%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP372-1 : 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 : n011.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 10:17:37 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 53
% Syntax : Number of formulae : 326 ( 24 unt; 16 def)
% Number of atoms : 1095 ( 320 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1430 ( 661 ~; 753 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c8) = sk_c7
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f30,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c8 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f38]) ).
fof(f42,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c7 = inverse(sk_c2)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c7 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c8) != sk_c7
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,sk_c6)
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f76]) ).
fof(f78,plain,
! [X2,X0,X1,X4] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,sk_c6)
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f77]) ).
fof(f80,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f81,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f84,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl0_3
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f87,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl0_4
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( sk_c7 != multiply(sk_c8,sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_6
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f98,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( inverse(sk_c8) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f78,f97,f83,f93,f90,f86,f83,f80]) ).
fof(f102,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f104,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f106,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f108,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f75,f106,f102]) ).
fof(f111,definition,
( spl0_9
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f113,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f73,f106,f111]) ).
fof(f116,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f118,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f71,f106,f116]) ).
fof(f121,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f123,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f69,f106,f121]) ).
fof(f126,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f67,f106,f126]) ).
fof(f130,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f65,f106,f86]) ).
fof(f132,definition,
( spl0_13
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f134,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f63,f132,f102]) ).
fof(f136,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f61,f132,f111]) ).
fof(f137,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f59,f132,f116]) ).
fof(f138,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f57,f132,f121]) ).
fof(f139,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f55,f132,f126]) ).
fof(f140,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f53,f132,f86]) ).
fof(f141,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f51,f93,f102]) ).
fof(f142,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f49,f93,f111]) ).
fof(f143,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f47,f93,f116]) ).
fof(f144,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f45,f93,f121]) ).
fof(f145,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f43,f93,f126]) ).
fof(f148,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f39,f148,f102]) ).
fof(f152,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f148,f111]) ).
fof(f153,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f35,f148,f116]) ).
fof(f154,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f33,f148,f121]) ).
fof(f155,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f31,f148,f126]) ).
fof(f158,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f160,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f27,f158,f102]) ).
fof(f162,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f25,f158,f111]) ).
fof(f163,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f23,f158,f116]) ).
fof(f164,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f21,f158,f121]) ).
fof(f165,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f19,f158,f126]) ).
fof(f167,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f15,f97,f102]) ).
fof(f168,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f13,f97,f111]) ).
fof(f169,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f11,f97,f116]) ).
fof(f170,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f9,f97,f121]) ).
fof(f171,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f7,f97,f126]) ).
fof(f172,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f5,f97,f86]) ).
fof(f173,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f3,f104]) ).
fof(f177,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f180,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f128]) ).
fof(f182,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f177,f1]) ).
fof(f185,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f173]) ).
fof(f186,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f185,f1]) ).
fof(f189,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f186,f113]) ).
fof(f196,plain,
( sk_c8 = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f118,f189]) ).
fof(f202,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f87,f196]) ).
fof(f210,plain,
( multiply(sk_c3,identity) = multiply(sk_c7,sk_c4)
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f180,f173]) ).
fof(f213,plain,
( multiply(sk_c8,sk_c4) = multiply(sk_c3,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f210,f196]) ).
fof(f222,plain,
( identity = multiply(sk_c3,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f213,f173]) ).
fof(f255,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f182,f3]) ).
fof(f256,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f182,f182]) ).
fof(f262,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f182,f189]) ).
fof(f267,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f182,f128]) ).
fof(f276,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f267,f196]) ).
fof(f280,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f262,f3]) ).
fof(f284,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f255,f256]) ).
fof(f285,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f276,f123]) ).
fof(f291,plain,
( ! [X0] : multiply(X0,sk_c5) = X0
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f284,f280]) ).
fof(f295,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f180,f285]) ).
fof(f296,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f182,f285]) ).
fof(f298,plain,
( identity = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f296,f3]) ).
fof(f299,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f295,f196]) ).
fof(f301,plain,
( sk_c6 = multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f299,f202]) ).
fof(f302,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f301,f128]) ).
fof(f303,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f302,f196]) ).
fof(f305,plain,
( sk_c8 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f280,f298]) ).
fof(f307,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1,f298]) ).
fof(f314,plain,
( sk_c7 != multiply(sk_c8,sk_c8)
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f95,f303]) ).
fof(f315,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f314,f202]) ).
fof(f316,plain,
( sk_c8 != sk_c7
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f315,f303]) ).
fof(f317,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f316,f196]) ).
fof(f318,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f319,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f94,f307]) ).
fof(f320,plain,
( sk_c8 != inverse(sk_c8)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f99,f196]) ).
fof(f336,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f291,f305]) ).
fof(f339,plain,
( identity = inverse(sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f291,f3]) ).
