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f201,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c1,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f181]) ).
fof(f203,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c9,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f92]) ).
fof(f205,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c1,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f201,f1]) ).
fof(f206,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f197,f1]) ).
fof(f230,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c8)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f203,f97]) ).
fof(f284,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_8 ),
inference(superposition,[],[f206,f102]) ).
fof(f288,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f206,f92]) ).
fof(f290,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f206,f117]) ).
fof(f295,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f290,f87]) ).
fof(f297,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f288,f83]) ).
fof(f300,plain,
( sk_c9 = sk_c8
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f295,f127]) ).
fof(f308,plain,
( sk_c9 = sk_c8
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f297,f97]) ).
fof(f327,definition,
( spl0_22
<=> sk_c9 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f328,plain,
( sk_c9 = sk_c7
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f333,plain,
( sk_c9 = multiply(sk_c1,sk_c9)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f137,f300]) ).
fof(f334,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| spl0_16 ),
inference(superposition,[],[f164,f300]) ).
fof(f340,plain,
( spl0_18
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f333,f135,f125,f115,f85,f177]) ).
fof(f342,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_18 ),
inference(superposition,[],[f206,f178]) ).
fof(f344,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f342,f147]) ).
fof(f394,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f334,f344]) ).
fof(f395,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f394]) ).
fof(f396,plain,
( ! [X6] :
( sk_c9 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f72,f300]) ).
fof(f407,plain,
( sk_c9 != multiply(sk_c9,sk_c3)
| sk_c9 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f396,f117]) ).
fof(f416,plain,
( sk_c9 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f407,f295]) ).
fof(f442,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f416,f87]) ).
fof(f443,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f480,plain,
( sk_c5 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_10 ),
inference(superposition,[],[f206,f112]) ).
fof(f481,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f112]) ).
fof(f482,plain,
( sk_c5 = multiply(sk_c5,sk_c9)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f480,f107]) ).
fof(f487,plain,
( sk_c9 != sk_c9
| inverse(sk_c1) != sk_c9
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f78,f137]) ).
fof(f490,plain,
( inverse(sk_c1) != sk_c9
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f487]) ).
fof(f491,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f490,f147]) ).
fof(f492,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f491]) ).
fof(f504,definition,
( spl0_29
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f505,plain,
( sk_c9 = sk_c8
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f538,plain,
( spl0_29
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f308,f95,f90,f81,f504]) ).
fof(f540,plain,
( sk_c9 = multiply(sk_c5,sk_c9)
| ~ spl0_8
| ~ spl0_29 ),
inference(superposition,[],[f102,f505]) ).
fof(f598,definition,
( spl0_33
<=> sk_c9 = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f599,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f622,plain,
( multiply(sk_c4,sk_c5) = multiply(sk_c9,sk_c9)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f481,f482]) ).
fof(f626,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f622,f112]) ).
fof(f627,plain,
( spl0_33
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f626,f110,f105,f598]) ).
fof(f635,plain,
( sk_c9 = sk_c5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_29 ),
inference(superposition,[],[f540,f482]) ).
fof(f679,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_29 ),
inference(forward_demodulation,[],[f284,f635]) ).
fof(f680,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_29 ),
inference(forward_demodulation,[],[f679,f505]) ).
fof(f693,plain,
( identity = sk_c9
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_29 ),
inference(superposition,[],[f3,f680]) ).
fof(f707,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f693,f504,f110,f105,f100,f191]) ).
fof(f711,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_20 ),
inference(superposition,[],[f1,f192]) ).
fof(f729,plain,
( sk_c8 = sk_c7
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f97,f711]) ).
fof(f738,plain,
( sk_c9 = sk_c7
| ~ spl0_7
| ~ spl0_20
| ~ spl0_29 ),
inference(forward_demodulation,[],[f729,f505]) ).
fof(f759,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_20
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f738,f504,f191,f95,f327]) ).
fof(f777,plain,
( multiply(sk_c6,sk_c9) = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_29 ),
inference(forward_demodulation,[],[f230,f505]) ).
