%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP310-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:36 AM UTC 2026
% Result : Unsatisfiable 2.20s 1.18s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 39
% Syntax : Number of formulae : 260 ( 21 unt; 15 def)
% Number of atoms : 879 ( 260 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1172 ( 553 ~; 604 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 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 : 42 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f30,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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(f40,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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(f50,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ 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_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8) )
| ~ 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(f95,plain,
( sk_c7 != multiply(sk_c8,sk_c5)
| spl0_9 ),
inference(avatar_component_clause,[],[f94]) ).
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(f104,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[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(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(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(f143,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f96]) ).
fof(f144,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f106]) ).
fof(f145,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f91]) ).
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(f159,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f153,f96]) ).
fof(f167,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f144,f159]) ).
fof(f171,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c4,sk_c6)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f145,f76]) ).
fof(f181,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c5,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f171,f159]) ).
fof(f193,plain,
( identity = multiply(sk_c3,identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f167,f138]) ).
fof(f210,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c7,X0))
| ~ spl0_9 ),
inference(superposition,[],[f146,f143]) ).
fof(f211,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f146,f76]) ).
fof(f212,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f146,f138]) ).
fof(f214,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f146,f96]) ).
fof(f215,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_6 ),
inference(superposition,[],[f146,f137]) ).
fof(f216,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f146,f106]) ).
fof(f229,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f216,f159]) ).
fof(f230,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f214,f159]) ).
fof(f233,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f210,f159]) ).
fof(f235,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f229,f101]) ).
fof(f236,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f230,f3]) ).
fof(f237,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f233,f146]) ).
fof(f239,plain,
( sk_c5 = multiply(sk_c3,sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f193,f236]) ).
fof(f248,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f146,f235]) ).
fof(f250,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f248,f3]) ).
fof(f258,plain,
( sk_c5 = multiply(inverse(sk_c3),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f146,f239]) ).
fof(f261,plain,
( sk_c5 = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f258,f101]) ).
fof(f262,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f261,f96]) ).
fof(f263,plain,
( sk_c8 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f262,f159]) ).
fof(f272,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f212,f236]) ).
fof(f273,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f272,f263]) ).
fof(f274,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f273,f3]) ).
fof(f275,plain,
( sk_c8 = sk_c3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f274,f250]) ).
fof(f276,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f101,f275]) ).
fof(f287,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f215,f236]) ).
fof(f288,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f287,f263]) ).
fof(f289,plain,
( identity = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f288,f3]) ).
fof(f290,plain,
( sk_c5 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f289,f236]) ).
fof(f291,plain,
( sk_c8 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f290,f263]) ).
fof(f304,plain,
( sk_c8 != sk_c6
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f73,f276]) ).
fof(f317,plain,
( sk_c8 = multiply(sk_c4,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f181,f237]) ).
fof(f318,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f317,f291]) ).
fof(f320,plain,
( multiply(sk_c4,sk_c8) = multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f318]) ).
fof(f324,plain,
( sk_c6 = multiply(sk_c4,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f320,f237]) ).
fof(f326,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f324,f291]) ).
fof(f329,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f326,f235]) ).
fof(f330,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f329,f304]) ).
fof(f331,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f330]) ).
fof(f332,plain,
( sk_c8 != multiply(sk_c6,sk_c8)
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f69,f159]) ).
fof(f333,plain,
( sk_c8 = sk_c6
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f72,f276]) ).
fof(f338,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f332,f333]) ).
fof(f339,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f338,f235]) ).
fof(f340,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f341,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f62,f159]) ).
fof(f342,plain,
( sk_c8 = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f68,f159]) ).
fof(f344,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f341,f82]) ).
fof(f349,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f344]) ).
fof(f352,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f349,f150]) ).
fof(f353,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f359,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c8) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f65,f159]) ).
fof(f361,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f359,f82]) ).
fof(f366,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f361]) ).
fof(f371,plain,
( sk_c8 != sk_c5
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f366,f91]) ).
fof(f380,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f72]) ).
fof(f381,plain,
( sk_c5 = multiply(sk_c6,sk_c8)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f380,f236]) ).
