%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP274-1 : 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:30 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.28s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 47
% Syntax : Number of formulae : 307 ( 21 unt; 18 def)
% Number of atoms : 974 ( 272 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1264 ( 597 ~; 649 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 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_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c5 = inverse(sk_c2)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c5 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c5 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c5 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c5 = inverse(sk_c2)
| 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(sk_c7,sk_c5) != sk_c6
| multiply(X1,sk_c5) != sk_c7
| inverse(X1) != sk_c5
| 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_c6 != multiply(sk_c7,sk_c5)
| sk_c7 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1)
| 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
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( ! [X1] :
( sk_c5 != inverse(X1)
| sk_c7 != multiply(X1,sk_c5) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f71,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f72,plain,
( sk_c6 != multiply(sk_c7,sk_c5)
| spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
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,f70,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(f82,definition,
( spl0_8
<=> sk_c5 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f84,plain,
( sk_c5 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f53,f82,f78]) ).
fof(f87,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f89,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f51,f82,f87]) ).
fof(f92,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f49,f82,f92]) ).
fof(f97,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f99,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f47,f82,f97]) ).
fof(f101,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f45,f82,f63]) ).
fof(f103,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 = multiply(sk_c2,sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f43,f103,f78]) ).
fof(f107,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f41,f103,f87]) ).
fof(f108,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f39,f103,f92]) ).
fof(f109,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f37,f103,f97]) ).
fof(f110,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f35,f103,f63]) ).
fof(f111,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f33,f70,f78]) ).
fof(f112,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f31,f70,f87]) ).
fof(f113,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f29,f70,f92]) ).
fof(f114,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f27,f70,f97]) ).
fof(f115,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f25,f70,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_9
| spl0_13 ),
inference(avatar_split_clause,[],[f21,f117,f87]) ).
fof(f122,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f19,f117,f92]) ).
fof(f123,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f17,f117,f97]) ).
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_9
| spl0_14 ),
inference(avatar_split_clause,[],[f11,f126,f87]) ).
fof(f131,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f9,f126,f92]) ).
fof(f132,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f7,f126,f97]) ).
fof(f133,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f5,f126,f63]) ).
fof(f134,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f3,f89]) ).
fof(f135,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f99]) ).
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_9 ),
inference(superposition,[],[f4,f134]) ).
fof(f141,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f94]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_9 ),
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_9 ),
inference(superposition,[],[f143,f80]) ).
fof(f156,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f141,f64]) ).
fof(f180,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f144,f135]) ).
fof(f186,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f144,f134]) ).
fof(f187,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f144,f94]) ).
fof(f196,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f187,f99]) ).
fof(f197,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f139,f196]) ).
fof(f200,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f197,f153]) ).
fof(f207,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f144,f200]) ).
fof(f209,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f207,f3]) ).
fof(f215,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f180,f209]) ).
fof(f217,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f215,f3]) ).
fof(f218,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f217,f209]) ).
fof(f223,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f135,f218]) ).
fof(f226,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f223,f196]) ).
fof(f227,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f226,f209]) ).
fof(f235,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f153,f227]) ).
fof(f237,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f186,f227]) ).
fof(f238,plain,
( sk_c3 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f237,f180]) ).
fof(f239,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f235,f196]) ).
fof(f244,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f238,f218]) ).
fof(f245,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f239,f227]) ).
fof(f247,plain,
( multiply(sk_c7,sk_c5) = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f156,f218]) ).
fof(f248,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f247,f196]) ).
fof(f249,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f248,f72]) ).
fof(f250,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f249]) ).
fof(f251,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f71,f227]) ).
fof(f265,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f144,f251]) ).
fof(f267,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f265,f3]) ).
fof(f269,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f267,f209]) ).
fof(f280,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c7)
| sk_c5 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f68,f269]) ).
fof(f281,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f280,f269]) ).
fof(f282,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f281,f89]) ).
fof(f286,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f282,f227]) ).
fof(f288,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f286,f244]) ).
fof(f291,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f288,f196]) ).
fof(f292,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f291,f227]) ).
fof(f293,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f292]) ).
fof(f302,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f144,f105]) ).
fof(f303,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c5,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f105]) ).
fof(f304,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f302,f84]) ).
fof(f305,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f144,f128]) ).
fof(f307,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f305,f119]) ).
