%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP237-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:24 AM UTC 2026
% Result : Unsatisfiable 0.58s 0.84s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 57
% Syntax : Number of formulae : 316 ( 17 unt; 18 def)
% Number of atoms : 961 ( 324 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1176 ( 531 ~; 627 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c9) = sk_c8
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c9) = sk_c8
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c9) = sk_c8
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c9) = sk_c8
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( inverse(sk_c9) = sk_c8
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,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_13) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,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_15) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,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_16) ).
fof(f36,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,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_17) ).
fof(f38,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,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_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,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_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,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_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,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_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,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_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,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_27) ).
fof(f58,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,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_28) ).
fof(f60,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,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_29) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| 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_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| 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,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X0,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| 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,[],[f78]) ).
fof(f80,plain,
! [X2,X3,X0,X6,X5] :
( inverse(sk_c9) != sk_c8
| 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,[],[f79]) ).
fof(f81,plain,
! [X2,X3,X0,X6] :
( inverse(sk_c9) != sk_c8
| 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,[],[f80]) ).
fof(f83,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(f84,plain,
( ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,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(f87,plain,
( ! [X3] :
( sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c9 != multiply(X3,inverse(X3)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,definition,
( spl0_3
<=> ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f90,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,definition,
( spl0_4
<=> inverse(sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f93,plain,
( inverse(sk_c9) = sk_c8
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( inverse(sk_c9) != sk_c8
| spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f81,f92,f89,f83,f86,f83]) ).
fof(f97,definition,
( spl0_5
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f99,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f103,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f76,f101,f97]) ).
fof(f106,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f108,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f74,f101,f106]) ).
fof(f111,definition,
( spl0_8
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f113,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f72,f101,f111]) ).
fof(f116,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f118,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f70,f101,f116]) ).
fof(f121,definition,
( spl0_10
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f123,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f68,f101,f121]) ).
fof(f126,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f128,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f66,f101,f126]) ).
fof(f131,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f133,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_5
| spl0_12 ),
inference(avatar_split_clause,[],[f64,f131,f97]) ).
fof(f135,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f62,f131,f106]) ).
fof(f136,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f60,f131,f111]) ).
fof(f137,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f58,f131,f116]) ).
fof(f138,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f56,f131,f121]) ).
fof(f139,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f131,f126]) ).
fof(f141,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c9,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f143,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f141,f97]) ).
fof(f145,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f141,f106]) ).
fof(f146,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f141,f111]) ).
fof(f147,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f141,f116]) ).
fof(f148,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f141,f121]) ).
fof(f149,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f141,f126]) ).
fof(f151,definition,
( spl0_14
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f153,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f151,f97]) ).
fof(f155,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f151,f106]) ).
fof(f156,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f151,f111]) ).
fof(f157,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f151,f116]) ).
fof(f158,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f151,f121]) ).
fof(f159,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f151,f126]) ).
fof(f161,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f163,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f161,f97]) ).
fof(f165,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f161,f106]) ).
fof(f166,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f161,f111]) ).
fof(f167,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f161,f116]) ).
fof(f168,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f161,f121]) ).
fof(f169,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f161,f126]) ).
fof(f170,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f16,f92,f97]) ).
fof(f171,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f14,f92,f106]) ).
fof(f172,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f12,f92,f111]) ).
fof(f174,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f92,f121]) ).
fof(f175,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f6,f92,f126]) ).
fof(f176,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f3,f99]) ).
fof(f177,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f123]) ).
fof(f180,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f185,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f180,f1]) ).
fof(f188,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f176]) ).
fof(f189,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c6,X0)) = X0
| ~ spl0_5 ),
inference(forward_demodulation,[],[f188,f1]) ).
fof(f192,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f189,f108]) ).
fof(f198,plain,
( sk_c9 = sk_c8
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f192,f113]) ).
fof(f244,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f185,f113]) ).
fof(f245,plain,
( sk_c6 = multiply(inverse(sk_c9),identity)
| ~ spl0_5 ),
inference(superposition,[],[f185,f176]) ).
fof(f248,plain,
( sk_c5 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_11 ),
inference(superposition,[],[f185,f128]) ).
fof(f252,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_9 ),
inference(superposition,[],[f185,f118]) ).
fof(f253,plain,
( sk_c4 = multiply(inverse(sk_c5),identity)
| ~ spl0_10 ),
inference(superposition,[],[f185,f177]) ).
