%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP304-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:35 AM UTC 2026
% Result : Unsatisfiable 1.83s 1.05s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 41
% Syntax : Number of formulae : 276 ( 25 unt; 16 def)
% Number of atoms : 939 ( 263 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1269 ( 606 ~; 647 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
multiply(sk_c7,sk_c6) = sk_c5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c5 = inverse(sk_c7)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c5
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c6
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c7,X2) != sk_c6
| multiply(X3,sk_c7) != X2
| inverse(X3) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c5 != inverse(sk_c7)
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,X2)
| multiply(X3,sk_c7) != X2
| sk_c7 != inverse(X3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
! [X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c5 != inverse(sk_c7)
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ),
inference(equality_resolution,[],[f47]) ).
fof(f50,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f51,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c6 != multiply(sk_c7,multiply(X3,sk_c7)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_2
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f54,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,definition,
( spl0_3
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f57,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,definition,
( spl0_4
<=> sk_c5 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f60,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( sk_c5 != inverse(sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl0_5
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f64,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_6
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f48,f67,f63,f59,f56,f53,f50]) ).
fof(f72,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f74,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f78,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f45,f76,f72]) ).
fof(f81,definition,
( spl0_9
<=> sk_c4 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f83,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f43,f76,f81]) ).
fof(f86,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c7,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f88,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f41,f76,f86]) ).
fof(f91,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f39,f76,f91]) ).
fof(f96,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f98,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f37,f76,f96]) ).
fof(f101,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f35,f101,f72]) ).
fof(f105,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f33,f101,f81]) ).
fof(f106,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f31,f101,f86]) ).
fof(f107,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f29,f101,f91]) ).
fof(f108,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f27,f101,f96]) ).
fof(f109,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f25,f59,f72]) ).
fof(f110,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f23,f59,f81]) ).
fof(f111,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f21,f59,f86]) ).
fof(f112,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f19,f59,f91]) ).
fof(f113,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f17,f59,f96]) ).
fof(f114,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f15,f63,f72]) ).
fof(f115,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f13,f63,f81]) ).
fof(f116,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f11,f63,f86]) ).
fof(f117,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f9,f63,f91]) ).
fof(f118,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f7,f63,f96]) ).
fof(f119,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f67]) ).
fof(f120,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_7 ),
inference(superposition,[],[f3,f74]) ).
fof(f121,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_11 ),
inference(superposition,[],[f3,f93]) ).
fof(f124,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f126,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c4,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f88]) ).
fof(f127,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c7,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f98]) ).
fof(f128,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c3,multiply(sk_c7,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f83]) ).
fof(f129,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f124,f1]) ).
fof(f132,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f120]) ).
fof(f133,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f132,f1]) ).
fof(f134,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c2,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f121]) ).
fof(f135,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c2,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f134,f1]) ).
fof(f136,plain,
( sk_c7 = multiply(sk_c7,sk_c4)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f133,f83]) ).
fof(f142,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f136,f88]) ).
fof(f151,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c7,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f127,f142]) ).
fof(f155,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c3,sk_c5)
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f128,f68]) ).
fof(f165,plain,
( multiply(sk_c3,sk_c5) = multiply(sk_c4,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f155,f142]) ).
fof(f177,plain,
( identity = multiply(sk_c2,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f151,f121]) ).
fof(f190,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f129,f3]) ).
fof(f191,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f129,f129]) ).
fof(f194,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c7),multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f129,f126]) ).
fof(f196,plain,
( sk_c2 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f129,f121]) ).
fof(f198,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f129,f88]) ).
fof(f199,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_7 ),
inference(superposition,[],[f129,f120]) ).
fof(f200,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f129,f98]) ).
fof(f201,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c2),multiply(sk_c7,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f129,f151]) ).
fof(f212,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c7,multiply(sk_c7,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f201,f93]) ).
fof(f213,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f200,f142]) ).
fof(f214,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f198,f142]) ).
fof(f217,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c7),multiply(sk_c7,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f194,f142]) ).
fof(f219,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f213,f93]) ).
fof(f220,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f214,f3]) ).
fof(f221,plain,
( ! [X0] : multiply(sk_c4,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f217,f129]) ).
fof(f223,plain,
( sk_c4 = multiply(sk_c2,sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f177,f220]) ).
fof(f232,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f129,f219]) ).
fof(f234,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f232,f3]) ).
fof(f242,plain,
( sk_c4 = multiply(inverse(sk_c2),sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f129,f223]) ).
fof(f245,plain,
( sk_c4 = multiply(sk_c7,sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f242,f93]) ).
fof(f246,plain,
( sk_c6 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f245,f88]) ).
fof(f247,plain,
( sk_c7 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f246,f142]) ).
