%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP310-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 10:17:27 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.46s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 43
% Syntax : Number of formulae : 268 ( 26 unt; 15 def)
% Number of atoms : 887 ( 268 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1153 ( 534 ~; 604 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = inverse(sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f24]) ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f34]) ).
fof(f38,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c8 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c8
| multiply(sk_c8,X0) != sk_c7
| multiply(X1,sk_c8) != X0
| inverse(X1) != sk_c8
| 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/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,X0)
| multiply(X1,sk_c8) != X0
| sk_c8 != inverse(X1)
| 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,[],[f56]) ).
fof(f58,plain,
! [X2,X3,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| 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(equality_resolution,[],[f57]) ).
fof(f59,plain,
! [X2,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| 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,[],[f58]) ).
fof(f61,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(f62,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f65,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,definition,
( spl0_3
<=> sk_c8 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f68,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( sk_c8 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_4
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f72,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( sk_c6 != inverse(sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl0_5
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f76,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
( spl0_1
| spl0_2
| spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f59,f75,f71,f67,f61,f64,f61]) ).
fof(f80,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f82,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f86,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f55,f84,f80]) ).
fof(f89,definition,
( spl0_8
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f91,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f53,f84,f89]) ).
fof(f94,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f96,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f51,f84,f94]) ).
fof(f99,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f101,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f49,f84,f99]) ).
fof(f104,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| spl0_11 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f106,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f47,f84,f104]) ).
fof(f109,definition,
( spl0_12
<=> sk_c2 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f111,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f45,f109,f80]) ).
fof(f113,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f43,f109,f89]) ).
fof(f114,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f41,f109,f94]) ).
fof(f115,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f39,f109,f99]) ).
fof(f118,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f120,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f35,f118,f80]) ).
fof(f122,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f33,f118,f89]) ).
fof(f123,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f31,f118,f94]) ).
fof(f124,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f29,f118,f99]) ).
fof(f126,plain,
( spl0_6
| spl0_3 ),
inference(avatar_split_clause,[],[f25,f67,f80]) ).
fof(f127,plain,
( spl0_8
| spl0_3 ),
inference(avatar_split_clause,[],[f23,f67,f89]) ).
fof(f128,plain,
( spl0_9
| spl0_3 ),
inference(avatar_split_clause,[],[f21,f67,f94]) ).
fof(f129,plain,
( spl0_10
| spl0_3 ),
inference(avatar_split_clause,[],[f19,f67,f99]) ).
fof(f130,plain,
( spl0_11
| spl0_3 ),
inference(avatar_split_clause,[],[f17,f67,f104]) ).
fof(f131,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f15,f71,f80]) ).
fof(f132,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f13,f71,f89]) ).
fof(f133,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f11,f71,f94]) ).
fof(f134,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f9,f71,f99]) ).
fof(f135,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f7,f71,f104]) ).
fof(f136,plain,
spl0_5,
inference(avatar_split_clause,[],[f5,f75]) ).
fof(f137,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f82]) ).
fof(f138,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f101]) ).
fof(f141,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f106]) ).
fof(f146,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f141,f1]) ).
fof(f149,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f137]) ).
fof(f150,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f149,f1]) ).
fof(f153,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f150,f91]) ).
fof(f160,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f96,f153]) ).
fof(f166,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f76,f160]) ).
fof(f219,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f146,f3]) ).
fof(f220,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f146,f146]) ).
fof(f224,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f146,f76]) ).
fof(f225,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f146,f138]) ).
fof(f226,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f146,f153]) ).
fof(f231,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f146,f106]) ).
fof(f240,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f231,f160]) ).
fof(f244,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f226,f3]) ).
fof(f248,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f219,f220]) ).
fof(f249,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f240,f101]) ).
fof(f255,plain,
( ! [X0] : multiply(X0,sk_c5) = X0
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f248,f244]) ).
fof(f259,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f144,f249]) ).
fof(f260,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f146,f249]) ).
fof(f262,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f260,f3]) ).
fof(f263,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f259,f160]) ).
fof(f265,plain,
( sk_c6 = multiply(sk_c3,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f263,f166]) ).
fof(f266,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f265,f106]) ).
fof(f267,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f266,f160]) ).
fof(f269,plain,
( sk_c8 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f244,f262]) ).
fof(f271,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1,f262]) ).
fof(f288,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f255,f269]) ).
fof(f297,plain,
( identity = inverse(sk_c5)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f3,f255]) ).
fof(f303,plain,
( sk_c5 = multiply(sk_c8,sk_c4)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f150,f255]) ).
fof(f304,plain,
( sk_c5 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f303,f271]) ).
fof(f309,plain,
( identity = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f297,f269]) ).
fof(f312,plain,
( sk_c8 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f304,f269]) ).
fof(f313,plain,
( inverse(sk_c8) = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f309,f244]) ).