fof(f383,definition,
( spl0_14
<=> sk_c8 = multiply(sk_c8,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f384,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f387,definition,
( spl0_15
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f388,plain,
( sk_c8 = sk_c6
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f393,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_7 ),
inference(superposition,[],[f3,f86]) ).
fof(f396,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_12 ),
inference(superposition,[],[f146,f111]) ).
fof(f398,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f396,f86]) ).
fof(f411,plain,
( sk_c8 = sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f381,f342]) ).
fof(f412,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f411,f371]) ).
fof(f413,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f412]) ).
fof(f414,plain,
( sk_c8 != sk_c7
| ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(forward_demodulation,[],[f95,f153]) ).
fof(f415,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f211,f72]) ).
fof(f423,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f146,f120]) ).
fof(f425,plain,
( multiply(sk_c6,sk_c7) = sk_c2
| ~ spl0_4
| ~ spl0_13 ),
inference(forward_demodulation,[],[f423,f72]) ).
fof(f426,plain,
( sk_c8 = sk_c2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_13 ),
inference(forward_demodulation,[],[f425,f68]) ).
fof(f431,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f65,f86]) ).
fof(f432,plain,
( sk_c7 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f431]) ).
fof(f435,plain,
( sk_c7 != sk_c2
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f432,f111]) ).
fof(f442,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f435,f426]) ).
fof(f451,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f398,f426]) ).
fof(f454,plain,
( spl0_14
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f451,f118,f109,f84,f71,f67,f383]) ).
fof(f456,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_14 ),
inference(superposition,[],[f146,f384]) ).
fof(f458,plain,
( identity = sk_c8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f456,f3]) ).
fof(f549,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[],[f415,f388]) ).
fof(f552,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f68,f388]) ).
fof(f555,plain,
( sk_c8 = sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f549,f384]) ).
fof(f556,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f555,f414]) ).
fof(f557,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f556]) ).
fof(f559,plain,
( sk_c8 = multiply(sk_c8,sk_c1)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f393,f458]) ).
fof(f577,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f146,f552]) ).
fof(f580,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f577,f3]) ).
fof(f582,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f580,f458]) ).
fof(f583,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f582,f442]) ).
fof(f584,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f583]) ).
fof(f589,plain,
( sk_c1 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f146,f559]) ).
fof(f591,plain,
( identity = sk_c1
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f589,f3]) ).
fof(f593,plain,
( sk_c8 = sk_c1
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f591,f458]) ).
fof(f597,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f86,f593]) ).
fof(f602,plain,
( sk_c8 = sk_c6
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f72,f597]) ).
fof(f616,plain,
( spl0_15
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f602,f383,f84,f71,f387]) ).
fof(f626,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f62,f86]) ).
fof(f627,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f626]) ).
fof(f630,plain,
( sk_c7 != multiply(sk_c8,sk_c2)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f627,f111]) ).
fof(f633,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f630,f120]) ).
fof(f634,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f633]) ).
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(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(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(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(s30,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f331]) ).
cnf(s31,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f340]) ).
cnf(s32,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f353]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f413]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f454]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f557]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f584]) ).
cnf(s51,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f616]) ).
cnf(s53,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f634]) ).
cnf(s54,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(rat,[],[s2,s28]) ).
cnf(s55,plain,
( spl0_3
| ~ spl0_11
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(rat,[],[s30,s31,s28]) ).
cnf(s56,plain,
spl0_3,
inference(rat,[],[s55,s18,s19,s20,s21,s22]) ).
cnf(s57,plain,
spl0_4,
inference(rat,[],[s30,s23,s24,s25,s26,s27,s28]) ).
cnf(s58,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s47,s51,s42,s5,s10,s15,s39,s56,s57,s28]) ).
cnf(s59,plain,
( spl0_8
| ~ spl0_2 ),
inference(rat,[],[s48,s51,s42,s4,s9,s14,s56,s57]) ).
cnf(s60,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s48,s51,s42,s3,s8,s13,s58,s57,s56]) ).
cnf(s61,plain,
~ spl0_2,
inference(rat,[],[s60,s59]) ).