fof(f778,plain,
( multiply(sk_c6,sk_c9) = multiply(sk_c9,sk_c9)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_22
| ~ spl0_29 ),
inference(forward_demodulation,[],[f777,f328]) ).
fof(f779,plain,
( sk_c9 = multiply(sk_c6,sk_c9)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_22
| ~ spl0_29
| ~ spl0_33 ),
inference(forward_demodulation,[],[f778,f599]) ).
fof(f783,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != multiply(sk_c9,multiply(X6,sk_c9)) )
| ~ spl0_1
| ~ spl0_29 ),
inference(forward_demodulation,[],[f72,f505]) ).
fof(f815,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c1,sk_c9))
| ~ spl0_1
| ~ spl0_14
| ~ spl0_29 ),
inference(superposition,[],[f783,f147]) ).
fof(f817,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_29 ),
inference(superposition,[],[f783,f83]) ).
fof(f818,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f817]) ).
fof(f819,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c1,sk_c9))
| ~ spl0_1
| ~ spl0_14
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f815]) ).
fof(f820,plain,
( sk_c9 != multiply(sk_c9,sk_c7)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_29 ),
inference(forward_demodulation,[],[f818,f92]) ).
fof(f822,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f819,f205]) ).
fof(f823,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f822]) ).
fof(f824,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_22
| ~ spl0_29 ),
inference(forward_demodulation,[],[f820,f328]) ).
fof(f826,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_22
| ~ spl0_29
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f824,f599]) ).
fof(f827,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_22
| ~ spl0_29
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f826]) ).
fof(f834,plain,
( ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c9) )
| ~ spl0_3
| ~ spl0_29 ),
inference(forward_demodulation,[],[f78,f505]) ).
fof(f855,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_7
| ~ spl0_22
| ~ spl0_29
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f779,f598,f504,f327,f95,f90,f158]) ).
fof(f867,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_29 ),
inference(superposition,[],[f834,f83]) ).
fof(f868,plain,
( sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f867]) ).
fof(f869,plain,
( ~ spl0_15
| ~ spl0_3
| ~ spl0_4
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f868,f504,f81,f77,f158]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f79]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f88]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f93]) ).
cnf(s5,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f98]) ).
cnf(s6,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f103]) ).
cnf(s7,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f108]) ).
cnf(s8,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s9,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f118]) ).
cnf(s10,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f119]) ).
cnf(s11,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f120]) ).
cnf(s12,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f121]) ).
cnf(s13,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f122]) ).
cnf(s14,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f123]) ).
cnf(s15,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f128]) ).
cnf(s16,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s17,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f130]) ).
cnf(s18,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f131]) ).
cnf(s19,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f132]) ).
cnf(s20,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s21,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s22,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s23,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s24,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f141]) ).
cnf(s25,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f142]) ).
cnf(s26,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f143]) ).
cnf(s27,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f148]) ).
cnf(s28,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s29,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s30,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s31,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s32,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s35,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f168]) ).
cnf(s37,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f180]) ).
cnf(s41,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f340]) ).
cnf(s43,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f395]) ).
cnf(s47,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f443]) ).
cnf(s59,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f492]) ).
cnf(s66,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| spl0_29 ),
inference(sat_conversion,[],[f538]) ).
cnf(s79,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_33 ),
inference(sat_conversion,[],[f627]) ).
cnf(s88,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_20
| ~ spl0_29 ),
inference(sat_conversion,[],[f707]) ).
cnf(s92,plain,
( ~ spl0_7
| ~ spl0_20
| spl0_22
| ~ spl0_29 ),
inference(sat_conversion,[],[f759]) ).
cnf(s97,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_29 ),
inference(sat_conversion,[],[f823]) ).
cnf(s98,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_22
| ~ spl0_29
| ~ spl0_33 ),
inference(sat_conversion,[],[f827]) ).
cnf(s101,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_15
| ~ spl0_22
| ~ spl0_29
| ~ spl0_33 ),
inference(sat_conversion,[],[f855]) ).
cnf(s104,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_15
| ~ spl0_29 ),
inference(sat_conversion,[],[f869]) ).
cnf(s106,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s59,s21,s27]) ).
