%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP247-1 : 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 : n009.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 10:17:16 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 47
% Syntax : Number of formulae : 301 ( 20 unt; 16 def)
% Number of atoms : 866 ( 277 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1035 ( 470 ~; 549 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c9 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f18]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f24]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c9 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f38]) ).
fof(f44,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = inverse(sk_c2)
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f46]) ).
fof(f52,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c9 = inverse(sk_c3)
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c7) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(X5) != sk_c9
| multiply(X5,sk_c8) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c7)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X5,sk_c8) ),
inference(reorient_equations,[],[f76]) ).
fof(f79,definition,
( spl0_1
<=> ! [X5] :
( sk_c9 != inverse(X5)
| sk_c9 != multiply(X5,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f80,plain,
( ! [X5] :
( sk_c9 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_2
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f83,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_3
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f86,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f89,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c7)
| sk_c9 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f77,f85,f82,f88,f85,f82,f79]) ).
fof(f92,definition,
( spl0_5
<=> sk_c9 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_6
<=> sk_c9 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f98,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f75,f96,f92]) ).
fof(f101,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f103,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f73,f96,f101]) ).
fof(f106,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f107,plain,
( sk_c8 != inverse(sk_c5)
| spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f108,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f71,f96,f106]) ).
fof(f111,definition,
( spl0_9
<=> multiply(sk_c5,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f113,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f69,f96,f111]) ).
fof(f116,definition,
( spl0_10
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f118,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f67,f96,f116]) ).
fof(f121,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f122,plain,
( sk_c8 != multiply(sk_c4,sk_c9)
| spl0_11 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f65,f96,f121]) ).
fof(f126,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f127,plain,
( sk_c9 != inverse(sk_c3)
| spl0_12 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f128,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_5
| spl0_12 ),
inference(avatar_split_clause,[],[f63,f126,f92]) ).
fof(f130,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f61,f126,f101]) ).
fof(f131,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f59,f126,f106]) ).
fof(f132,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f57,f126,f111]) ).
fof(f133,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f55,f126,f116]) ).
fof(f134,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f53,f126,f121]) ).
fof(f136,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f137,plain,
( sk_c8 != inverse(sk_c2)
| spl0_13 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f138,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f141,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f47,f136,f106]) ).
fof(f142,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f45,f136,f111]) ).
fof(f146,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f148,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f39,f146,f92]) ).
fof(f150,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f146,f101]) ).
fof(f151,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f35,f146,f106]) ).
fof(f152,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f33,f146,f111]) ).
fof(f156,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f157,plain,
( sk_c9 != inverse(sk_c1)
| spl0_15 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f158,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f160,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f25,f156,f101]) ).
fof(f161,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f23,f156,f106]) ).
fof(f163,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f19,f156,f116]) ).
fof(f164,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f17,f156,f121]) ).
fof(f166,definition,
( spl0_16
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f168,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f169,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f15,f166,f92]) ).
fof(f170,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f13,f166,f101]) ).
fof(f171,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f11,f166,f106]) ).
fof(f173,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f8,f166,f116]) ).
fof(f174,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f6,f166,f121]) ).
fof(f176,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f83,f113]) ).
fof(f177,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f176]) ).
fof(f178,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f177,f108]) ).
fof(f179,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f178]) ).
fof(f190,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f83,f148]) ).
fof(f191,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f190]) ).
fof(f192,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f191,f138]) ).
fof(f193,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f194,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f89,f98]) ).
fof(f198,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f80,f94]) ).
fof(f201,plain,
( sk_c9 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f198]) ).
fof(f208,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f201,f103]) ).
fof(f209,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f211,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f158]) ).
fof(f212,plain,
( identity = multiply(sk_c9,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f118]) ).
fof(f213,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f3,f138]) ).
fof(f214,plain,
( identity = multiply(sk_c9,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f128]) ).
fof(f226,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f229,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c9,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f168]) ).
