%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP261-1 : 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 : n013.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 2.79s 1.31s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 51
% Syntax : Number of formulae : 284 ( 20 unt; 17 def)
% Number of atoms : 829 ( 265 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 986 ( 441 ~; 528 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 30 !; 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_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = inverse(sk_c1)
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c7 = inverse(sk_c2)
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(reorient_equations,[],[f64]) ).
fof(f67,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f68,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f71,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_3
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f74,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_4
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f77,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f65,f73,f70,f76,f73,f70,f67]) ).
fof(f81,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f63,f76,f81]) ).
fof(f86,definition,
( spl0_6
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f88,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f61,f76,f86]) ).
fof(f91,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f59,f76,f91]) ).
fof(f96,definition,
( spl0_8
<=> multiply(sk_c4,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f57,f76,f96]) ).
fof(f101,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f103,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f55,f76,f101]) ).
fof(f106,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f108,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f53,f76,f106]) ).
fof(f111,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f113,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_5
| spl0_11 ),
inference(avatar_split_clause,[],[f51,f111,f81]) ).
fof(f115,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f49,f111,f86]) ).
fof(f116,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f47,f111,f91]) ).
fof(f117,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f45,f111,f96]) ).
fof(f118,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f43,f111,f101]) ).
fof(f119,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f41,f111,f106]) ).
fof(f121,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f123,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_5
| spl0_12 ),
inference(avatar_split_clause,[],[f39,f121,f81]) ).
fof(f125,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f37,f121,f86]) ).
fof(f126,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f35,f121,f91]) ).
fof(f127,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f33,f121,f96]) ).
fof(f128,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f31,f121,f101]) ).
fof(f129,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f29,f121,f106]) ).
fof(f131,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f133,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f27,f131,f81]) ).
fof(f135,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f25,f131,f86]) ).
fof(f136,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f23,f131,f91]) ).
fof(f137,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f21,f131,f96]) ).
fof(f138,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f19,f131,f101]) ).
fof(f139,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f17,f131,f106]) ).
fof(f141,definition,
( spl0_14
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f143,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f15,f141,f81]) ).
fof(f145,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f13,f141,f86]) ).
fof(f146,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f11,f141,f91]) ).
fof(f147,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f9,f141,f96]) ).
fof(f148,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f8,f141,f101]) ).
fof(f149,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f6,f141,f106]) ).
fof(f150,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f88]) ).
fof(f152,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_9 ),
inference(superposition,[],[f3,f103]) ).
fof(f155,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(sk_c7,X0)
| ~ spl0_10 ),
inference(superposition,[],[f4,f108]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f155,f1]) ).
fof(f168,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c3,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f156,f152]) ).
fof(f197,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_9 ),
inference(superposition,[],[f159,f152]) ).
fof(f200,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f159,f108]) ).
fof(f202,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f159,f98]) ).
fof(f204,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_6 ),
inference(superposition,[],[f159,f150]) ).
fof(f214,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f202,f93]) ).
fof(f216,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f200,f103]) ).
fof(f218,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f159,f214]) ).
fof(f220,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f218,f3]) ).
fof(f223,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f156,f216]) ).
fof(f224,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f159,f216]) ).
fof(f226,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f224,f3]) ).
fof(f227,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f223,f108]) ).
fof(f230,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f197,f220]) ).
fof(f231,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f226,f220]) ).
fof(f242,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f204,f220]) ).
fof(f243,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f242,f3]) ).
fof(f244,plain,
( sk_c6 = sk_c5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f243,f220]) ).
fof(f245,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f244,f231]) ).
fof(f249,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f83,f245]) ).
fof(f252,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f249,f231]) ).
fof(f258,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f230,f231]) ).
fof(f287,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c3,sk_c6)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f168,f220]) ).
fof(f288,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c3,sk_c7)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f287,f231]) ).
fof(f311,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f159,f252]) ).
fof(f313,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f311,f3]) ).
fof(f315,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f313,f226]) ).
fof(f319,plain,
( sk_c7 != multiply(sk_c6,sk_c7)
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f78,f315]) ).