fof(f314,plain,
( sk_c5 != sk_c5
| sk_c7 != multiply(sk_c2,sk_c5)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f68,f84]) ).
fof(f315,plain,
( sk_c7 != multiply(sk_c2,sk_c5)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f314]) ).
fof(f316,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f315,f105]) ).
fof(f317,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f323,definition,
( spl0_16
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f324,plain,
( sk_c6 = sk_c5
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f325,plain,
( sk_c6 != sk_c5
| spl0_16 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f332,definition,
( spl0_18
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f337,definition,
( spl0_19
<=> sk_c7 = multiply(sk_c1,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f338,plain,
( sk_c7 = multiply(sk_c1,sk_c5)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f339,plain,
( sk_c7 != multiply(sk_c1,sk_c5)
| spl0_19 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f345,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f61,f119]) ).
fof(f346,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f61,f99]) ).
fof(f349,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f346]) ).
fof(f350,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f345]) ).
fof(f361,definition,
( spl0_22
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f362,plain,
( sk_c7 = sk_c6
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f363,plain,
( sk_c7 != sk_c6
| spl0_22 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f365,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f349,f94]) ).
fof(f366,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f371,plain,
( sk_c7 != sk_c7
| multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f75,f119]) ).
fof(f376,plain,
( multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_6
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f371]) ).
fof(f387,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f376,f128]) ).
fof(f388,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f389,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f144,f304]) ).
fof(f391,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f389,f3]) ).
fof(f394,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c5)
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f58,f89]) ).
fof(f395,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c2,sk_c5)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f58,f84]) ).
fof(f397,plain,
( sk_c7 != sk_c6
| sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f395,f105]) ).
fof(f404,plain,
( ~ spl0_16
| ~ spl0_22
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f397,f103,f82,f57,f361,f323]) ).
fof(f420,plain,
( multiply(sk_c2,sk_c5) = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f303,f304]) ).
fof(f425,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f420,f196]) ).
fof(f428,plain,
( sk_c7 = sk_c6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f425,f105]) ).
fof(f429,plain,
( $false
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_22 ),
inference(forward_subsumption_resolution,[],[f428,f363]) ).
fof(f430,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f429]) ).
fof(f444,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f144,f307]) ).
fof(f446,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f444,f3]) ).
fof(f449,plain,
( sk_c7 = sk_c6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f446,f391]) ).
fof(f450,plain,
( spl0_22
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f449,f126,f117,f103,f82,f361]) ).
fof(f451,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_22 ),
inference(superposition,[],[f64,f362]) ).
fof(f477,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_22 ),
inference(superposition,[],[f139,f451]) ).
fof(f480,plain,
( multiply(sk_c7,sk_c5) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_22 ),
inference(forward_demodulation,[],[f477,f362]) ).
fof(f482,plain,
( sk_c5 = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f480,f304]) ).
fof(f483,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f482,f71]) ).
fof(f484,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f483,f325]) ).
fof(f485,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f490,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_demodulation,[],[f350,f362]) ).
fof(f500,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f490,f128]) ).
fof(f506,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f500,f362]) ).
fof(f507,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f508,plain,
( sk_c6 != multiply(sk_c4,sk_c5)
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f394]) ).
fof(f514,plain,
( ~ spl0_7
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f508,f87,f57,f78]) ).
fof(f515,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f245,f97,f92,f87,f78,f63,f332]) ).
fof(f516,plain,
( spl0_22
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f227,f97,f92,f87,f78,f63,f361]) ).
fof(f561,plain,
( sk_c6 = multiply(sk_c4,sk_c6)
| ~ spl0_7
| ~ spl0_16 ),
inference(forward_demodulation,[],[f80,f324]) ).
fof(f562,plain,
( sk_c7 = multiply(sk_c4,sk_c7)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f561,f362]) ).
fof(f582,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c7) )
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[],[f75,f362]) ).
fof(f586,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f582,f89]) ).
fof(f590,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f586,f362]) ).
fof(f593,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f590,f562]) ).
fof(f594,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f593]) ).
fof(f629,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f119]) ).
fof(f630,plain,
( sk_c7 = multiply(sk_c7,sk_c1)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f629,f391]) ).
fof(f659,plain,
( sk_c7 != sk_c5
| spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f325,f362]) ).
fof(f662,plain,
( sk_c5 != multiply(sk_c7,sk_c7)
| spl0_3
| ~ spl0_22 ),
inference(forward_demodulation,[],[f65,f362]) ).
