%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP381-1 : 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 : n014.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 10:13:48 AM UTC 2026
% Result : Unsatisfiable 2.68s 1.27s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 41
% Syntax : Number of formulae : 295 ( 20 unt; 15 def)
% Number of atoms : 1125 ( 278 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1639 ( 809 ~; 815 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(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,
( inverse(sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c7) = sk_c6
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f22]) ).
fof(f32,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_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f42,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c6 = inverse(sk_c2)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1] :
( inverse(sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| 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_31) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( inverse(sk_c7) != sk_c6
| sk_c7 != multiply(sk_c6,sk_c5)
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != 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,[],[f64]) ).
fof(f67,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f68,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f71,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_3
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f74,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| spl0_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f78,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,definition,
( spl0_5
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f81,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_6
<=> sk_c7 = multiply(sk_c6,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f84,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( sk_c7 != multiply(sk_c6,sk_c5)
| spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f87,definition,
( spl0_7
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f88,plain,
( inverse(sk_c7) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f89,plain,
( inverse(sk_c7) != sk_c6
| spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f65,f87,f83,f80,f77,f73,f70,f67]) ).
fof(f92,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f94,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f98,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f63,f96,f92]) ).
fof(f101,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f103,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f61,f96,f101]) ).
fof(f106,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f108,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f59,f96,f106]) ).
fof(f111,definition,
( spl0_12
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f113,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f57,f96,f111]) ).
fof(f115,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f55,f96,f73]) ).
fof(f117,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f119,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f53,f117,f92]) ).
fof(f121,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f51,f117,f101]) ).
fof(f122,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f49,f117,f106]) ).
fof(f123,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f47,f117,f111]) ).
fof(f124,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f45,f117,f73]) ).
fof(f126,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f43,f126,f92]) ).
fof(f135,definition,
( spl0_15
<=> sk_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f137,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f33,f135,f92]) ).
fof(f143,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f23,f83,f92]) ).
fof(f144,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f21,f83,f101]) ).
fof(f145,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f19,f83,f106]) ).
fof(f146,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f17,f83,f111]) ).
fof(f147,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f15,f83,f73]) ).
fof(f148,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f13,f87,f92]) ).
fof(f149,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f11,f87,f101]) ).
fof(f150,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f9,f87,f106]) ).
fof(f151,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f7,f87,f111]) ).
fof(f152,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f5,f87,f73]) ).
fof(f153,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f103]) ).
fof(f154,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f113]) ).
fof(f157,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f158,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f74]) ).
fof(f159,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f153]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f108]) ).
fof(f162,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f159,f1]) ).
fof(f163,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f157,f1]) ).
fof(f172,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f162,f94]) ).
fof(f175,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f160,f74]) ).
fof(f199,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_12 ),
inference(superposition,[],[f163,f154]) ).
fof(f205,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f163,f153]) ).
fof(f206,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f163,f108]) ).
fof(f215,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f206,f113]) ).
fof(f216,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f158,f215]) ).
fof(f219,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f216,f172]) ).
fof(f226,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f163,f219]) ).
fof(f228,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f226,f3]) ).
fof(f234,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f199,f228]) ).
fof(f236,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f234,f3]) ).
fof(f237,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f236,f228]) ).
fof(f242,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f154,f237]) ).
fof(f245,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f242,f215]) ).
fof(f247,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f245,f228]) ).
fof(f249,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f205,f245]) ).
fof(f253,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f249,f3]) ).
fof(f254,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f253,f228]) ).
fof(f255,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f175,f237]) ).
fof(f256,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f255,f215]) ).
fof(f274,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f256,f247]) ).
fof(f275,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f85,f274]) ).
fof(f277,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f163,f274]) ).
fof(f279,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f277,f3]) ).
fof(f281,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f275,f247]) ).
fof(f282,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f281]) ).
fof(f283,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f279,f228]) ).
fof(f285,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f283,f247]) ).
