%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP262-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 10:13:28 AM UTC 2026
% Result : Unsatisfiable 2.37s 1.15s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 44
% Syntax : Number of formulae : 278 ( 20 unt; 15 def)
% Number of atoms : 864 ( 258 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1105 ( 519 ~; 571 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = inverse(sk_c1)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c6 = inverse(sk_c2)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(sk_c5,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f54]) ).
fof(f57,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f61,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_3
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_4
<=> sk_c6 = multiply(sk_c5,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( sk_c6 != multiply(sk_c5,sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_5
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f72,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_6
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f55,f74,f71,f67,f63,f60,f57]) ).
fof(f78,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f80,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f53,f67,f78]) ).
fof(f83,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f85,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f51,f67,f83]) ).
fof(f88,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f90,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f49,f67,f88]) ).
fof(f93,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f95,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f47,f67,f93]) ).
fof(f97,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f45,f67,f63]) ).
fof(f99,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f101,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f43,f99,f78]) ).
fof(f103,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f41,f99,f83]) ).
fof(f104,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f39,f99,f88]) ).
fof(f105,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f37,f99,f93]) ).
fof(f106,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f35,f99,f63]) ).
fof(f108,definition,
( spl0_12
<=> sk_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f110,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f33,f108,f78]) ).
fof(f112,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f31,f108,f83]) ).
fof(f113,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f29,f108,f88]) ).
fof(f114,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f27,f108,f93]) ).
fof(f115,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f25,f108,f63]) ).
fof(f117,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f119,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f23,f117,f78]) ).
fof(f121,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f21,f117,f83]) ).
fof(f122,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f19,f117,f88]) ).
fof(f123,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f17,f117,f93]) ).
fof(f124,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f15,f117,f63]) ).
fof(f126,definition,
( spl0_14
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f128,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f13,f126,f78]) ).
fof(f130,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f11,f126,f83]) ).
fof(f131,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f9,f126,f88]) ).
fof(f132,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f7,f126,f93]) ).
fof(f133,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f5,f126,f63]) ).
fof(f134,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_8 ),
inference(superposition,[],[f3,f85]) ).
fof(f135,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f95]) ).
fof(f138,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f139,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f64]) ).
fof(f140,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f134]) ).
fof(f141,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f90]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f140,f1]) ).
fof(f144,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f138,f1]) ).
fof(f153,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f143,f80]) ).
fof(f156,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f141,f64]) ).
fof(f180,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_10 ),
inference(superposition,[],[f144,f135]) ).
fof(f186,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f144,f134]) ).
fof(f187,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f144,f90]) ).
fof(f196,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f187,f95]) ).
fof(f197,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f139,f196]) ).
fof(f200,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f197,f153]) ).
fof(f206,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f69,f200]) ).
fof(f208,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f144,f200]) ).
fof(f210,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f208,f3]) ).
fof(f221,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f180,f210]) ).
fof(f223,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f221,f3]) ).
fof(f224,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f223,f210]) ).
fof(f225,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f156,f196]) ).
fof(f228,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f135,f224]) ).
fof(f233,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f228,f196]) ).
fof(f236,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f233,f210]) ).
fof(f238,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f186,f233]) ).
fof(f242,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f238,f3]) ).
fof(f243,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f242,f210]) ).
fof(f250,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f135,f236]) ).
fof(f259,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f250,f224]) ).
fof(f262,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f259,f64]) ).
fof(f264,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f262,f210]) ).
fof(f266,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f264,f236]) ).
fof(f267,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f266,f206]) ).
fof(f268,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f275,plain,
( sk_c7 != sk_c6
| sk_c5 != multiply(sk_c3,sk_c6)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f72,f95]) ).
fof(f277,plain,
( sk_c5 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f275,f236]) ).
fof(f278,plain,
( sk_c7 != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f277,f90]) ).
fof(f279,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f278,f236]) ).
fof(f280,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f243,f236]) ).
fof(f294,plain,
( identity = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f134,f280]) ).
fof(f300,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f294,f153]) ).
fof(f301,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f300,f210]) ).
fof(f302,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f301,f236]) ).
fof(f303,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f302,f279]) ).
fof(f304,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f307,definition,
( spl0_15
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f308,plain,
( sk_c7 = sk_c6
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f315,plain,
( sk_c6 != sk_c6
| sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f72,f101]) ).
fof(f318,plain,
( sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_5
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f315]) ).
fof(f319,plain,
( ~ spl0_12
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f318,f99,f71,f108]) ).
fof(f320,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f236,f93,f88,f83,f78,f63,f307]) ).
fof(f327,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f119,f308]) ).