fof(f262,plain,
( sk_c9 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f252,f198]) ).
fof(f264,plain,
( sk_c5 = multiply(sk_c5,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f248,f123]) ).
fof(f266,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f244,f198]) ).
fof(f270,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f266,f3]) ).
fof(f274,plain,
( sk_c9 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f185,f264]) ).
fof(f277,plain,
( identity = sk_c9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f274,f3]) ).
fof(f282,plain,
( sk_c9 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f277,f270]) ).
fof(f286,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f245,f270]) ).
fof(f287,plain,
( sk_c4 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f253,f270]) ).
fof(f297,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f286,f282]) ).
fof(f298,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f297,f3]) ).
fof(f299,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f298,f270]) ).
fof(f300,plain,
( sk_c9 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f299,f282]) ).
fof(f305,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f99,f300]) ).
fof(f310,plain,
( sk_c4 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f287,f282]) ).
fof(f311,plain,
( sk_c9 = sk_c4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f310,f262]) ).
fof(f313,plain,
( identity = multiply(sk_c5,sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f177,f311]) ).
fof(f316,plain,
( identity = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f313,f264]) ).
fof(f317,plain,
( sk_c9 = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f316,f277]) ).
fof(f338,plain,
( sk_c9 != sk_c8
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f94,f305]) ).
fof(f342,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f338,f198]) ).
fof(f343,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f342]) ).
fof(f357,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != multiply(sk_c9,multiply(X6,sk_c9)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f84,f198]) ).
fof(f359,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f357,f99]) ).
fof(f363,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f359]) ).
fof(f365,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f363,f189]) ).
fof(f366,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f368,plain,
( ! [X3] :
( sk_c9 != multiply(inverse(X3),sk_c9)
| sk_c9 != multiply(X3,inverse(X3)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f87,f198]) ).
fof(f371,plain,
( sk_c9 != multiply(sk_c5,sk_c9)
| sk_c9 != multiply(sk_c4,sk_c5)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f368,f123]) ).
fof(f379,plain,
( sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f371,f128]) ).
fof(f383,plain,
( sk_c9 != sk_c5
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f379,f264]) ).
fof(f385,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f383,f317]) ).
fof(f386,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f387,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f245,f277]) ).
fof(f389,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f387,f3]) ).
fof(f390,plain,
( sk_c9 = sk_c6
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f389,f277]) ).
fof(f393,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f99,f390]) ).
fof(f402,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f163]) ).
fof(f404,plain,
( sk_c9 = sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f393,f93]) ).
fof(f411,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f185,f133]) ).
fof(f413,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f411,f103]) ).
fof(f424,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f90,f404]) ).
fof(f428,plain,
( identity != sk_c9
| sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f424,f3]) ).
fof(f446,plain,
( sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f428,f277]) ).
fof(f450,plain,
( sk_c9 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f446,f93]) ).
fof(f453,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f450,f404]) ).
fof(f454,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f453,f393]) ).
fof(f455,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f470,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f90,f153]) ).
fof(f471,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f470]) ).
fof(f473,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f471,f163]) ).
fof(f474,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f490,definition,
( spl0_21
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f491,plain,
( sk_c9 = sk_c8
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f501,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f87,f163]) ).
fof(f511,definition,
( spl0_23
<=> sk_c9 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f515,definition,
( spl0_24
<=> sk_c9 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f517,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| spl0_24 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f518,plain,
( ~ spl0_23
| ~ spl0_24
| ~ spl0_2
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f501,f161,f86,f515,f511]) ).
fof(f534,plain,
( sk_c1 = multiply(inverse(sk_c9),identity)
| ~ spl0_15 ),
inference(superposition,[],[f185,f402]) ).
fof(f537,plain,
( sk_c1 = multiply(sk_c8,identity)
| ~ spl0_4
| ~ spl0_15 ),
inference(forward_demodulation,[],[f534,f93]) ).
fof(f544,plain,
( sk_c9 = sk_c8
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f143,f413]) ).
fof(f545,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[],[f185,f413]) ).
fof(f547,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f545,f3]) ).
fof(f548,plain,
( spl0_21
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f544,f141,f131,f101,f490]) ).
fof(f551,plain,
( sk_c9 = multiply(sk_c1,sk_c9)
| ~ spl0_14
| ~ spl0_21 ),
inference(superposition,[],[f153,f491]) ).
fof(f555,plain,
( spl0_23
| ~ spl0_14
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f551,f490,f151,f511]) ).
