%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP250-1 : 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 : n006.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 10:17:17 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 53
% Syntax : Number of formulae : 296 ( 19 unt; 18 def)
% Number of atoms : 818 ( 280 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 950 ( 428 ~; 504 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 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 : 40 ( 0 sgn 40 !; 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(f9,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
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_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c7 = 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(f20,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c9 = inverse(sk_c1)
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f20]) ).
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_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f26]) ).
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_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c7 = 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(f48,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c8 = 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_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c8 = 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_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f72]) ).
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_c8
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(X5) != sk_c7
| multiply(X5,sk_c8) != sk_c7 ),
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_c8 != inverse(X2)
| sk_c8 != 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_c7 != inverse(X5)
| sk_c7 != multiply(X5,sk_c8) ),
inference(reorient_equations,[],[f76]) ).
fof(f79,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != inverse(X5)
| sk_c7 != multiply(X5,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f80,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c8)
| sk_c7 != 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_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f89,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c7)
| sk_c8 != 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_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_6
<=> sk_c8 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f98,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f101,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = 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(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(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_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f128,plain,
( sk_c8 = 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(f138,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f51,f136,f92]) ).
fof(f140,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f49,f136,f101]) ).
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(f158,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f27,f156,f92]) ).
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(f162,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f21,f156,f111]) ).
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(f172,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f9,f166,f111]) ).
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(f182,plain,
( ~ spl0_8
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f177,f111,f82,f106]) ).
fof(f183,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f83,f148]) ).
fof(f184,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f183]) ).
fof(f185,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f184,f138]) ).
fof(f186,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f187,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f80,f94]) ).
fof(f189,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f80,f148]) ).
fof(f190,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f189]) ).
fof(f192,plain,
( sk_c7 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f187]) ).
fof(f194,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f192,f103]) ).
fof(f195,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f197,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f158]) ).
fof(f199,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_7 ),
inference(superposition,[],[f3,f103]) ).
fof(f201,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f128]) ).
fof(f208,definition,
( spl0_18
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f209,plain,
( identity = sk_c7
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f210,plain,
( identity != sk_c7
| spl0_18 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f213,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f222,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f213,f1]) ).
fof(f224,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c1,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f197]) ).
fof(f225,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c1,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f224,f1]) ).
fof(f234,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f225,f168]) ).
fof(f336,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_11 ),
inference(superposition,[],[f222,f123]) ).
fof(f338,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f222,f234]) ).
fof(f342,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f222,f148]) ).
fof(f352,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f342,f138]) ).
fof(f355,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f338,f3]) ).
fof(f357,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f336,f118]) ).
fof(f399,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f201,f355]) ).
fof(f406,plain,
( identity = sk_c3
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f399,f1]) ).
fof(f412,plain,
( sk_c8 = inverse(identity)
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f128,f406]) ).
fof(f413,plain,
( identity = inverse(identity)
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f412,f355]) ).
fof(f424,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_7
| ~ spl0_18 ),
inference(superposition,[],[f199,f209]) ).
fof(f427,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f424,f1]) ).
fof(f431,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c8 != multiply(X2,sk_c7) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f89,f355]) ).
fof(f432,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f431,f209]) ).
fof(f433,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f432,f355]) ).
fof(f435,plain,
( sk_c7 != multiply(identity,sk_c8)
| spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(superposition,[],[f93,f427]) ).
fof(f438,plain,
( sk_c8 != sk_c7
| spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f435,f1]) ).
fof(f440,plain,
( identity != sk_c8
| spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f438,f209]) ).
fof(f441,plain,
( $false
| spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f440,f355]) ).
fof(f442,plain,
( spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f441]) ).
fof(f446,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f433,f1]) ).
fof(f450,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f446]) ).
fof(f463,plain,
( ! [X3] :
( identity != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) )
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f86,f355]) ).
fof(f464,plain,
( identity != sk_c8
| sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f463,f168]) ).
fof(f478,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f464,f355]) ).
fof(f479,plain,
( $false
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f478,f158]) ).
fof(f480,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f488,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f190,f138]) ).
fof(f499,plain,
( identity != sk_c8
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f488,f209]) ).
fof(f508,plain,
( $false
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f499,f355]) ).
fof(f509,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f530,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f413,f450]) ).
fof(f531,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f532,plain,
( identity = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f103,f209]) ).
fof(f533,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f94,f209]) ).
fof(f536,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f3,f108]) ).
fof(f537,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f532,f427]) ).
fof(f544,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f533,f427]) ).
fof(f545,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f544,f1]) ).
fof(f580,plain,
( ! [X3] :
( identity != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f86,f545]) ).
fof(f592,plain,
( identity != sk_c8
| sk_c9 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f580,f123]) ).
fof(f599,plain,
( sk_c9 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f592,f545]) ).
fof(f601,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f599,f118]) ).
fof(f602,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f603,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c8 != multiply(X2,sk_c7) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f89,f545]) ).
fof(f604,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f603,f209]) ).
fof(f605,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f604,f545]) ).
fof(f609,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(superposition,[],[f605,f3]) ).
fof(f611,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f609]) ).
fof(f613,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f611,f537]) ).
fof(f616,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f613,f537]) ).
fof(f617,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f616]) ).
fof(f623,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f89,f98]) ).
fof(f627,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f623]) ).