fof(f339,plain,
( sk_c6 = multiply(sk_c5,sk_c6)
| ~ spl0_4
| ~ spl0_15 ),
inference(forward_demodulation,[],[f68,f308]) ).
fof(f350,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f144,f110]) ).
fof(f351,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c2,multiply(sk_c6,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f110]) ).
fof(f365,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f128,f308]) ).
fof(f379,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_15 ),
inference(forward_demodulation,[],[f61,f308]) ).
fof(f380,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_15 ),
inference(forward_demodulation,[],[f379,f308]) ).
fof(f383,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f380,f327]) ).
fof(f384,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f383]) ).
fof(f386,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f384,f365]) ).
fof(f387,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f407,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_6
| ~ spl0_15 ),
inference(forward_demodulation,[],[f75,f308]) ).
fof(f408,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_6
| ~ spl0_15 ),
inference(forward_demodulation,[],[f407,f308]) ).
fof(f420,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f408,f95]) ).
fof(f426,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f420,f308]) ).
fof(f429,plain,
( sk_c7 != sk_c6
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f426,f90]) ).
fof(f430,plain,
( $false
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f429,f308]) ).
fof(f431,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f437,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c5)
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f58,f95]) ).
fof(f438,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c5)
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f58,f101]) ).
fof(f439,plain,
( sk_c6 != multiply(sk_c2,sk_c5)
| ~ spl0_1
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f438]) ).
fof(f441,plain,
( sk_c6 != multiply(sk_c3,sk_c5)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f437,f308]) ).
fof(f459,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f225,f441]) ).
fof(f460,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f459]) ).
fof(f463,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c6)
| ~ spl0_4 ),
inference(superposition,[],[f144,f68]) ).
fof(f465,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f144,f128]) ).
fof(f467,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f465,f119]) ).
fof(f468,plain,
( sk_c7 != sk_c7
| multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f75,f119]) ).
fof(f472,plain,
( multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_6
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f468]) ).
fof(f473,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f472,f128]) ).
fof(f474,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f480,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f61,f95]) ).
fof(f482,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f480]) ).
fof(f484,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f482,f90]) ).
fof(f485,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f503,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f351,f64]) ).
fof(f509,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12 ),
inference(forward_demodulation,[],[f503,f68]) ).
fof(f511,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f509,f439]) ).
fof(f512,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f522,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f144,f467]) ).
fof(f524,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f522,f3]) ).
fof(f539,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f350,f101]) ).
fof(f542,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f144,f539]) ).
fof(f544,plain,
( identity = sk_c5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f542,f3]) ).
fof(f547,plain,
( sk_c6 = sk_c5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f544,f524]) ).
fof(f559,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f463,f547]) ).
fof(f562,plain,
( identity = sk_c7
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f559,f3]) ).
fof(f563,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f562,f524]) ).
fof(f566,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f339,f547]) ).
fof(f569,plain,
( spl0_15
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f563,f126,f117,f108,f99,f67,f307]) ).
fof(f575,plain,
( sk_c5 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f65,f308]) ).
fof(f591,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f575,f547]) ).
fof(f645,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f591,f566]) ).
fof(f646,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f645]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s2,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f81]) ).
cnf(s3,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s6,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f97]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s8,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f103]) ).
cnf(s9,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s10,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f105]) ).
cnf(s11,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f106]) ).
cnf(s12,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s13,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s14,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s15,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f114]) ).
cnf(s16,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s17,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s18,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s19,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s20,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s21,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s22,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s23,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s24,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f131]) ).
cnf(s25,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s26,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f268]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f304]) ).
cnf(s31,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f319]) ).
cnf(s32,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f320]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f387]) ).
cnf(s38,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(sat_conversion,[],[f431]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_15 ),
inference(sat_conversion,[],[f460]) ).
cnf(s40,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f474]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f485]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f512]) ).
cnf(s44,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f569]) ).
cnf(s45,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f646]) ).
cnf(s46,plain,
spl0_3,
inference(rat,[],[s45,s44,s6,s11,s16,s21,s26]) ).
cnf(s47,plain,
( spl0_7
| ~ spl0_6 ),
inference(rat,[],[s40,s17,s22]) ).
cnf(s48,plain,
( spl0_14
| ~ spl0_6 ),
inference(rat,[],[s32,s38,s23,s24,s25,s47,s46]) ).
cnf(s49,plain,
~ spl0_6,
inference(rat,[],[s32,s38,s18,s19,s20,s40,s48,s47,s46]) ).
cnf(s51,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s31,s10,s15]) ).
cnf(s52,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s31,s9,s14]) ).
cnf(s53,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s31,s8,s13]) ).