fof(f328,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f258,f315]) ).
fof(f329,plain,
( identity = sk_c3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f328,f3]) ).
fof(f333,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f319,f231]) ).
fof(f334,plain,
( sk_c3 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f329,f220]) ).
fof(f338,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f333,f227]) ).
fof(f339,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f340,plain,
( sk_c7 = sk_c3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f334,f231]) ).
fof(f362,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f68,f231]) ).
fof(f363,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f362,f315]) ).
fof(f364,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c7) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f363,f231]) ).
fof(f376,plain,
( sk_c8 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f364,f103]) ).
fof(f383,plain,
( sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f376,f315]) ).
fof(f389,plain,
( sk_c7 != multiply(sk_c7,sk_c3)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f383,f288]) ).
fof(f392,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f389,f340]) ).
fof(f393,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f392,f227]) ).
fof(f394,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f433,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f159,f143]) ).
fof(f435,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f433,f133]) ).
fof(f450,plain,
( sk_c8 != sk_c8
| multiply(sk_c1,sk_c8) != sk_c7
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f74,f133]) ).
fof(f452,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f74,f103]) ).
fof(f455,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f452]) ).
fof(f456,plain,
( multiply(sk_c1,sk_c8) != sk_c7
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f450]) ).
fof(f462,definition,
( spl0_16
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f464,plain,
( sk_c8 != sk_c7
| spl0_16 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f467,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f455,f108]) ).
fof(f468,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f467]) ).
fof(f470,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f456,f143]) ).
fof(f471,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f470]) ).
fof(f477,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f159,f123]) ).
fof(f479,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f477,f113]) ).
fof(f484,plain,
( sk_c7 != sk_c7
| multiply(sk_c4,sk_c7) != sk_c6
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f71,f93]) ).
fof(f485,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c2,sk_c7)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f71,f113]) ).
fof(f486,plain,
( sk_c6 != multiply(sk_c2,sk_c7)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f485]) ).
fof(f487,plain,
( multiply(sk_c4,sk_c7) != sk_c6
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f484]) ).
fof(f488,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f486,f123]) ).
fof(f489,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f490,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f487,f98]) ).
fof(f491,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f501,plain,
( sk_c8 != sk_c6
| multiply(sk_c1,sk_c8) != sk_c6
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[],[f68,f133]) ).
fof(f509,definition,
( spl0_19
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f510,plain,
( sk_c7 = sk_c6
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f511,plain,
( sk_c7 != sk_c6
| spl0_19 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f518,plain,
( sk_c7 != sk_c6
| sk_c8 != sk_c6
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f501,f143]) ).
fof(f520,definition,
( spl0_21
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f522,plain,
( sk_c8 != sk_c6
| spl0_21 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f523,plain,
( ~ spl0_21
| ~ spl0_19
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f518,f141,f131,f67,f509,f520]) ).
fof(f533,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f159,f435]) ).
fof(f535,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f533,f3]) ).
fof(f555,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_4
| ~ spl0_19 ),
inference(superposition,[],[f77,f510]) ).
fof(f557,plain,
( sk_c8 != sk_c7
| ~ spl0_19
| spl0_21 ),
inference(forward_demodulation,[],[f522,f510]) ).
fof(f558,plain,
( ~ spl0_16
| ~ spl0_19
| spl0_21 ),
inference(avatar_split_clause,[],[f557,f520,f509,f462]) ).
fof(f563,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_4
| ~ spl0_19 ),
inference(superposition,[],[f159,f555]) ).
fof(f565,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_19 ),
inference(forward_demodulation,[],[f563,f3]) ).
fof(f567,plain,
( sk_c8 = sk_c7
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_19 ),
inference(forward_demodulation,[],[f565,f535]) ).
fof(f568,plain,
( $false
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| spl0_16
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f567,f464]) ).
fof(f569,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| spl0_16
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f568]) ).
fof(f600,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f159,f479]) ).
fof(f602,plain,
( identity = sk_c6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f600,f3]) ).
fof(f603,plain,
( sk_c7 = sk_c6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f602,f535]) ).
fof(f604,plain,
( $false
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f603,f511]) ).