fof(f633,definition,
( spl0_27
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f634,plain,
( identity = sk_c8
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f648,plain,
( ~ spl0_12
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f627,f96,f88,f126]) ).
fof(f663,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f222,f352]) ).
fof(f666,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f663,f3]) ).
fof(f669,plain,
( $false
| ~ spl0_13
| ~ spl0_14
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f666,f210]) ).
fof(f670,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f672,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f222,f357]) ).
fof(f674,plain,
( identity = sk_c8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f672,f3]) ).
fof(f676,plain,
( spl0_27
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f674,f121,f116,f633]) ).
fof(f684,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_8
| ~ spl0_27 ),
inference(superposition,[],[f536,f634]) ).
fof(f685,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_27 ),
inference(forward_demodulation,[],[f684,f1]) ).
fof(f691,plain,
( sk_c7 = multiply(identity,sk_c8)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_27 ),
inference(superposition,[],[f113,f685]) ).
fof(f692,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_27 ),
inference(forward_demodulation,[],[f691,f1]) ).
fof(f702,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_27 ),
inference(forward_demodulation,[],[f692,f634]) ).
fof(f705,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| spl0_18
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f702,f210]) ).
fof(f706,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_18
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f705]) ).
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(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(s15,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s16,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
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(s27,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f159]) ).
cnf(s28,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f160]) ).
cnf(s29,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s30,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f162]) ).
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(s36,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f172]) ).
cnf(s37,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f173]) ).
cnf(s38,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f174]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f182]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f186]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f195]) ).
cnf(s51,plain,
( spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f442]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f480]) ).
cnf(s57,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f509]) ).
cnf(s58,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f531]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(sat_conversion,[],[f602]) ).
cnf(s63,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_18 ),
inference(sat_conversion,[],[f617]) ).
cnf(s67,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_12 ),
inference(sat_conversion,[],[f648]) ).
cnf(s68,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f670]) ).
cnf(s69,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_27 ),
inference(sat_conversion,[],[f676]) ).
cnf(s72,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_18
| ~ spl0_27 ),
inference(sat_conversion,[],[f706]) ).
cnf(s73,plain,
( spl0_5
| ~ spl0_4 ),
inference(rat,[],[s58,s68,s9,s15,s21,s27,s33]) ).
cnf(s74,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s63,s72,s69,s4,s5,s6,s7,s8,s73]) ).
cnf(s75,plain,
~ spl0_4,
inference(rat,[],[s63,s72,s69,s10,s11,s12,s13,s14,s67,s74,s73]) ).
cnf(s77,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s54,s32,s38]) ).
cnf(s78,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s54,s31,s37]) ).
cnf(s79,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s54,s28,s34]) ).
cnf(s80,plain,
( spl0_16
| spl0_18
| ~ spl0_27 ),
inference(rat,[],[s72,s35,s36]) ).
cnf(s81,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s72,s29,s30,s54,s80,s69,s78,s77]) ).
cnf(s82,plain,
( ~ spl0_18
| ~ spl0_10
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11 ),
inference(rat,[],[s51,s27,s33,s61]) ).
cnf(s83,plain,
~ spl0_3,
inference(rat,[],[s82,s81,s79,s78,s77]) ).
cnf(s85,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s41,s18,s24]) ).
cnf(s86,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s41,s17,s23,s40]) ).
cnf(s87,plain,
~ spl0_2,
inference(rat,[],[s86,s85]) ).
cnf(s88,plain,
spl0_1,
inference(rat,[],[s2,s75,s83,s87]) ).
cnf(s89,plain,
spl0_7,
inference(rat,[],[s57,s68,s16,s22,s28,s34,s88]) ).
cnf(s90,plain,
~ spl0_5,
inference(rat,[],[s42,s88,s89]) ).
cnf(s91,plain,
spl0_16,
inference(rat,[],[s33,s90]) ).
cnf(s92,plain,
spl0_15,
inference(rat,[],[s27,s90]) ).
cnf(s93,plain,
spl0_14,
inference(rat,[],[s21,s90]) ).
cnf(s94,plain,
spl0_13,
inference(rat,[],[s15,s90]) ).
cnf(s97,plain,
~ spl0_18,
inference(rat,[],[s51,s89,s91,s90,s92]) ).
cnf(s98,plain,
$false,
inference(rat,[],[s68,s93,s97,s94]) ).
fof(f707,plain,
$false,
inference(avatar_sat_refutation,[],[s98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP250-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n006.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 09:42:55 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.48 % (2739395)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (2739408)dis+10_1_sil=32000:sp=arity:random_seed=166846695:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (2739406)% WARNING: option uhcvi not known.
% 0.16/0.48 % (2739408) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2739395-2739408"...
% 0.16/0.48 % (2739405)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=436333375_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (2739407)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=818257441:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (2739409)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1600987989:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (2739406)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2774181973:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (2739410)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=120247733:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (2739411)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=685318224:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (2739408)...printing done.
% 0.16/0.48 % (2739408)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (2739408)------------------------------
% 0.16/0.48 % (2739408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (2739408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (2739408)CaDiCaL version: 2.1.3
% 0.16/0.48 % (2739408)Termination reason: Refutation
% 0.16/0.48 % (2739408)Time elapsed: 0.009 s
% 0.16/0.48 % (2739408)Peak memory usage: 12 MB
% 0.16/0.48 % (2739408)Instructions burned: 24 (million)
% 0.16/0.48 % (2739395)Success in time 0.045 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------