%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP272-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 2.72s 1.28s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 47
% Syntax : Number of formulae : 318 ( 20 unt; 18 def)
% Number of atoms : 1083 ( 284 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1461 ( 696 ~; 747 |; 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 : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c6 = inverse(sk_c2)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c6 = 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_c6) != sk_c5
| inverse(X1) != 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/sandbox/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_c5 != multiply(X1,sk_c6)
| sk_c6 != 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_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6) )
| ~ 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(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(f79,plain,
( sk_c6 != multiply(sk_c4,sk_c5)
| spl0_7 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f84,plain,
( sk_c6 = 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_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f105,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ 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(f184,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3 ),
inference(superposition,[],[f144,f64]) ).
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(f224,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f94,f218]) ).
fof(f226,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f223,f196]) ).
fof(f228,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f226,f209]) ).
fof(f236,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(f237,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f236,f196]) ).
fof(f240,plain,
( spl0_5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f237,f97,f92,f87,f78,f63,f70]) ).
fof(f258,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f71,f228]) ).
fof(f260,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f144,f258]) ).
fof(f262,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f260,f3]) ).
fof(f264,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f262,f209]) ).
fof(f266,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f264,f228]) ).
fof(f276,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f68,f266]) ).
fof(f279,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f276,f99]) ).
fof(f281,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f279,f228]) ).
fof(f282,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f281,f94]) ).
fof(f283,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f282,f228]) ).
fof(f284,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f283]) ).
fof(f288,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f119]) ).
fof(f289,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f139,f71]) ).
fof(f290,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f144,f71]) ).
fof(f292,plain,
( sk_c5 = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f289,f153]) ).
fof(f293,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f144,f105]) ).
fof(f295,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f293,f84]) ).
fof(f296,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f144,f128]) ).
fof(f297,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f128]) ).
fof(f298,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f296,f119]) ).
fof(f305,plain,
( sk_c6 != sk_c6
| sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f68,f84]) ).
fof(f307,plain,
( sk_c5 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f305]) ).
fof(f314,definition,
( spl0_16
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f315,plain,
( sk_c7 = sk_c6
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f316,plain,
( sk_c7 != sk_c6
| spl0_16 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f318,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f307,f105]) ).
fof(f319,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f325,plain,
( sk_c7 != sk_c7
| multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f75,f119]) ).
fof(f326,plain,
( multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_6
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f325]) ).
fof(f327,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f326,f128]) ).
fof(f328,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f337,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_13 ),
inference(superposition,[],[f144,f288]) ).
fof(f341,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f61,f84]) ).
fof(f344,plain,
( sk_c7 != sk_c5
| sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f341,f105]) ).
fof(f351,definition,
( spl0_19
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f353,plain,
( sk_c7 != sk_c5
| spl0_19 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f354,plain,
( ~ spl0_16
| ~ spl0_19
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f344,f103,f82,f60,f351,f314]) ).
fof(f356,plain,
( sk_c5 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f144,f292]) ).
fof(f358,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f356,f3]) ).
fof(f367,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f186,f358]) ).
fof(f369,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f367,f184]) ).
fof(f375,plain,
( sk_c6 = inverse(sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f89,f369]) ).
fof(f386,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c7,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f61,f375]) ).
fof(f392,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f144,f295]) ).
fof(f394,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f392,f3]) ).
fof(f422,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f297,f298]) ).
fof(f424,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f144,f298]) ).
fof(f426,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f424,f3]) ).
fof(f428,plain,
( multiply(sk_c1,sk_c7) = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f422,f153]) ).
fof(f429,plain,
( sk_c6 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f428,f128]) ).
fof(f439,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f186,f426]) ).
fof(f440,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f1,f426]) ).
fof(f441,plain,
( identity = sk_c4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f439,f3]) ).
fof(f447,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f386,f298]) ).
fof(f451,plain,
( ~ spl0_16
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f447,f126,f117,f87,f78,f70,f63,f60,f314]) ).
fof(f455,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c5)
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f58,f89]) ).
fof(f458,plain,
( sk_c6 != multiply(sk_c4,sk_c5)
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f455]) ).
fof(f466,definition,
( spl0_20
<=> sk_c6 = multiply(sk_c1,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f467,plain,
( sk_c6 = multiply(sk_c1,sk_c5)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f468,plain,
( sk_c6 != multiply(sk_c1,sk_c5)
| spl0_20 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f473,plain,
( sk_c6 = sk_c5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f394,f426]) ).
fof(f474,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f422,f128]) ).
fof(f475,plain,
( sk_c6 = sk_c4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f441,f426]) ).
fof(f476,plain,
( ~ spl0_7
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f458,f87,f57,f78]) ).
fof(f487,plain,
( sk_c6 != sk_c5
| ~ spl0_16
| spl0_19 ),
inference(forward_demodulation,[],[f353,f315]) ).
fof(f488,plain,
( $false
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f473,f487]) ).
fof(f489,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f501,plain,
( sk_c6 != multiply(sk_c6,sk_c5)
| spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f79,f475]) ).