fof(f605,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f604]) ).
cnf(s1,plain,
( spl0_2
| spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f79]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f84]) ).
cnf(s4,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f89]) ).
cnf(s5,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f99]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f104]) ).
cnf(s8,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f109]) ).
cnf(s9,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f114]) ).
cnf(s10,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f115]) ).
cnf(s11,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f116]) ).
cnf(s12,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f117]) ).
cnf(s13,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f118]) ).
cnf(s14,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f119]) ).
cnf(s15,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f124]) ).
cnf(s16,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f125]) ).
cnf(s17,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f126]) ).
cnf(s18,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f127]) ).
cnf(s19,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f128]) ).
cnf(s20,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s21,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f134]) ).
cnf(s22,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s23,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s24,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s25,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s26,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s27,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f144]) ).
cnf(s28,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s29,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s30,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s31,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f148]) ).
cnf(s32,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s33,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f339]) ).
cnf(s40,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f394]) ).
cnf(s46,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f468]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f471]) ).
cnf(s50,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f489]) ).
cnf(s51,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f491]) ).
cnf(s55,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_19
| ~ spl0_21 ),
inference(sat_conversion,[],[f523]) ).
cnf(s60,plain,
( ~ spl0_16
| ~ spl0_19
| spl0_21 ),
inference(sat_conversion,[],[f558]) ).
cnf(s62,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| spl0_16
| ~ spl0_19 ),
inference(sat_conversion,[],[f569]) ).
cnf(s63,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f605]) ).
cnf(s64,plain,
spl0_4,
inference(rat,[],[s33,s3,s4,s5,s6,s7,s8]) ).
cnf(s65,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s47,s26,s32]) ).
cnf(s66,plain,
( ~ spl0_10
| ~ spl0_3 ),
inference(rat,[],[s47,s25,s31,s46]) ).
cnf(s67,plain,
~ spl0_3,
inference(rat,[],[s66,s65]) ).
cnf(s69,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s51,s17,s18]) ).
cnf(s70,plain,
( ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s51,s11,s12,s50]) ).
cnf(s71,plain,
~ spl0_2,
inference(rat,[],[s70,s69]) ).
cnf(s72,plain,
spl0_1,
inference(rat,[],[s2,s64,s67,s71]) ).
cnf(s73,plain,
( ~ spl0_19
| ~ spl0_13
| ~ spl0_14 ),
inference(rat,[],[s60,s55,s62,s64,s72]) ).
cnf(s74,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s73,s63]) ).
cnf(s75,plain,
( spl0_10
| ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s74,s26,s32]) ).
cnf(s76,plain,
( spl0_14
| ~ spl0_10 ),
inference(rat,[],[s40,s27,s28,s29,s30,s31,s72]) ).
cnf(s77,plain,
( ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s40,s21,s22,s23,s24,s25,s74,s76,s75,s72]) ).
cnf(s78,plain,
spl0_12,
inference(rat,[],[s40,s15,s16,s17,s18,s19,s20,s72]) ).
cnf(s79,plain,
~ spl0_11,
inference(rat,[],[s77,s78]) ).
cnf(s80,plain,
spl0_10,
inference(rat,[],[s14,s79]) ).
cnf(s81,plain,
spl0_9,
inference(rat,[],[s13,s79]) ).
cnf(s82,plain,
spl0_8,
inference(rat,[],[s12,s79]) ).
cnf(s83,plain,
spl0_7,
inference(rat,[],[s11,s79]) ).
cnf(s84,plain,
spl0_6,
inference(rat,[],[s10,s79]) ).
cnf(s85,plain,
spl0_5,
inference(rat,[],[s9,s79]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s40,s80,s81,s84,s85,s72,s82,s83]) ).
fof(f606,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP261-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:42:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.79/1.31 % (4162280)Input is clausal, will run a generic CNF schedule.