fof(f639,plain,
( sk_c1 = multiply(sk_c8,sk_c3)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f537,f547]) ).
fof(f640,plain,
( sk_c1 = multiply(sk_c9,sk_c3)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f639,f491]) ).
fof(f641,plain,
( sk_c8 = sk_c1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f640,f143]) ).
fof(f642,plain,
( sk_c9 = sk_c1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f641,f491]) ).
fof(f646,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f153,f642]) ).
fof(f648,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f646,f517]) ).
fof(f649,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f648]) ).
fof(f651,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != multiply(sk_c9,multiply(X6,sk_c9)) )
| ~ spl0_1
| ~ spl0_21 ),
inference(forward_demodulation,[],[f84,f491]) ).
fof(f658,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(superposition,[],[f651,f99]) ).
fof(f660,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_21 ),
inference(superposition,[],[f651,f103]) ).
fof(f661,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f660]) ).
fof(f663,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f658]) ).
fof(f665,plain,
( sk_c9 != multiply(sk_c9,sk_c3)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_21 ),
inference(forward_demodulation,[],[f661,f133]) ).
fof(f667,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f663,f189]) ).
fof(f668,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f675,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f665,f413]) ).
fof(f676,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f675]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f95]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f104]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f114]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f124]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f129]) ).
cnf(s9,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f134]) ).
cnf(s10,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s11,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f136]) ).
cnf(s12,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s13,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f138]) ).
cnf(s14,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f139]) ).
cnf(s15,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s16,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f145]) ).
cnf(s17,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f146]) ).
cnf(s18,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f147]) ).
cnf(s19,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s20,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f149]) ).
cnf(s21,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s22,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s23,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s24,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
cnf(s25,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f158]) ).
cnf(s26,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f159]) ).
cnf(s27,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s28,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s29,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
cnf(s30,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s31,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f168]) ).
cnf(s32,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f169]) ).
cnf(s33,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f170]) ).
cnf(s34,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f171]) ).
cnf(s35,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f172]) ).
cnf(s37,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f174]) ).
cnf(s38,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f175]) ).
cnf(s39,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f343]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f366]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f386]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f455]) ).
cnf(s48,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f474]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f518]) ).
cnf(s57,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| spl0_21 ),
inference(sat_conversion,[],[f548]) ).
cnf(s59,plain,
( ~ spl0_14
| ~ spl0_21
| spl0_23 ),
inference(sat_conversion,[],[f555]) ).
cnf(s61,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21
| spl0_24 ),
inference(sat_conversion,[],[f649]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(sat_conversion,[],[f668]) ).
cnf(s64,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_21 ),
inference(sat_conversion,[],[f676]) ).
cnf(s65,plain,
spl0_4,
inference(rat,[],[s39,s33,s34,s35,s37,s38]) ).
cnf(s67,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s48,s26,s32]) ).
cnf(s68,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s48,s25,s31]) ).
cnf(s69,plain,
( ~ spl0_10
| ~ spl0_3
| ~ spl0_11 ),
inference(rat,[],[s48,s21,s27,s47,s65]) ).
cnf(s70,plain,
~ spl0_3,
inference(rat,[],[s69,s68,s67]) ).
cnf(s71,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s53,s59,s61,s57,s8,s14,s20,s26,s32,s65]) ).
cnf(s72,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_6
| ~ spl0_15
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s53,s59,s61,s57,s65]) ).
cnf(s73,plain,
( spl0_13
| ~ spl0_10
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s42,s16,s17,s18,s71]) ).
cnf(s74,plain,
( spl0_12
| ~ spl0_10
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s42,s10,s11,s12,s71]) ).
cnf(s75,plain,
( spl0_6
| ~ spl0_10
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s42,s4,s5,s6,s71]) ).
cnf(s76,plain,
( spl0_15
| ~ spl0_10
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s42,s28,s29,s30,s71]) ).
cnf(s77,plain,
( ~ spl0_10
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s42,s22,s23,s24,s72,s76,s75,s74,s73,s71]) ).
cnf(s78,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s72,s7,s13,s19,s25,s31]) ).
cnf(s79,plain,
( ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s72,s3,s9,s15,s21,s27,s77]) ).
cnf(s80,plain,
~ spl0_2,
inference(rat,[],[s79,s78]) ).
cnf(s81,plain,
spl0_1,
inference(rat,[],[s2,s65,s70,s80]) ).