fof(f359,plain,
( identity = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f339,f305]) ).
fof(f362,plain,
( inverse(sk_c8) = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f359,f280]) ).
fof(f364,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f362,f305]) ).
fof(f367,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f364,f320]) ).
fof(f368,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f367]) ).
fof(f375,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f319,f196]) ).
fof(f382,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f267,f123]) ).
fof(f387,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_6 ),
inference(superposition,[],[f3,f98]) ).
fof(f389,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f108]) ).
fof(f397,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c7,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f134]) ).
fof(f399,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f182,f160]) ).
fof(f401,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f399,f150]) ).
fof(f402,plain,
( sk_c8 = multiply(inverse(sk_c7),identity)
| ~ spl0_6 ),
inference(superposition,[],[f182,f387]) ).
fof(f405,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f402,f284]) ).
fof(f407,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f3,f405]) ).
fof(f408,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f407,f382]) ).
fof(f409,plain,
( sk_c2 = multiply(inverse(sk_c7),identity)
| ~ spl0_8 ),
inference(superposition,[],[f182,f389]) ).
fof(f412,plain,
( sk_c2 = inverse(sk_c7)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f409,f284]) ).
fof(f413,plain,
( sk_c8 = sk_c2
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f412,f405]) ).
fof(f415,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f134,f413]) ).
fof(f417,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f415,f88]) ).
fof(f418,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f422,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1,f408]) ).
fof(f426,plain,
( sk_c7 != multiply(sk_c8,identity)
| sk_c8 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f81,f387]) ).
fof(f427,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f81,f128]) ).
fof(f434,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f427,f422]) ).
fof(f435,plain,
( sk_c7 != multiply(sk_c8,identity)
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f426,f405]) ).
fof(f442,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f434,f123]) ).
fof(f443,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f449,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f407,f401]) ).
fof(f450,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f87,f401]) ).
fof(f459,definition,
( spl0_17
<=> sk_c7 = multiply(sk_c8,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f460,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f472,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f435,f284]) ).
fof(f477,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f94,f450]) ).
fof(f478,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f477,f158,f148,f93,f86,f459]) ).
fof(f491,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f1,f449]) ).
fof(f511,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c2,identity)
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f397,f387]) ).
fof(f512,plain,
( multiply(sk_c2,identity) = multiply(sk_c6,sk_c2)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f397,f389]) ).
fof(f517,plain,
( multiply(sk_c8,identity) = multiply(sk_c6,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f512,f413]) ).
fof(f518,plain,
( sk_c2 = multiply(sk_c6,sk_c8)
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f511,f284]) ).
fof(f522,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c8,identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f517,f450]) ).
fof(f523,plain,
( sk_c2 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f518,f450]) ).
fof(f525,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f522,f491]) ).
fof(f526,plain,
( sk_c7 = sk_c2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f523,f460]) ).
fof(f527,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f525,f460]) ).
fof(f528,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f526,f413]) ).
fof(f529,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f527,f449]) ).
fof(f543,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f529,f472]) ).
fof(f544,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f580,plain,
( identity != sk_c7
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2 ),
inference(superposition,[],[f84,f3]) ).
fof(f583,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f84,f160]) ).
fof(f584,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f583]) ).
fof(f586,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f584,f150]) ).
fof(f587,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f604,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f91,f528]) ).
fof(f605,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c8)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f604,f450]) ).
fof(f606,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f605,f528]) ).
fof(f613,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f606,f3]) ).
fof(f621,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f613,f449]) ).
fof(f629,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f621,f98]) ).
fof(f632,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f629,f405]) ).
fof(f633,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f642,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f222,f284]) ).
fof(f652,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f91,f196]) ).
fof(f663,plain,
( ! [X1] :
( sk_c6 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f652,f336]) ).
fof(f687,plain,
( sk_c8 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f642,f298]) ).
fof(f688,plain,
( ! [X1] :
( sk_c8 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f663,f375]) ).
fof(f703,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != X1 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f688,f196]) ).
fof(f742,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f703,f123]) ).
fof(f745,plain,
( sk_c8 != sk_c3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f742]) ).
fof(f750,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f745,f687]) ).
fof(f751,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f750]) ).
fof(f759,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f580,f196]) ).
fof(f771,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f759,f298]) ).
fof(f775,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f771,f98]) ).
fof(f778,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f775,f405]) ).
fof(f779,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f778]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f100]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f109]) ).
cnf(s4,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f114]) ).
cnf(s5,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f119]) ).
cnf(s6,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f124]) ).
cnf(s7,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s8,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f130]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s10,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s11,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s12,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s13,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s14,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s15,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f141]) ).
cnf(s16,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f142]) ).