fof(f233,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c3,multiply(sk_c7,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f98]) ).
fof(f236,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f226,f1]) ).
fof(f238,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c1,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f211]) ).
fof(f239,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c1,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f238,f1]) ).
fof(f240,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c4,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f212]) ).
fof(f241,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c4,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f240,f1]) ).
fof(f252,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f239,f168]) ).
fof(f259,plain,
( multiply(sk_c8,sk_c3) = multiply(sk_c1,identity)
| ~ spl0_12
| ~ spl0_16 ),
inference(superposition,[],[f229,f214]) ).
fof(f264,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c9)
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f80,f252]) ).
fof(f268,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f264]) ).
fof(f357,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f236,f3]) ).
fof(f361,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c9),X0)
| ~ spl0_10 ),
inference(superposition,[],[f236,f241]) ).
fof(f368,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f236,f236]) ).
fof(f369,plain,
( sk_c1 = multiply(inverse(sk_c9),identity)
| ~ spl0_15 ),
inference(superposition,[],[f236,f211]) ).
fof(f372,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f236,f252]) ).
fof(f380,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_13 ),
inference(superposition,[],[f236,f213]) ).
fof(f381,plain,
( sk_c3 = multiply(inverse(sk_c9),identity)
| ~ spl0_12 ),
inference(superposition,[],[f236,f214]) ).
fof(f389,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f372,f3]) ).
fof(f397,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f357,f368]) ).
fof(f444,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(inverse(sk_c9),multiply(identity,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f369]) ).
fof(f445,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(sk_c4,multiply(identity,X0))
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f444,f361]) ).
fof(f448,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(sk_c4,X0)
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f445,f1]) ).
fof(f475,plain,
( multiply(sk_c1,sk_c9) != sk_c8
| ~ spl0_10
| spl0_11
| ~ spl0_15 ),
inference(forward_demodulation,[],[f122,f448]) ).
fof(f479,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f397,f389]) ).
fof(f480,plain,
( $false
| ~ spl0_10
| spl0_11
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f475,f168]) ).
fof(f481,plain,
( ~ spl0_10
| spl0_11
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f480]) ).
fof(f486,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f1,f389]) ).
fof(f496,plain,
( sk_c5 = sk_c7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f113,f479]) ).
fof(f497,plain,
( sk_c9 = sk_c6
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f94,f479]) ).
fof(f498,plain,
( sk_c7 = sk_c2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f148,f479]) ).
fof(f522,plain,
( sk_c8 != inverse(sk_c7)
| spl0_8
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f107,f496]) ).
fof(f524,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f380,f389]) ).
fof(f529,plain,
( identity = sk_c2
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f524,f3]) ).
fof(f531,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f529,f498]) ).
fof(f532,plain,
( sk_c8 = sk_c7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f531,f389]) ).
fof(f539,plain,
( sk_c1 = sk_c3
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f369,f381]) ).
fof(f551,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f138,f498]) ).
fof(f552,plain,
( $false
| spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f551,f522]) ).
fof(f553,plain,
( spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f552]) ).
fof(f557,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f108,f496]) ).
fof(f592,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_6
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f233,f539]) ).
fof(f596,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f592,f532]) ).
fof(f597,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c1,X0)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f596,f486]) ).
fof(f598,plain,
( multiply(sk_c8,sk_c3) = multiply(sk_c1,sk_c8)
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f259,f389]) ).
fof(f609,plain,
( multiply(sk_c8,sk_c3) = multiply(sk_c9,sk_c8)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f598,f597]) ).
fof(f614,plain,
( sk_c9 = multiply(sk_c8,sk_c3)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f609,f252]) ).
fof(f616,plain,
( sk_c9 = sk_c3
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f614,f486]) ).
fof(f623,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f98,f532]) ).
fof(f624,plain,
( sk_c9 = sk_c3
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f623,f479]) ).
fof(f645,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f128,f616]) ).
fof(f652,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f645,f268]) ).