fof(f506,plain,
( $false
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f501,f295]) ).
fof(f507,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f601,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f290,f429]) ).
fof(f611,plain,
( sk_c1 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f337,f426]) ).
fof(f615,plain,
( sk_c1 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f611,f601]) ).
fof(f618,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f288,f615]) ).
fof(f623,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f618,f298]) ).
fof(f631,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f623,f426]) ).
fof(f633,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f631,f316]) ).
fof(f634,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f633]) ).
fof(f639,definition,
( spl0_21
<=> sk_c7 = multiply(sk_c7,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f642,plain,
( ~ spl0_21
| ~ spl0_16
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f386,f87,f78,f70,f63,f60,f314,f639]) ).
fof(f643,plain,
( spl0_21
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f224,f97,f92,f87,f78,f63,f639]) ).
fof(f644,plain,
( spl0_16
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f228,f97,f92,f87,f78,f63,f314]) ).
fof(f671,plain,
( sk_c6 = multiply(sk_c3,sk_c6)
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f94,f315]) ).
fof(f695,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f75,f315]) ).
fof(f696,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f695,f315]) ).
fof(f698,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f696,f99]) ).
fof(f706,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f698,f315]) ).
fof(f709,plain,
( $false
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f706,f671]) ).
fof(f710,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f709]) ).
fof(f744,plain,
( sk_c6 = multiply(sk_c7,sk_c6)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f71,f473]) ).
fof(f762,plain,
( sk_c6 != multiply(sk_c6,sk_c7)
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f65,f473]) ).
fof(f763,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f58,f473]) ).
fof(f768,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f763,f84]) ).
fof(f769,plain,
( sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f768]) ).
fof(f770,plain,
( sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f769,f105]) ).
fof(f771,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f770,f473]) ).
fof(f772,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f771]) ).
fof(f775,plain,
( sk_c6 != multiply(sk_c1,sk_c6)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_20 ),
inference(forward_demodulation,[],[f468,f473]) ).
fof(f791,plain,
( sk_c7 != sk_c6
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f762,f440]) ).
fof(f849,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c6)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f297,f744]) ).
fof(f853,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f849,f474]) ).
fof(f854,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f853,f775]) ).
fof(f855,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f854]) ).
fof(f856,plain,
( sk_c6 = multiply(sk_c1,sk_c6)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f467,f473]) ).
fof(f858,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f4,f856]) ).
fof(f859,plain,
( ! [X0] : multiply(sk_c1,X0) = X0
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f858,f440]) ).
fof(f864,plain,
( sk_c7 = sk_c6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f128,f859]) ).
fof(f890,plain,
( ~ spl0_16
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f791,f126,f117,f103,f82,f63,f314]) ).
fof(f892,plain,
( spl0_16
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f864,f466,f126,f117,f103,f82,f314]) ).
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(s28,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f240]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f284]) ).
cnf(s31,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f319]) ).
cnf(s32,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f328]) ).
cnf(s36,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_16
| ~ spl0_19 ),
inference(sat_conversion,[],[f354]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(sat_conversion,[],[f451]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f476]) ).
cnf(s47,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f489]) ).
cnf(s48,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f507]) ).
cnf(s60,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f634]) ).
cnf(s63,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_16
| ~ spl0_21 ),
inference(sat_conversion,[],[f642]) ).
cnf(s64,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_21 ),
inference(sat_conversion,[],[f643]) ).
cnf(s65,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f644]) ).
cnf(s77,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f710]) ).
cnf(s86,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f772]) ).
cnf(s90,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f855]) ).
cnf(s100,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(sat_conversion,[],[f890]) ).
cnf(s102,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_16
| ~ spl0_20 ),
inference(sat_conversion,[],[f892]) ).
cnf(s108,plain,
spl0_3,
inference(rat,[],[s102,s90,s100,s6,s11,s16,s21,s26]) ).
cnf(s109,plain,
( spl0_7
| ~ spl0_6 ),
inference(rat,[],[s32,s17,s22]) ).
cnf(s110,plain,
( spl0_14
| ~ spl0_6 ),
inference(rat,[],[s65,s77,s23,s24,s25,s109,s108]) ).
cnf(s111,plain,
~ spl0_6,
inference(rat,[],[s65,s77,s18,s19,s20,s32,s110,s109,s108]) ).
cnf(s112,plain,
spl0_5,
inference(rat,[],[s28,s12,s13,s14,s15,s108]) ).
cnf(s114,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s31,s5,s10]) ).
cnf(s115,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s31,s4,s9]) ).
cnf(s116,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s31,s3,s8]) ).
cnf(s117,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s48,s2,s7,s17,s22,s29,s112,s108]) ).
cnf(s118,plain,
~ spl0_4,
inference(rat,[],[s117,s116,s115,s114]) ).
cnf(s119,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s40,s60,s20,s25,s108,s112]) ).
cnf(s120,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s63,s64,s65,s119,s108,s112]) ).
cnf(s121,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s40,s60,s19,s24,s120,s112,s108]) ).