cnf(s17,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f143]) ).
cnf(s18,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f144]) ).
cnf(s19,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f145]) ).
cnf(s21,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s22,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s23,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s24,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s25,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s27,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s28,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f162]) ).
cnf(s29,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s30,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s31,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s33,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f167]) ).
cnf(s34,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f168]) ).
cnf(s35,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f169]) ).
cnf(s36,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f170]) ).
cnf(s37,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f171]) ).
cnf(s38,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f172]) ).
cnf(s39,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f318]) ).
cnf(s41,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f368]) ).
cnf(s43,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f418]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f443]) ).
cnf(s48,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f478]) ).
cnf(s52,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f544]) ).
cnf(s58,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f587]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f633]) ).
cnf(s72,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f751]) ).
cnf(s80,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f779]) ).
cnf(s81,plain,
spl0_3,
inference(rat,[],[s43,s8,s14,s38]) ).
cnf(s82,plain,
spl0_6,
inference(rat,[],[s41,s33,s34,s35,s36,s37]) ).
cnf(s83,plain,
spl0_5,
inference(rat,[],[s39,s15,s16,s17,s18,s19,s81]) ).
cnf(s84,plain,
( spl0_12
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s67,s48,s13,s25,s31,s81,s82,s83]) ).
cnf(s85,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s67,s48,s12,s24,s30,s81,s82,s83]) ).
cnf(s86,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s67,s48,s11,s23,s29,s81,s82,s83]) ).
cnf(s87,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s67,s48,s10,s22,s28,s72,s86,s85,s84,s81,s82,s83]) ).
cnf(s88,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s72,s4,s5,s6,s7,s87,s83]) ).
cnf(s89,plain,
~ spl0_4,
inference(rat,[],[s67,s48,s3,s9,s21,s27,s88,s81,s82,s83]) ).
cnf(s90,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s58,s25,s31]) ).
cnf(s91,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s58,s24,s30]) ).
cnf(s92,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s58,s23,s29]) ).
cnf(s93,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s58,s22,s28]) ).
cnf(s94,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_2
| ~ spl0_10 ),
inference(rat,[],[s58,s21,s27,s80,s82]) ).
cnf(s95,plain,
~ spl0_2,
inference(rat,[],[s94,s93,s92,s91,s90]) ).
cnf(s96,plain,
spl0_1,
inference(rat,[],[s2,s82,s81,s83,s89,s95]) ).
cnf(s97,plain,
spl0_12,
inference(rat,[],[s52,s48,s7,s13,s25,s31,s96,s81,s82,s83]) ).
cnf(s98,plain,
~ spl0_11,
inference(rat,[],[s45,s96,s82,s97]) ).
cnf(s99,plain,
spl0_15,
inference(rat,[],[s30,s98]) ).
cnf(s100,plain,
spl0_14,
inference(rat,[],[s24,s98]) ).
cnf(s101,plain,
spl0_13,
inference(rat,[],[s12,s98]) ).
cnf(s102,plain,
spl0_8,
inference(rat,[],[s6,s98]) ).
cnf(s103,plain,
spl0_17,
inference(rat,[],[s48,s83,s99,s81,s100]) ).
cnf(s105,plain,
$false,
inference(rat,[],[s52,s103,s99,s100,s82,s81,s96,s101,s102]) ).
fof(f780,plain,
$false,
inference(avatar_sat_refutation,[],[s105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP372-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:59:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 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
% 0.10/0.43 % (2163534)Will run a generic schedule for satisfiability detection.
% 0.10/0.43 % (2163543)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=387885263:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.43 % (2163540)% WARNING: option uhcvi not known.
% 0.10/0.43 % (2163539)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=169284104_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.43 % (2163540)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=200264038:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.43 % (2163541)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2370277533:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.43 % (2163542)dis+10_1_sil=32000:sp=arity:random_seed=3732640161:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.43 % (2163544)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2793245606:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.43 % (2163543) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2163534-2163543"...
% 0.10/0.43 % (2163545)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4062283591:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.43 % (2163543)...printing done.
% 0.10/0.43 % TRYING [1]
% 0.10/0.43 % TRYING [2]
% 0.10/0.43 % (2163543)Refutation found. Thanks to Tanya!
% 0.10/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (2163543)------------------------------
% 0.10/0.44 % (2163543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (2163543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (2163543)CaDiCaL version: 2.1.3
% 0.10/0.44 % (2163543)Termination reason: Refutation
% 0.10/0.44 % (2163543)Time elapsed: 0.009 s
% 0.10/0.44 % (2163543)Peak memory usage: 12 MB
% 0.10/0.44 % (2163543)Instructions burned: 25 (million)
% 0.10/0.44 % (2163534)Success in time 0.037 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------