fof(f653,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f652]) ).
fof(f658,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f103,f497]) ).
fof(f660,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f86,f168]) ).
fof(f663,plain,
( identity != sk_c8
| sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_3 ),
inference(superposition,[],[f86,f3]) ).
fof(f665,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f660]) ).
fof(f669,plain,
( $false
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f665,f158]) ).
fof(f670,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f680,plain,
( sk_c9 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f194]) ).
fof(f682,plain,
( ~ spl0_12
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f680,f96,f88,f126]) ).
fof(f697,plain,
( identity = multiply(sk_c9,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f118]) ).
fof(f701,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_6
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f127,f624]) ).
fof(f702,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f701,f658]) ).
fof(f703,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f702]) ).
fof(f738,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_7 ),
inference(superposition,[],[f3,f103]) ).
fof(f742,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f3,f108]) ).
fof(f744,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c9,X0)) = multiply(sk_c8,X0)
| ~ spl0_11 ),
inference(superposition,[],[f4,f123]) ).
fof(f751,plain,
( sk_c4 = multiply(inverse(sk_c9),identity)
| ~ spl0_10 ),
inference(superposition,[],[f236,f697]) ).
fof(f754,plain,
( sk_c4 = inverse(sk_c9)
| ~ spl0_10 ),
inference(forward_demodulation,[],[f751,f397]) ).
fof(f756,plain,
( multiply(sk_c1,identity) = multiply(sk_c8,sk_c6)
| ~ spl0_7
| ~ spl0_16 ),
inference(superposition,[],[f229,f738]) ).
fof(f761,plain,
( sk_c1 = multiply(sk_c8,sk_c6)
| ~ spl0_7
| ~ spl0_16 ),
inference(forward_demodulation,[],[f756,f397]) ).
fof(f774,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_8 ),
inference(superposition,[],[f236,f742]) ).
fof(f784,plain,
( identity = multiply(sk_c4,sk_c9)
| ~ spl0_10 ),
inference(superposition,[],[f3,f754]) ).
fof(f785,plain,
( identity = sk_c8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f784,f123]) ).
fof(f787,plain,
( multiply(sk_c4,identity) = multiply(sk_c8,sk_c6)
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f744,f738]) ).
fof(f792,plain,
( sk_c1 = multiply(sk_c4,identity)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f787,f761]) ).
fof(f795,plain,
( sk_c1 = sk_c4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f792,f397]) ).
fof(f800,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f118,f795]) ).
fof(f801,plain,
( $false
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f800,f157]) ).
fof(f802,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f801]) ).
fof(f808,plain,
( sk_c5 = inverse(sk_c8)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f774,f397]) ).
fof(f863,plain,
( sk_c8 != inverse(sk_c7)
| spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f137,f498]) ).
fof(f866,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f863,f557]) ).
fof(f867,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f866]) ).
fof(f914,plain,
( sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f663,f785]) ).
fof(f920,plain,
( sk_c9 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f914,f754]) ).
fof(f923,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f920,f118]) ).
fof(f924,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f923]) ).
fof(f929,plain,
( identity = multiply(sk_c5,sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f3,f808]) ).
fof(f930,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f929,f113]) ).
fof(f932,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f930,f785]) ).
fof(f938,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f89,f932]) ).
fof(f945,plain,
( spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f938,f121,f116,f111,f106,f88,f79]) ).
cnf(s1,plain,
( spl0_2
| spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f90]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f99]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f104]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f109]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f114]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f119]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f124]) ).
cnf(s9,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s10,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f130]) ).
cnf(s11,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f131]) ).
cnf(s12,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f132]) ).
cnf(s13,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s14,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f134]) ).
cnf(s17,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f141]) ).
cnf(s18,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f142]) ).
cnf(s21,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s22,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s23,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s24,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s28,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f160]) ).
cnf(s29,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s31,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s32,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s33,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f169]) ).
cnf(s34,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f170]) ).