cnf(s54,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_5 ),
inference(rat,[],[s31,s7,s12,s29,s46]) ).
cnf(s55,plain,
~ spl0_5,
inference(rat,[],[s54,s53,s52,s51]) ).
cnf(s56,plain,
spl0_4,
inference(rat,[],[s27,s2,s3,s4,s5,s46]) ).
cnf(s57,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s44,s33,s10,s15,s20,s25,s56]) ).
cnf(s58,plain,
( ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s44,s33,s9,s14,s19,s24,s41,s56]) ).
cnf(s59,plain,
~ spl0_2,
inference(rat,[],[s58,s57]) ).
cnf(s60,plain,
spl0_1,
inference(rat,[],[s1,s49,s55,s46,s56,s59]) ).
cnf(s61,plain,
spl0_10,
inference(rat,[],[s42,s10,s15,s60,s46,s56]) ).
cnf(s62,plain,
spl0_8,
inference(rat,[],[s42,s8,s13,s60,s46,s56]) ).
cnf(s63,plain,
spl0_7,
inference(rat,[],[s42,s7,s12,s60,s46,s56]) ).
cnf(s64,plain,
~ spl0_9,
inference(rat,[],[s32,s39,s46,s62,s63,s61,s60]) ).
cnf(s67,plain,
spl0_12,
inference(rat,[],[s14,s64]) ).
cnf(s68,plain,
spl0_11,
inference(rat,[],[s9,s64]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s42,s56,s46,s60,s67,s68]) ).
fof(f647,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP262-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n002.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 09:46:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.37/1.15 % (3300898)Input is clausal, will run a generic CNF schedule.
% 2.37/1.15 % (3300908)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3568360560:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.37/1.15 % (3300908)First to succeed.
% 2.37/1.15 % (3300908)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3300898"
% 2.37/1.15 % (3300905)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1742500552:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.37/1.15 % (3300904)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3298939160:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.37/1.15 % (3300907)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1858930737:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.37/1.15 % (3300903)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=1028745705:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.37/1.15 % (3300906)lrs+10_1_sil=8000:sp=occurrence:random_seed=3834065207:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.37/1.15 % (3300906)Refutation not found, incomplete strategy
% 2.37/1.15 % (3300906)------------------------------
% 2.37/1.15 % (3300906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/1.15 % (3300906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/1.15 % (3300906)CaDiCaL version: 2.1.3
% 2.37/1.15 % (3300906)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.15 % (3300906)Time elapsed: 0.003 s
% 2.37/1.15 % (3300906)Peak memory usage: 88 MB
% 2.37/1.15 % (3300906)Instructions burned: 3 (million)
% 2.37/1.15 % (3300909)dis-21_1_sil=8000:lcm=predicate:random_seed=4116727347: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)
% 2.37/1.15 % (3300909)Refutation not found, incomplete strategy
% 2.37/1.15 % (3300909)------------------------------
% 2.37/1.15 % (3300909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/1.15 % (3300909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/1.15 % (3300909)CaDiCaL version: 2.1.3
% 2.37/1.15 % (3300909)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.15 % (3300909)Time elapsed: 0.002 s
% 2.37/1.15 % (3300909)Peak memory usage: 88 MB
% 2.37/1.15 % (3300909)Instructions burned: 1 (million)
% 2.37/1.15 % (3300907)Instruction limit reached!
% 2.37/1.15 % (3300907)------------------------------
% 2.37/1.15 % (3300907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/1.15 % (3300907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/1.15 % (3300907)CaDiCaL version: 2.1.3
% 2.37/1.15 % (3300907)Termination reason: Instruction limit
% 2.37/1.15 % (3300907)Termination phase: Saturation
% 2.37/1.15 % (3300907)Time elapsed: 0.068 s
% 2.37/1.15 % (3300907)Peak memory usage: 89 MB
% 2.37/1.15 % (3300907)Instructions burned: 114 (million)
% 2.37/1.15 % (3300908)Refutation found. Thanks to Tanya!
% 2.37/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.37/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.35 % (3300908)------------------------------
% 2.73/1.35 % (3300908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (3300908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (3300908)CaDiCaL version: 2.1.3
% 2.73/1.35 % (3300908)Termination reason: Refutation
% 2.73/1.35 % (3300908)Time elapsed: 0.010 s
% 2.73/1.35 % (3300908)Peak memory usage: 89 MB
% 2.73/1.35 % (3300908)Instructions burned: 25 (million)
% 2.73/1.35 % (3300908)------------------------------
% 2.73/1.35 % (3300908)------------------------------
% 2.73/1.35 % (3300898)Success in time 0.306 s
% 2.73/1.35 % Vampire exiting
%------------------------------------------------------------------------------