fof(f289,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f89,f247]) ).
fof(f297,plain,
( sk_c6 = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f254,f247]) ).
fof(f306,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f103,f297]) ).
fof(f307,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f306,f289]) ).
fof(f308,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f312,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f81,f247]) ).
fof(f314,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f312,f247]) ).
fof(f325,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f314,f103]) ).
fof(f329,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f325]) ).
fof(f332,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f329,f297]) ).
fof(f336,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f332,f172]) ).
fof(f339,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f336,f285]) ).
fof(f340,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f341,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f68,f285]) ).
fof(f343,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f341,f103]) ).
fof(f347,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f343]) ).
fof(f350,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f347,f297]) ).
fof(f354,plain,
( sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f350,f172]) ).
fof(f357,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f354,f285]) ).
fof(f358,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f357]) ).
fof(f359,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f71,f247]) ).
fof(f360,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f359,f247]) ).
fof(f361,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f360,f103]) ).
fof(f365,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f361]) ).
fof(f368,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f365,f297]) ).
fof(f372,plain,
( sk_c6 != sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f368,f172]) ).
fof(f375,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f372,f285]) ).
fof(f376,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f375]) ).
fof(f377,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f78,f247]) ).
fof(f389,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f377,f113]) ).
fof(f395,plain,
( sk_c6 != multiply(sk_c3,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f389,f247]) ).
fof(f397,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f395,f108]) ).
fof(f400,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f397,f247]) ).
fof(f401,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f404,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f3,f88]) ).
fof(f410,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f163,f84]) ).
fof(f412,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f163,f119]) ).
fof(f414,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f412,f98]) ).
fof(f415,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_15 ),
inference(superposition,[],[f163,f137]) ).
fof(f417,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f415,f128]) ).
fof(f418,plain,
( identity != sk_c5
| spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f75,f404]) ).
fof(f444,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f414,f404]) ).
fof(f448,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f163,f414]) ).
fof(f450,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f448,f3]) ).
fof(f500,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f450,f444]) ).
fof(f555,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f410,f500]) ).
fof(f556,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f555,f3]) ).
fof(f557,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f556,f418]) ).
fof(f558,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f557]) ).
fof(f559,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f71,f500]) ).
fof(f560,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f74,f414]) ).
fof(f562,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f559,f500]) ).
fof(f568,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f562,f88]) ).
fof(f572,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f562,f98]) ).
fof(f573,plain,
( sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f572]) ).
fof(f575,plain,
( sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f568]) ).
fof(f576,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f573,f119]) ).
fof(f579,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f575,f417]) ).
fof(f580,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f576,f500]) ).
fof(f581,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f580]) ).
fof(f583,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f579,f500]) ).
fof(f584,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f583]) ).
fof(f585,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f81,f500]) ).
fof(f586,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f585,f500]) ).
fof(f590,plain,
( sk_c7 != sk_c6
| inverse(sk_c7) != sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f586,f417]) ).
fof(f591,plain,
( sk_c7 != sk_c6
| sk_c6 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f586,f119]) ).
fof(f593,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f591,f500]) ).
fof(f594,plain,
( inverse(sk_c7) != sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f590,f500]) ).
fof(f597,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f593,f98]) ).
fof(f598,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f597]) ).
fof(f599,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f594,f88]) ).
fof(f600,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f599]) ).
fof(f601,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f78,f500]) ).
fof(f621,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f601,f88]) ).
fof(f624,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f601,f98]) ).
fof(f625,plain,
( sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f624]) ).
fof(f626,plain,
( sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f621]) ).
fof(f627,plain,
( sk_c7 != sk_c6
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f625,f119]) ).
fof(f630,plain,
( sk_c7 != sk_c6
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f626,f417]) ).
fof(f631,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f627,f500]) ).
fof(f632,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f631]) ).
fof(f634,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f630,f500]) ).
fof(f635,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f634]) ).
fof(f636,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f68,f560]) ).