cnf(s35,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f171]) ).
cnf(s37,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f173]) ).
cnf(s38,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f174]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f179]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f193]) ).
cnf(s44,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f209]) ).
cnf(s50,plain,
( ~ spl0_10
| spl0_11
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f481]) ).
cnf(s51,plain,
( spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f553]) ).
cnf(s52,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f653]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f670]) ).
cnf(s58,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_12 ),
inference(sat_conversion,[],[f682]) ).
cnf(s60,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f703]) ).
cnf(s64,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f802]) ).
cnf(s65,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f867]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f924]) ).
cnf(s68,plain,
( spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f945]) ).
cnf(s70,plain,
( spl0_12
| ~ spl0_4
| spl0_1 ),
inference(rat,[],[s68,s11,s12,s13,s14]) ).
cnf(s71,plain,
( ~ spl0_4
| spl0_1 ),
inference(rat,[],[s68,s5,s6,s7,s8,s58,s70]) ).
cnf(s73,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s54,s32,s38]) ).
cnf(s74,plain,
( ~ spl0_11
| ~ spl0_3 ),
inference(rat,[],[s54,s31,s37,s67]) ).
cnf(s75,plain,
~ spl0_3,
inference(rat,[],[s74,s73]) ).
cnf(s76,plain,
( spl0_11
| ~ spl0_10 ),
inference(rat,[],[s50,s32,s38]) ).
cnf(s77,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s41,s18,s24]) ).
cnf(s78,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s51,s17,s23,s29,s35,s39]) ).
cnf(s79,plain,
~ spl0_2,
inference(rat,[],[s78,s77]) ).
cnf(s80,plain,
spl0_1,
inference(rat,[],[s2,s71,s79,s75]) ).
cnf(s81,plain,
( spl0_9
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s52,s6,s12,s18,s24,s80]) ).
cnf(s82,plain,
spl0_14,
inference(rat,[],[s44,s21,s22,s80]) ).
cnf(s83,plain,
spl0_6,
inference(rat,[],[s44,s3,s4,s80]) ).
cnf(s84,plain,
( spl0_13
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s65,s17,s81,s82]) ).
cnf(s85,plain,
( ~ spl0_13
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s60,s9,s10,s52,s80,s82,s83]) ).
cnf(s86,plain,
( ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s85,s84]) ).
cnf(s87,plain,
spl0_16,
inference(rat,[],[s44,s33,s34,s80]) ).
cnf(s88,plain,
~ spl0_15,
inference(rat,[],[s86,s87]) ).
cnf(s91,plain,
spl0_7,
inference(rat,[],[s28,s88]) ).
cnf(s93,plain,
~ spl0_10,
inference(rat,[],[s64,s76,s91,s88,s87]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s31,s88,s93]) ).
fof(f946,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP247-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:43:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.17/0.46 % (1782278)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (1782294)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1542902195:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (1782291)% WARNING: option uhcvi not known.
% 0.17/0.46 % (1782295)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4028171817:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % (1782293)dis+10_1_sil=32000:sp=arity:random_seed=3560382964:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (1782290)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=557574951_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (1782296)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3660399322:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % (1782291)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3901957646:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (1782294) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1782278-1782294"...
% 0.17/0.46 % (1782292)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3195269958:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % TRYING [1]
% 0.17/0.46 % TRYING [2]
% 0.17/0.46 % (1782294)...printing done.
% 0.17/0.46 % (1782294)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (1782294)------------------------------
% 0.17/0.46 % (1782294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (1782294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (1782294)CaDiCaL version: 2.1.3
% 0.17/0.46 % (1782294)Termination reason: Refutation
% 0.17/0.46 % (1782294)Time elapsed: 0.012 s
% 0.17/0.46 % (1782294)Peak memory usage: 12 MB
% 0.17/0.46 % (1782294)Instructions burned: 31 (million)
% 0.17/0.46 % (1782278)Success in time 0.051 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------