fof(f664,plain,
( ~ spl0_18
| spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f659,f361,f323,f332]) ).
fof(f675,plain,
( sk_c5 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_19 ),
inference(superposition,[],[f144,f338]) ).
fof(f677,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f675,f119]) ).
fof(f678,plain,
( $false
| spl0_3
| ~ spl0_13
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f677,f662]) ).
fof(f679,plain,
( spl0_3
| ~ spl0_13
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f690,plain,
( sk_c1 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f144,f630]) ).
fof(f692,plain,
( identity = sk_c1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f690,f3]) ).
fof(f694,plain,
( sk_c1 = sk_c7
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f692,f391]) ).
fof(f701,plain,
( sk_c7 != multiply(sk_c7,sk_c5)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(superposition,[],[f339,f694]) ).
fof(f707,plain,
( sk_c7 != sk_c6
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(forward_demodulation,[],[f701,f71]) ).
fof(f708,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_19
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f707,f362]) ).
fof(f709,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_19
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f708]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f85]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f90]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f95]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f100]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f101]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s9,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s10,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s12,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f111]) ).
cnf(s13,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f112]) ).
cnf(s14,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s15,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f114]) ).
cnf(s16,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f115]) ).
cnf(s17,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s18,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s19,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s20,plain,
( spl0_11
| 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_9
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s24,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f131]) ).
cnf(s25,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s26,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f250]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f293]) ).
cnf(s30,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f317]) ).
cnf(s36,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f366]) ).
cnf(s39,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f388]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f404]) ).
cnf(s43,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_22 ),
inference(sat_conversion,[],[f430]) ).
cnf(s44,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_22 ),
inference(sat_conversion,[],[f450]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f485]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f507]) ).
cnf(s55,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f514]) ).
cnf(s58,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f515]) ).
cnf(s60,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_22 ),
inference(sat_conversion,[],[f516]) ).
cnf(s75,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f594]) ).
cnf(s86,plain,
( spl0_16
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f664]) ).
cnf(s89,plain,
( spl0_3
| ~ spl0_13
| ~ spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f679]) ).
cnf(s91,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f709]) ).
cnf(s92,plain,
spl0_3,
inference(rat,[],[s89,s91,s44,s6,s11,s16,s21,s26]) ).
cnf(s93,plain,
( spl0_7
| ~ spl0_6 ),
inference(rat,[],[s39,s17,s22]) ).
cnf(s94,plain,
( spl0_14
| ~ spl0_6 ),
inference(rat,[],[s86,s75,s58,s60,s23,s24,s25,s93,s92]) ).
cnf(s95,plain,
~ spl0_6,
inference(rat,[],[s86,s75,s58,s60,s18,s19,s20,s39,s94,s93,s92]) ).
cnf(s96,plain,
spl0_5,
inference(rat,[],[s27,s12,s13,s14,s15,s92]) ).
cnf(s98,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s30,s5,s10]) ).
cnf(s99,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s30,s4,s9]) ).
cnf(s100,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s30,s3,s8]) ).
cnf(s101,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s30,s2,s7,s29,s96,s92]) ).
cnf(s102,plain,
~ spl0_4,
inference(rat,[],[s101,s100,s99,s98]) ).
cnf(s103,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s44,s53,s5,s10,s20,s25]) ).
cnf(s104,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s44,s53,s4,s9,s19,s24,s36]) ).
cnf(s105,plain,
~ spl0_2,
inference(rat,[],[s104,s103]) ).
cnf(s106,plain,
spl0_1,
inference(rat,[],[s1,s95,s96,s92,s102,s105]) ).
cnf(s107,plain,
( ~ spl0_8
| ~ spl0_22
| ~ spl0_12 ),
inference(rat,[],[s47,s41,s106,s96,s92]) ).
cnf(s108,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(rat,[],[s107,s44]) ).
cnf(s109,plain,
spl0_11,
inference(rat,[],[s108,s5,s10,s20,s25]) ).
cnf(s110,plain,
spl0_12,
inference(rat,[],[s55,s7,s8,s106]) ).
cnf(s111,plain,
spl0_8,
inference(rat,[],[s55,s2,s3,s106]) ).
cnf(s112,plain,
~ spl0_22,
inference(rat,[],[s107,s110,s111]) ).
cnf(s113,plain,
~ spl0_10,
inference(rat,[],[s43,s111,s110,s109,s112]) ).
cnf(s114,plain,
spl0_14,
inference(rat,[],[s24,s113]) ).
cnf(s115,plain,
spl0_13,
inference(rat,[],[s19,s113]) ).
cnf(s116,plain,
$false,
inference(rat,[],[s108,s111,s110,s114,s115]) ).
fof(f710,plain,
$false,
inference(avatar_sat_refutation,[],[s116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP274-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.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 09:49:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.62/1.28 % (3308251)Input is clausal, will run a generic CNF schedule.