fof(f646,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f636,f88]) ).
fof(f649,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f636,f98]) ).
fof(f650,plain,
( sk_c6 != multiply(sk_c2,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f649]) ).
fof(f651,plain,
( sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f646]) ).
fof(f652,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f650,f119]) ).
fof(f655,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f651,f417]) ).
fof(f656,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f652,f500]) ).
fof(f657,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f656]) ).
fof(f660,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f655,f500]) ).
fof(f661,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f660]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f90]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f99]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f104]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f114]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f115]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s8,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s9,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s10,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s11,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s12,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s17,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f138]) ).
cnf(s22,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f143]) ).
cnf(s23,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f144]) ).
cnf(s24,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f145]) ).
cnf(s25,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f146]) ).
cnf(s26,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f147]) ).
cnf(s27,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f148]) ).
cnf(s28,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f149]) ).
cnf(s29,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f150]) ).
cnf(s30,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f151]) ).
cnf(s31,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f152]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f282]) ).
cnf(s33,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f308]) ).
cnf(s36,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f340]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f358]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f376]) ).
cnf(s45,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f401]) ).
cnf(s50,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f558]) ).
cnf(s51,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f581]) ).
cnf(s52,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f584]) ).
cnf(s53,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f598]) ).
cnf(s54,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f600]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f632]) ).
cnf(s57,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f635]) ).
cnf(s58,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f657]) ).
cnf(s59,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f661]) ).
cnf(s60,plain,
spl0_3,
inference(rat,[],[s50,s6,s11,s26,s31]) ).
cnf(s61,plain,
spl0_7,
inference(rat,[],[s33,s27,s28,s29,s30,s60]) ).
cnf(s62,plain,
spl0_6,
inference(rat,[],[s32,s22,s23,s24,s25,s60]) ).
cnf(s63,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s36,s8,s9,s10,s60]) ).
cnf(s64,plain,
( ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s36,s3,s4,s5,s53,s63,s61,s60]) ).
cnf(s65,plain,
~ spl0_5,
inference(rat,[],[s54,s2,s7,s12,s17,s64,s61]) ).
cnf(s66,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s45,s8,s9,s10,s60]) ).
cnf(s67,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s45,s3,s4,s5,s56,s66,s61,s60]) ).
cnf(s68,plain,
~ spl0_4,
inference(rat,[],[s57,s2,s7,s12,s17,s67,s61]) ).
cnf(s69,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s42,s8,s9,s10,s60]) ).
cnf(s70,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s42,s3,s4,s5,s51,s69,s61,s60]) ).
cnf(s71,plain,
~ spl0_2,
inference(rat,[],[s52,s2,s7,s12,s17,s70,s61]) ).
cnf(s72,plain,
spl0_1,
inference(rat,[],[s1,s61,s65,s62,s60,s68,s71]) ).
cnf(s73,plain,
( spl0_13
| ~ spl0_8 ),
inference(rat,[],[s39,s8,s9,s10,s60,s72]) ).
cnf(s74,plain,
~ spl0_8,
inference(rat,[],[s39,s3,s4,s5,s58,s73,s60,s72,s61]) ).
cnf(s75,plain,
spl0_15,
inference(rat,[],[s17,s74]) ).
cnf(s76,plain,
spl0_14,
inference(rat,[],[s12,s74]) ).
cnf(s77,plain,
spl0_13,
inference(rat,[],[s7,s74]) ).
cnf(s78,plain,
spl0_9,
inference(rat,[],[s2,s74]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s59,s75,s77,s72,s60,s61,s78,s76]) ).
fof(f663,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP381-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:59:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.68/1.27 % (557849)Input is clausal, will run a generic CNF schedule.