cnf(s82,plain,
( spl0_13
| ~ spl0_5 ),
inference(rat,[],[s41,s16,s17,s81]) ).
cnf(s83,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s41,s10,s11,s81]) ).
cnf(s84,plain,
~ spl0_5,
inference(rat,[],[s41,s4,s5,s57,s83,s82,s62,s81]) ).
cnf(s85,plain,
spl0_13,
inference(rat,[],[s15,s84]) ).
cnf(s86,plain,
spl0_12,
inference(rat,[],[s9,s84]) ).
cnf(s87,plain,
spl0_6,
inference(rat,[],[s3,s84]) ).
cnf(s88,plain,
~ spl0_21,
inference(rat,[],[s64,s86,s81,s87]) ).
cnf(s89,plain,
$false,
inference(rat,[],[s57,s86,s85,s88,s87]) ).
fof(f677,plain,
$false,
inference(avatar_sat_refutation,[],[s89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP237-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 09:37:50 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.58/0.84 % (2120357)Input is clausal, will run a generic CNF schedule.
% 0.58/0.84 % (2120368)dis-21_1_sil=8000:lcm=predicate:random_seed=2518231424:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.58/0.84 % (2120365)lrs+10_1_sil=8000:sp=occurrence:random_seed=2359440252:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.58/0.84 % (2120362)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1569680768:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.58/0.84 % (2120364)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3106943247:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.58/0.84 % (2120366)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3736114776:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.58/0.84 % (2120363)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3444298771:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.58/0.84 % (2120367)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=812739550:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.58/0.84 % (2120368)Refutation not found, incomplete strategy
% 0.58/0.84 % (2120368)------------------------------
% 0.58/0.84 % (2120368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.58/0.84 % (2120368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.84 % (2120368)CaDiCaL version: 2.1.3
% 0.58/0.84 % (2120368)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.84 % (2120368)Time elapsed: 0.001 s
% 0.58/0.84 % (2120368)Peak memory usage: 88 MB
% 0.58/0.84 % (2120368)Instructions burned: 2 (million)
% 0.58/0.84 % (2120367)First to succeed.
% 0.58/0.84 % (2120367)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2120357"
% 0.58/0.84 % (2120365)Instruction limit reached!
% 0.58/0.84 % (2120365)------------------------------
% 0.58/0.84 % (2120365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.58/0.84 % (2120365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.84 % (2120365)CaDiCaL version: 2.1.3
% 0.58/0.84 % (2120365)Termination reason: Instruction limit
% 0.58/0.84 % (2120365)Termination phase: Saturation
% 0.58/0.84 % (2120365)Time elapsed: 0.028 s
% 0.58/0.84 % (2120365)Peak memory usage: 88 MB
% 0.58/0.84 % (2120365)Instructions burned: 111 (million)
% 0.58/0.84 % (2120366)Instruction limit reached!
% 0.58/0.84 % (2120366)------------------------------
% 0.58/0.84 % (2120366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.58/0.84 % (2120366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.84 % (2120366)CaDiCaL version: 2.1.3
% 0.58/0.84 % (2120366)Termination reason: Instruction limit
% 0.58/0.84 % (2120366)Termination phase: Saturation
% 0.58/0.84 % (2120366)Time elapsed: 0.035 s
% 0.58/0.84 % (2120366)Peak memory usage: 89 MB
% 0.58/0.84 % (2120366)Instructions burned: 115 (million)
% 0.58/0.84 % (2120376)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1967966478:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.58/0.84 % (2120368)------------------------------
% 0.58/0.84 % (2120368)------------------------------
% 0.58/0.84 % (2120367)Refutation found. Thanks to Tanya!
% 0.58/0.84 % SZS status Unsatisfiable for theBenchmark
% 0.58/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.39/0.94 % (2120367)------------------------------
% 2.39/0.94 % (2120367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/0.94 % (2120367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.94 % (2120367)CaDiCaL version: 2.1.3
% 2.39/0.94 % (2120367)Termination reason: Refutation
% 2.39/0.94 % (2120367)Time elapsed: 0.009 s
% 2.39/0.94 % (2120367)Peak memory usage: 89 MB
% 2.39/0.94 % (2120367)Instructions burned: 24 (million)
% 2.39/0.94 % (2120367)------------------------------
% 2.39/0.94 % (2120367)------------------------------
% 2.39/0.94 % (2120357)Success in time 0.305 s
% 2.39/0.94 % Vampire exiting
%------------------------------------------------------------------------------