% 2.62/1.28 % (3308260)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2874644821:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.28 % (3308258)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1893091685:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.28 % (3308259)lrs+10_1_sil=8000:sp=occurrence:random_seed=1450611855:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.28 % (3308256)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=1255283269:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.28 % (3308257)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4184237918:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.28 % (3308262)dis-21_1_sil=8000:lcm=predicate:random_seed=1477869906: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)
% 2.62/1.28 % (3308260)Instruction limit reached!
% 2.62/1.28 % (3308260)------------------------------
% 2.62/1.28 % (3308260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (3308260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (3308260)CaDiCaL version: 2.1.3
% 2.62/1.28 % (3308260)Termination reason: Instruction limit
% 2.62/1.28 % (3308260)Termination phase: Saturation
% 2.62/1.28 % (3308260)Time elapsed: 0.040 s
% 2.62/1.28 % (3308260)Peak memory usage: 89 MB
% 2.62/1.28 % (3308260)Instructions burned: 122 (million)
% 2.62/1.28 % (3308261)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3680994268:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.28 % (3308262)Refutation not found, incomplete strategy
% 2.62/1.28 % (3308262)------------------------------
% 2.62/1.28 % (3308262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (3308262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (3308262)CaDiCaL version: 2.1.3
% 2.62/1.28 % (3308262)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.28 % (3308262)Time elapsed: 0.002 s
% 2.62/1.28 % (3308262)Peak memory usage: 88 MB
% 2.62/1.28 % (3308262)Instructions burned: 1 (million)
% 2.62/1.28 % (3308259)Refutation not found, incomplete strategy
% 2.62/1.28 % (3308259)------------------------------
% 2.62/1.28 % (3308259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (3308259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (3308259)CaDiCaL version: 2.1.3
% 2.62/1.28 % (3308259)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.28 % (3308259)Time elapsed: 0.002 s
% 2.62/1.28 % (3308259)Peak memory usage: 88 MB
% 2.62/1.28 % (3308259)Instructions burned: 3 (million)
% 2.62/1.28 % (3308261)First to succeed.
% 2.62/1.28 % (3308261)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3308251"
% 2.62/1.28 % (3308270)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=1974102389:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.62/1.28 % (3308270)Refutation not found, incomplete strategy
% 2.62/1.28 % (3308270)------------------------------
% 2.62/1.28 % (3308270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.28 % (3308270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.28 % (3308270)CaDiCaL version: 2.1.3
% 2.62/1.28 % (3308270)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.28 % (3308270)Time elapsed: 0.001 s
% 2.62/1.28 % (3308270)Peak memory usage: 88 MB
% 2.62/1.28 % (3308270)Instructions burned: 3 (million)
% 2.62/1.28 % (3308270)------------------------------
% 2.62/1.28 % (3308270)------------------------------
% 2.62/1.28 % (3308259)------------------------------
% 2.62/1.28 % (3308259)------------------------------
% 2.62/1.28 % (3308262)------------------------------
% 2.62/1.28 % (3308262)------------------------------
% 2.62/1.28 % (3308261)Refutation found. Thanks to Tanya!
% 2.62/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.48 % (3308261)------------------------------
% 3.56/1.48 % (3308261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (3308261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (3308261)CaDiCaL version: 2.1.3
% 3.56/1.48 % (3308261)Termination reason: Refutation
% 3.56/1.48 % (3308261)Time elapsed: 0.019 s
% 3.56/1.48 % (3308261)Peak memory usage: 89 MB
% 3.56/1.48 % (3308261)Instructions burned: 26 (million)
% 3.56/1.48 % (3308261)------------------------------
% 3.56/1.48 % (3308261)------------------------------
% 3.56/1.48 % (3308251)Success in time 0.418 s
% 3.56/1.48 % Vampire exiting
%------------------------------------------------------------------------------