fof(f315,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f313,f269]) ).
fof(f371,plain,
( sk_c8 != sk_c6
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f73,f315]) ).
fof(f376,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f371,f267]) ).
fof(f377,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f376]) ).
fof(f383,plain,
( sk_c8 != multiply(sk_c6,sk_c8)
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f69,f160]) ).
fof(f385,plain,
( sk_c8 != sk_c6
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f383,f288]) ).
fof(f386,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f385,f267]) ).
fof(f387,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f388,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f62,f271]) ).
fof(f389,plain,
( sk_c8 = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f68,f160]) ).
fof(f390,plain,
( ! [X4] :
( sk_c7 != X4
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f388,f288]) ).
fof(f392,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != X4 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f390,f160]) ).
fof(f393,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f392,f82]) ).
fof(f400,plain,
( sk_c8 != sk_c4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f393]) ).
fof(f403,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f400,f312]) ).
fof(f404,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f405,plain,
( ! [X2] :
( sk_c7 != X2
| sk_c8 != inverse(X2) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f65,f288]) ).
fof(f406,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != X2 )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f405,f160]) ).
fof(f419,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c4
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f406,f82]) ).
fof(f426,plain,
( sk_c8 != sk_c4
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f419]) ).
fof(f429,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f426,f312]) ).
fof(f430,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f429]) ).
fof(f431,plain,
( sk_c8 != multiply(sk_c3,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_11 ),
inference(forward_demodulation,[],[f105,f160]) ).
fof(f444,plain,
( sk_c3 = multiply(sk_c6,identity)
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f225,f72]) ).
fof(f446,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f72]) ).
fof(f448,plain,
( sk_c3 = multiply(sk_c6,sk_c5)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f444,f244]) ).
fof(f450,plain,
( sk_c6 = sk_c3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f448,f255]) ).
fof(f465,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_7 ),
inference(superposition,[],[f3,f86]) ).
fof(f473,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(sk_c2,X0)
| ~ spl0_12 ),
inference(superposition,[],[f4,f111]) ).
fof(f489,plain,
( sk_c8 != multiply(sk_c6,sk_c8)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_11 ),
inference(superposition,[],[f431,f450]) ).
fof(f490,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f489,f389]) ).
fof(f491,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_11 ),
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f493,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f224,f72]) ).
fof(f512,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f146,f120]) ).
fof(f514,plain,
( multiply(sk_c6,sk_c7) = sk_c2
| ~ spl0_4
| ~ spl0_13 ),
inference(forward_demodulation,[],[f512,f72]) ).
fof(f516,plain,
( sk_c8 = sk_c2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_13 ),
inference(forward_demodulation,[],[f514,f68]) ).
fof(f521,plain,
( identity != sk_c7
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2 ),
inference(superposition,[],[f65,f3]) ).
fof(f537,plain,
( sk_c8 = multiply(inverse(sk_c6),identity)
| ~ spl0_4 ),
inference(superposition,[],[f146,f446]) ).
fof(f540,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f537,f248]) ).
fof(f542,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_7 ),
inference(superposition,[],[f146,f465]) ).
fof(f552,plain,
( multiply(sk_c2,sk_c7) = multiply(sk_c1,sk_c6)
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f473,f76]) ).
fof(f556,plain,
( multiply(sk_c1,identity) = multiply(sk_c2,sk_c1)
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f473,f465]) ).
fof(f621,plain,
( sk_c7 != multiply(sk_c8,sk_c2)
| sk_c8 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f62,f111]) ).
fof(f624,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f621,f120]) ).
fof(f630,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f624,f86]) ).
fof(f631,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f644,definition,
( spl0_16
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f648,definition,
( spl0_17
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f650,plain,
( identity != sk_c7
| spl0_17 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f652,plain,
( sk_c8 != inverse(sk_c6)
| identity != sk_c7
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f521,f72]) ).
fof(f653,plain,
( spl0_16
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f540,f71,f644]) ).
fof(f654,plain,
( inverse(sk_c8) = sk_c1
| ~ spl0_7 ),
inference(forward_demodulation,[],[f542,f248]) ).
fof(f655,plain,
( multiply(sk_c8,sk_c1) = multiply(sk_c1,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f556,f516]) ).
fof(f656,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c1,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f552,f516]) ).
fof(f659,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f652,f71,f64,f644,f648]) ).
fof(f660,plain,
( sk_c6 = sk_c1
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f654,f72]) ).
fof(f661,plain,
( sk_c1 = multiply(sk_c8,sk_c1)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f655,f248]) ).
fof(f662,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f656,f76]) ).
fof(f664,plain,
( sk_c6 = multiply(sk_c8,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f661,f660]) ).
fof(f665,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f662,f660]) ).
fof(f667,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f665,f493]) ).