% 2.79/1.31 % (4162291)dis-21_1_sil=8000:lcm=predicate:random_seed=3301043759: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)
% 2.79/1.31 % (4162291)Refutation not found, incomplete strategy
% 2.79/1.31 % (4162291)------------------------------
% 2.79/1.31 % (4162291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (4162291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (4162291)CaDiCaL version: 2.1.3
% 2.79/1.31 % (4162291)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.31 % (4162291)Time elapsed: 0.001 s
% 2.79/1.31 % (4162291)Peak memory usage: 88 MB
% 2.79/1.31 % (4162291)Instructions burned: 1 (million)
% 2.79/1.31 % (4162286)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2048209332:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.79/1.31 % (4162285)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=1097399149:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.79/1.31 % (4162287)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=807459585:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.79/1.31 % (4162289)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=889320961:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.79/1.31 % (4162288)lrs+10_1_sil=8000:sp=occurrence:random_seed=365876979:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.79/1.31 % (4162288)Refutation not found, incomplete strategy
% 2.79/1.31 % (4162288)------------------------------
% 2.79/1.31 % (4162288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (4162288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (4162288)CaDiCaL version: 2.1.3
% 2.79/1.31 % (4162288)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.31 % (4162288)Time elapsed: 0.003 s
% 2.79/1.31 % (4162288)Peak memory usage: 88 MB
% 2.79/1.31 % (4162288)Instructions burned: 2 (million)
% 2.79/1.31 % (4162290)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2730010337:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.79/1.31 % (4162290)First to succeed.
% 2.79/1.31 % (4162290)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4162280"
% 2.79/1.31 % (4162289)Instruction limit reached!
% 2.79/1.31 % (4162289)------------------------------
% 2.79/1.31 % (4162289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (4162289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (4162289)CaDiCaL version: 2.1.3
% 2.79/1.31 % (4162289)Termination reason: Instruction limit
% 2.79/1.31 % (4162289)Termination phase: Saturation
% 2.79/1.31 % (4162289)Time elapsed: 0.067 s
% 2.79/1.31 % (4162289)Peak memory usage: 89 MB
% 2.79/1.31 % (4162289)Instructions burned: 115 (million)
% 2.79/1.31 % (4162291)------------------------------
% 2.79/1.31 % (4162291)------------------------------
% 2.79/1.31 % (4162300)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3062990112:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.79/1.31 % (4162299)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=1170830349:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.79/1.31 % (4162300)Refutation not found, incomplete strategy
% 2.79/1.31 % (4162300)------------------------------
% 2.79/1.31 % (4162300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (4162300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (4162300)CaDiCaL version: 2.1.3
% 2.79/1.31 % (4162300)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.31 % (4162300)Time elapsed: 0.002 s
% 2.79/1.31 % (4162300)Peak memory usage: 88 MB
% 2.79/1.31 % (4162300)Instructions burned: 3 (million)
% 2.79/1.31 % (4162299)Refutation not found, incomplete strategy
% 2.79/1.31 % (4162299)------------------------------
% 2.79/1.31 % (4162299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (4162299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (4162299)CaDiCaL version: 2.1.3
% 2.79/1.31 % (4162299)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.31 % (4162299)Time elapsed: 0.002 s
% 2.79/1.31 % (4162299)Peak memory usage: 88 MB
% 2.79/1.31 % (4162299)Instructions burned: 2 (million)
% 2.79/1.31 % (4162288)------------------------------
% 2.79/1.31 % (4162288)------------------------------
% 2.79/1.31 % (4162290)Refutation found. Thanks to Tanya!
% 2.79/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.79/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.51 % (4162290)------------------------------
% 0.16/1.51 % (4162290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.51 % (4162290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.51 % (4162290)CaDiCaL version: 2.1.3
% 0.16/1.51 % (4162290)Termination reason: Refutation
% 0.16/1.51 % (4162290)Time elapsed: 0.015 s
% 0.16/1.51 % (4162290)Peak memory usage: 89 MB
% 0.16/1.51 % (4162290)Instructions burned: 22 (million)
% 0.16/1.51 % (4162290)------------------------------
% 0.16/1.51 % (4162290)------------------------------
% 0.16/1.51 % (4162280)Success in time 0.457 s
% 0.16/1.51 % Vampire exiting
%------------------------------------------------------------------------------