% 2.68/1.27 % (557857)lrs+10_1_sil=8000:sp=occurrence:random_seed=2364373107:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.68/1.27 % (557857)Refutation not found, incomplete strategy
% 2.68/1.27 % (557857)------------------------------
% 2.68/1.27 % (557857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (557857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (557857)CaDiCaL version: 2.1.3
% 2.68/1.27 % (557857)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.27 % (557857)Time elapsed: 0.001 s
% 2.68/1.27 % (557857)Peak memory usage: 88 MB
% 2.68/1.27 % (557857)Instructions burned: 3 (million)
% 2.68/1.27 % (557859)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2797471728:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.68/1.27 % (557858)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3065707648:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.68/1.27 % (557854)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=1425236954:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.68/1.27 % (557860)dis-21_1_sil=8000:lcm=predicate:random_seed=3516308836: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)
% 2.68/1.27 % (557855)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1117544557:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.68/1.27 % (557856)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2756098826:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.68/1.27 % (557860)Refutation not found, incomplete strategy
% 2.68/1.27 % (557860)------------------------------
% 2.68/1.27 % (557860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (557860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (557860)CaDiCaL version: 2.1.3
% 2.68/1.27 % (557860)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.27 % (557860)Time elapsed: 0.002 s
% 2.68/1.27 % (557860)Peak memory usage: 88 MB
% 2.68/1.27 % (557860)Instructions burned: 1 (million)
% 2.68/1.27 % (557859)First to succeed.
% 2.68/1.27 % (557859)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-557849"
% 2.68/1.27 % (557858)Instruction limit reached!
% 2.68/1.27 % (557858)------------------------------
% 2.68/1.27 % (557858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (557858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (557858)CaDiCaL version: 2.1.3
% 2.68/1.27 % (557858)Termination reason: Instruction limit
% 2.68/1.27 % (557858)Termination phase: Saturation
% 2.68/1.27 % (557858)Time elapsed: 0.067 s
% 2.68/1.27 % (557858)Peak memory usage: 89 MB
% 2.68/1.27 % (557858)Instructions burned: 115 (million)
% 2.68/1.27 % (557857)------------------------------
% 2.68/1.27 % (557857)------------------------------
% 2.68/1.27 % (557868)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=989213762:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.68/1.27 % (557868)Refutation not found, incomplete strategy
% 2.68/1.27 % (557868)------------------------------
% 2.68/1.27 % (557868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (557868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (557868)CaDiCaL version: 2.1.3
% 2.68/1.27 % (557868)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.27 % (557868)Time elapsed: 0.003 s
% 2.68/1.27 % (557868)Peak memory usage: 88 MB
% 2.68/1.27 % (557868)Instructions burned: 3 (million)
% 2.68/1.27 % (557869)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2741961724:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.68/1.27 % (557869)Refutation not found, incomplete strategy
% 2.68/1.27 % (557869)------------------------------
% 2.68/1.27 % (557869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (557869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (557869)CaDiCaL version: 2.1.3
% 2.68/1.27 % (557869)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.27 % (557869)Time elapsed: 0.002 s
% 2.68/1.27 % (557869)Peak memory usage: 88 MB
% 2.68/1.27 % (557869)Instructions burned: 3 (million)
% 2.68/1.27 % (557860)------------------------------
% 2.68/1.27 % (557860)------------------------------
% 2.68/1.27 % (557859)Refutation found. Thanks to Tanya!
% 2.68/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.47 % (557859)------------------------------
% 3.57/1.47 % (557859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.47 % (557859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.47 % (557859)CaDiCaL version: 2.1.3
% 3.57/1.47 % (557859)Termination reason: Refutation
% 3.57/1.47 % (557859)Time elapsed: 0.017 s
% 3.57/1.47 % (557859)Peak memory usage: 89 MB
% 3.57/1.47 % (557859)Instructions burned: 23 (million)
% 3.57/1.47 % (557859)------------------------------
% 3.57/1.47 % (557859)------------------------------
% 3.57/1.47 % (557849)Success in time 0.424 s
% 3.57/1.47 % Vampire exiting
%------------------------------------------------------------------------------