fof(f678,plain,
( identity = multiply(sk_c8,sk_c6)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f465,f660]) ).
fof(f683,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f678,f664]) ).
fof(f686,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f683,f667]) ).
fof(f688,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f686,f650]) ).
fof(f689,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f688]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f78]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f92]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f97]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f102]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s9,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s10,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f114]) ).
cnf(s11,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s13,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s14,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s15,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s16,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s18,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f126]) ).
cnf(s19,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f127]) ).
cnf(s20,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f128]) ).
cnf(s21,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f129]) ).
cnf(s22,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f130]) ).
cnf(s23,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f131]) ).
cnf(s24,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f132]) ).
cnf(s25,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f133]) ).
cnf(s26,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f134]) ).
cnf(s27,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f135]) ).
cnf(s28,plain,
spl0_5,
inference(sat_conversion,[],[f136]) ).
cnf(s29,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f377]) ).
cnf(s30,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f387]) ).
cnf(s33,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f404]) ).
cnf(s36,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f430]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f491]) ).
cnf(s43,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f631]) ).
cnf(s48,plain,
( ~ spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f653]) ).
cnf(s49,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f659]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f689]) ).
cnf(s51,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(rat,[],[s2,s28]) ).
cnf(s52,plain,
spl0_3,
inference(rat,[],[s30,s18,s19,s20,s21,s22,s28]) ).
cnf(s53,plain,
spl0_4,
inference(rat,[],[s29,s23,s24,s25,s26,s27,s28]) ).
cnf(s54,plain,
spl0_16,
inference(rat,[],[s48,s53]) ).
cnf(s55,plain,
( spl0_7
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s36,s4,s5,s6,s7]) ).
cnf(s56,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(rat,[],[s37,s36,s53,s52]) ).
cnf(s57,plain,
( spl0_10
| ~ spl0_7
| spl0_17 ),
inference(rat,[],[s50,s11,s16,s28,s52,s53]) ).
cnf(s58,plain,
( spl0_9
| ~ spl0_7
| spl0_17 ),
inference(rat,[],[s50,s10,s15,s28,s52,s53]) ).
cnf(s59,plain,
( ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s50,s9,s14,s56,s58,s57,s55,s49,s28,s52,s53,s54]) ).
cnf(s60,plain,
~ spl0_2,
inference(rat,[],[s50,s3,s8,s13,s59,s49,s28,s52,s53,s54]) ).
cnf(s61,plain,
spl0_1,
inference(rat,[],[s51,s52,s53,s60]) ).
cnf(s62,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_6 ),
inference(rat,[],[s37,s33,s61,s53,s52]) ).
cnf(s63,plain,
spl0_10,
inference(rat,[],[s43,s6,s11,s16,s61]) ).
cnf(s65,plain,
spl0_9,
inference(rat,[],[s43,s5,s10,s15,s61]) ).
cnf(s66,plain,
spl0_8,
inference(rat,[],[s43,s4,s9,s14,s61]) ).
cnf(s67,plain,
~ spl0_6,
inference(rat,[],[s62,s65,s63,s66]) ).
cnf(s68,plain,
spl0_13,
inference(rat,[],[s13,s67]) ).
cnf(s69,plain,
spl0_12,
inference(rat,[],[s8,s67]) ).
cnf(s70,plain,
spl0_7,
inference(rat,[],[s3,s67]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s43,s68,s61,s69,s70]) ).
fof(f690,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP310-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:55:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.46 % (3314834)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (3314841)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2019518285:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (3314840)% WARNING: option uhcvi not known.
% 0.10/0.46 % (3314842)dis+10_1_sil=32000:sp=arity:random_seed=1990040200:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (3314839)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4053768653_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (3314843)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3286440277:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (3314844)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=81779592:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (3314845)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2558878898:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % (3314840)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3370591381:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % TRYING [4]
% 0.10/0.46 % (3314842) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3314834-3314842"...
% 0.10/0.46 % (3314843) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3314834-3314843"...
% 0.10/0.46 % (3314844) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3314834-3314844"...
% 0.10/0.46 % TRYING [5]
% 0.10/0.46 % (3314842)...printing done.
% 0.10/0.46 % (3314843)...printing done.
% 0.10/0.46 % (3314843)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.45/0.46 % (3314843)------------------------------
% 0.45/0.46 % (3314843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.46 % (3314843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.46 % (3314843)CaDiCaL version: 2.1.3
% 0.45/0.46 % (3314843)Termination reason: Refutation
% 0.45/0.46 % (3314843)Time elapsed: 0.015 s
% 0.45/0.46 % (3314843)Peak memory usage: 12 MB
% 0.45/0.46 % (3314843)Instructions burned: 23 (million)
% 0.45/0.46 % (3314834)Success in time 0.049 s
% 0.45/0.46 % Vampire exiting
%------------------------------------------------------------------------------