cnf(s122,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s36,s47,s102,s90,s3,s8,s18,s23,s112]) ).
cnf(s123,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s48,s2,s7,s17,s22,s121]) ).
cnf(s124,plain,
~ spl0_2,
inference(rat,[],[s123,s122]) ).
cnf(s125,plain,
spl0_1,
inference(rat,[],[s1,s111,s112,s108,s118,s124]) ).
cnf(s126,plain,
spl0_9,
inference(rat,[],[s86,s3,s8,s18,s23,s125]) ).
cnf(s127,plain,
~ spl0_7,
inference(rat,[],[s45,s125,s126]) ).
cnf(s128,plain,
spl0_14,
inference(rat,[],[s22,s127]) ).
cnf(s129,plain,
spl0_13,
inference(rat,[],[s17,s127]) ).
cnf(s130,plain,
spl0_12,
inference(rat,[],[s7,s127]) ).
cnf(s131,plain,
spl0_8,
inference(rat,[],[s2,s127]) ).
cnf(s132,plain,
$false,
inference(rat,[],[s48,s128,s129,s130,s126,s127,s131]) ).
fof(f894,plain,
$false,
inference(avatar_sat_refutation,[],[s132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP272-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.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 09:47:00 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.72/1.28 % (1411514)Input is clausal, will run a generic CNF schedule.
% 2.72/1.28 % (1411520)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3235554869:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.72/1.28 % (1411519)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=482244079:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.72/1.28 % (1411521)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1579788724:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.72/1.28 % (1411525)dis-21_1_sil=8000:lcm=predicate:random_seed=1863144571: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)
% 2.72/1.28 % (1411522)lrs+10_1_sil=8000:sp=occurrence:random_seed=1507588801:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.72/1.28 % (1411523)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4124619006:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.72/1.28 % (1411524)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2538296353:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.72/1.28 % (1411525)Refutation not found, incomplete strategy
% 2.72/1.28 % (1411525)------------------------------
% 2.72/1.28 % (1411525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (1411525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (1411525)CaDiCaL version: 2.1.3
% 2.72/1.28 % (1411525)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.28 % (1411525)Time elapsed: 0.002 s
% 2.72/1.28 % (1411525)Peak memory usage: 88 MB
% 2.72/1.28 % (1411525)Instructions burned: 1 (million)
% 2.72/1.28 % (1411522)Refutation not found, incomplete strategy
% 2.72/1.28 % (1411522)------------------------------
% 2.72/1.28 % (1411522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (1411522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (1411522)CaDiCaL version: 2.1.3
% 2.72/1.28 % (1411522)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.28 % (1411522)Time elapsed: 0.003 s
% 2.72/1.28 % (1411522)Peak memory usage: 88 MB
% 2.72/1.28 % (1411522)Instructions burned: 2 (million)
% 2.72/1.28 % (1411524)First to succeed.
% 2.72/1.28 % (1411524)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1411514"
% 2.72/1.28 % (1411523)Instruction limit reached!
% 2.72/1.28 % (1411523)------------------------------
% 2.72/1.28 % (1411523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (1411523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (1411523)CaDiCaL version: 2.1.3
% 2.72/1.28 % (1411523)Termination reason: Instruction limit
% 2.72/1.28 % (1411523)Termination phase: Saturation
% 2.72/1.28 % (1411523)Time elapsed: 0.069 s
% 2.72/1.28 % (1411523)Peak memory usage: 89 MB
% 2.72/1.28 % (1411523)Instructions burned: 115 (million)
% 2.72/1.28 % (1411533)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=2983625298:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.72/1.28 % (1411533)Refutation not found, incomplete strategy
% 2.72/1.28 % (1411533)------------------------------
% 2.72/1.28 % (1411533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (1411533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (1411533)CaDiCaL version: 2.1.3
% 2.72/1.28 % (1411533)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.28 % (1411533)Time elapsed: 0.003 s
% 2.72/1.28 % (1411533)Peak memory usage: 88 MB
% 2.72/1.28 % (1411533)Instructions burned: 3 (million)
% 2.72/1.28 % (1411522)------------------------------
% 2.72/1.28 % (1411522)------------------------------
% 2.72/1.28 % (1411525)------------------------------
% 2.72/1.28 % (1411525)------------------------------
% 2.72/1.28 % (1411524)Refutation found. Thanks to Tanya!
% 2.72/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.72/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.47 % (1411524)------------------------------
% 3.61/1.47 % (1411524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.47 % (1411524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.47 % (1411524)CaDiCaL version: 2.1.3
% 3.61/1.47 % (1411524)Termination reason: Refutation
% 3.61/1.47 % (1411524)Time elapsed: 0.023 s
% 3.61/1.47 % (1411524)Peak memory usage: 89 MB
% 3.61/1.47 % (1411524)Instructions burned: 33 (million)
% 3.61/1.47 % (1411524)------------------------------
% 3.61/1.47 % (1411524)------------------------------
% 3.61/1.47 % (1411514)Success in time 0.428 s
% 3.61/1.47 % Vampire exiting
%------------------------------------------------------------------------------