cnf(s107,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s92,s101,s88,s104,s66,s79,s28,s29,s30,s31,s32,s106]) ).
cnf(s108,plain,
~ spl0_3,
inference(rat,[],[s92,s101,s88,s104,s66,s79,s22,s23,s24,s25,s26,s59,s107,s106]) ).
cnf(s109,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s35,s30,s31,s32]) ).
cnf(s110,plain,
( spl0_10
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s37,s43,s41,s8,s14,s20,s109]) ).
cnf(s111,plain,
( spl0_9
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s37,s43,s41,s7,s13,s19,s109]) ).
cnf(s112,plain,
( ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s37,s43,s41,s6,s12,s18,s35,s111,s110,s109]) ).
cnf(s113,plain,
~ spl0_2,
inference(rat,[],[s35,s24,s25,s26,s112]) ).
cnf(s114,plain,
spl0_1,
inference(rat,[],[s2,s108,s113]) ).
cnf(s115,plain,
spl0_10,
inference(rat,[],[s47,s8,s14,s20,s114]) ).
cnf(s116,plain,
( spl0_12
| spl0_29 ),
inference(rat,[],[s66,s15,s16,s17]) ).
cnf(s117,plain,
( spl0_11
| spl0_29 ),
inference(rat,[],[s66,s9,s10,s11]) ).
cnf(s118,plain,
spl0_29,
inference(rat,[],[s66,s3,s4,s5,s47,s117,s116,s114]) ).
cnf(s119,plain,
~ spl0_14,
inference(rat,[],[s97,s114,s118]) ).
cnf(s120,plain,
spl0_9,
inference(rat,[],[s31,s119]) ).
cnf(s121,plain,
spl0_8,
inference(rat,[],[s30,s119]) ).
cnf(s122,plain,
spl0_7,
inference(rat,[],[s29,s119]) ).
cnf(s123,plain,
spl0_6,
inference(rat,[],[s28,s119]) ).
cnf(s124,plain,
spl0_4,
inference(rat,[],[s27,s119]) ).
cnf(s125,plain,
spl0_33,
inference(rat,[],[s79,s115,s120]) ).
cnf(s126,plain,
spl0_20,
inference(rat,[],[s88,s118,s120,s115,s121]) ).
cnf(s128,plain,
~ spl0_22,
inference(rat,[],[s98,s125,s114,s123,s118,s124]) ).
cnf(s130,plain,
$false,
inference(rat,[],[s92,s118,s122,s128,s126]) ).
fof(f873,plain,
$false,
inference(avatar_sat_refutation,[],[s130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP223-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.47 % Computer : n010.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 27 09:38:16 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.53 Running first-order model finding
% 0.25/0.53 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
% 0.25/0.59 % (703492)Will run a generic schedule for satisfiability detection.
% 0.25/0.59 % (703498)% WARNING: option uhcvi not known.
% 0.25/0.59 % (703498)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2138408007:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.59 % (703501)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4000497575:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.59 % (703499)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2704944599:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.59 % (703502)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2155057867:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.59 % (703500)dis+10_1_sil=32000:sp=arity:random_seed=4577391:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.59 % (703497)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4238203551_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.59 % (703503)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=932840266:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.59 % (703498) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-703492-703498"...
% 0.25/0.59 % (703498)...printing done.
% 0.25/0.59 % TRYING [1]
% 0.25/0.59 % TRYING [2]
% 0.25/0.59 % (703498)Refutation found. Thanks to Tanya!
% 0.25/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.25/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.60 % (703498)------------------------------
% 0.25/0.60 % (703498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.60 % (703498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.60 % (703498)CaDiCaL version: 2.1.3
% 0.25/0.60 % (703498)Termination reason: Refutation
% 0.25/0.60 % (703498)Time elapsed: 0.019 s
% 0.25/0.60 % (703498)Peak memory usage: 13 MB
% 0.25/0.60 % (703498)Instructions burned: 32 (million)
% 0.25/0.60 % (703492)Success in time 0.054 s
% 0.25/0.60 % Vampire exiting
%------------------------------------------------------------------------------