cnf(s62,plain,
spl0_1,
inference(rat,[],[s54,s56,s57,s61]) ).
cnf(s63,plain,
spl0_9,
inference(rat,[],[s53,s5,s10,s15,s62]) ).
cnf(s64,plain,
spl0_8,
inference(rat,[],[s53,s4,s9,s14,s62]) ).
cnf(s65,plain,
~ spl0_6,
inference(rat,[],[s32,s62,s63,s64]) ).
cnf(s66,plain,
spl0_13,
inference(rat,[],[s13,s65]) ).
cnf(s67,plain,
spl0_12,
inference(rat,[],[s8,s65]) ).
cnf(s68,plain,
spl0_7,
inference(rat,[],[s3,s65]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s53,s66,s62,s67,s68]) ).
fof(f638,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:52:41 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.20/1.18 % (2588120)Input is clausal, will run a generic CNF schedule.
% 2.20/1.18 % (2588129)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3442352202:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.20/1.18 % (2588129)Instruction limit reached!
% 2.20/1.18 % (2588129)------------------------------
% 2.20/1.18 % (2588129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.20/1.18 % (2588129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/1.18 % (2588129)CaDiCaL version: 2.1.3
% 2.20/1.18 % (2588129)Termination reason: Instruction limit
% 2.20/1.18 % (2588129)Termination phase: Saturation
% 2.20/1.18 % (2588129)Time elapsed: 0.036 s
% 2.20/1.18 % (2588129)Peak memory usage: 89 MB
% 2.20/1.18 % (2588129)Instructions burned: 117 (million)
% 2.20/1.18 % (2588130)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3441675327:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.20/1.18 % (2588125)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=641689488:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.20/1.18 % (2588126)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4264292236:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.20/1.18 % (2588128)lrs+10_1_sil=8000:sp=occurrence:random_seed=2288970490:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.20/1.18 % (2588127)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=15066724:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.20/1.18 % (2588128)Refutation not found, incomplete strategy
% 2.20/1.18 % (2588128)------------------------------
% 2.20/1.18 % (2588128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.20/1.18 % (2588128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/1.18 % (2588128)CaDiCaL version: 2.1.3
% 2.20/1.18 % (2588128)Termination reason: Refutation not found, incomplete strategy
% 2.20/1.18 % (2588128)Time elapsed: 0.003 s
% 2.20/1.18 % (2588128)Peak memory usage: 88 MB
% 2.20/1.18 % (2588128)Instructions burned: 4 (million)
% 2.20/1.18 % (2588130)First to succeed.
% 2.20/1.18 % (2588130)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2588120"
% 2.20/1.18 % (2588131)dis-21_1_sil=8000:lcm=predicate:random_seed=2784004730:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.20/1.18 % (2588131)Refutation not found, incomplete strategy
% 2.20/1.18 % (2588131)------------------------------
% 2.20/1.18 % (2588131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.20/1.18 % (2588131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/1.18 % (2588131)CaDiCaL version: 2.1.3
% 2.20/1.18 % (2588131)Termination reason: Refutation not found, incomplete strategy
% 2.20/1.18 % (2588131)Time elapsed: 0.002 s
% 2.20/1.18 % (2588131)Peak memory usage: 88 MB
% 2.20/1.18 % (2588131)Instructions burned: 1 (million)
% 2.20/1.18 % (2588133)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=135503678:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.20/1.18 % (2588130)Refutation found. Thanks to Tanya!
% 2.20/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.20/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.27 % (2588130)------------------------------
% 2.70/1.27 % (2588130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.27 % (2588130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.27 % (2588130)CaDiCaL version: 2.1.3
% 2.70/1.27 % (2588130)Termination reason: Refutation
% 2.70/1.27 % (2588130)Time elapsed: 0.008 s
% 2.70/1.27 % (2588130)Peak memory usage: 89 MB
% 2.70/1.27 % (2588130)Instructions burned: 23 (million)
% 2.70/1.27 % (2588130)------------------------------
% 2.70/1.27 % (2588130)------------------------------
% 2.70/1.27 % (2588120)Success in time 0.318 s
% 2.70/1.27 % Vampire exiting
%------------------------------------------------------------------------------