fof(f256,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f196,f220]) ).
fof(f257,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f256,f247]) ).
fof(f258,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f257,f3]) ).
fof(f259,plain,
( sk_c7 = sk_c2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f258,f234]) ).
fof(f260,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f93,f259]) ).
fof(f271,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c4)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f199,f220]) ).
fof(f272,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f271,f247]) ).
fof(f273,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f272,f3]) ).
fof(f274,plain,
( sk_c4 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f273,f220]) ).
fof(f275,plain,
( sk_c7 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f274,f247]) ).
fof(f286,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c7,X0)) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f135,f259]) ).
fof(f301,plain,
( sk_c7 = multiply(sk_c3,sk_c5)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f165,f221]) ).
fof(f302,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f301,f275]) ).
fof(f305,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f129,f302]) ).
fof(f307,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f305,f3]) ).
fof(f309,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f307,f234]) ).
fof(f352,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f212,f286]) ).
fof(f412,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c4) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f190,f220]) ).
fof(f413,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c7) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f412,f247]) ).
fof(f428,plain,
( ! [X0] : multiply(X0,sk_c7) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f191,f413]) ).
fof(f463,plain,
( sk_c6 != sk_c5
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f65,f428]) ).
fof(f476,plain,
( sk_c7 != sk_c6
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f463,f309]) ).
fof(f484,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f476,f142]) ).
fof(f485,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f487,plain,
( sk_c7 != sk_c5
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f61,f260]) ).
fof(f489,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f487,f309]) ).
fof(f490,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f492,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c6 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f57,f142]) ).
fof(f494,plain,
( ! [X0] :
( sk_c7 != X0
| inverse(X0) != sk_c6 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f492,f428]) ).
fof(f495,plain,
( ! [X0] :
( sk_c7 != X0
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f494,f142]) ).
fof(f496,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(equality_resolution,[],[f495]) ).
fof(f497,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f496,f260]) ).
fof(f498,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f497]) ).
fof(f499,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f51,f352]) ).
fof(f500,plain,
( ! [X3] :
( sk_c6 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f499,f428]) ).
fof(f501,plain,
( ! [X3] :
( sk_c7 != X3
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f500,f142]) ).
fof(f502,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(equality_resolution,[],[f501]) ).
fof(f503,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f502,f260]) ).
fof(f504,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f503]) ).
fof(f515,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_4 ),
inference(superposition,[],[f3,f60]) ).
fof(f524,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f129,f103]) ).
fof(f526,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f524,f78]) ).
fof(f529,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c2,sk_c7)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f54,f93]) ).
fof(f531,plain,
( sk_c7 != sk_c6
| sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f54,f78]) ).
fof(f533,plain,
( sk_c6 != multiply(sk_c2,sk_c7)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f529]) ).
fof(f535,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f533,f98]) ).
fof(f536,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f535]) ).
fof(f542,definition,
( spl0_15
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f544,plain,
( sk_c7 != sk_c5
| spl0_15 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f550,plain,
( sk_c7 != sk_c5
| sk_c6 != multiply(sk_c7,multiply(sk_c7,sk_c7))
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f51,f60]) ).
fof(f559,definition,
( spl0_16
<=> sk_c6 = multiply(sk_c7,multiply(sk_c7,sk_c7)) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f561,plain,
( sk_c6 != multiply(sk_c7,multiply(sk_c7,sk_c7))
| spl0_16 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f562,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f550,f59,f50,f542,f559]) ).
fof(f611,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f526,f64]) ).
fof(f615,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f129,f526]) ).
fof(f617,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f615,f3]) ).
fof(f649,plain,
( sk_c7 != sk_c6
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| spl0_15 ),
inference(superposition,[],[f544,f611]) ).
fof(f681,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f515,f611]) ).
fof(f687,definition,
( spl0_18
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f688,plain,
( sk_c7 = sk_c6
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f692,plain,
( ~ spl0_18
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f649,f542,f101,f76,f63,f687]) ).
fof(f694,plain,
( identity = sk_c5
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f681,f64]) ).
fof(f696,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f694,f611]) ).
fof(f697,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f696,f617]) ).
fof(f698,plain,
( spl0_18
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f697,f101,f76,f63,f59,f687]) ).
fof(f703,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_18 ),
inference(superposition,[],[f68,f688]) ).
fof(f704,plain,
( sk_c7 = multiply(sk_c1,sk_c7)
| ~ spl0_13
| ~ spl0_18 ),
inference(superposition,[],[f103,f688]) ).
fof(f712,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_demodulation,[],[f703,f611]) ).
fof(f716,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_demodulation,[],[f712,f688]) ).
fof(f726,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f561,f716]) ).
fof(f735,plain,
( sk_c7 != sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f726,f716]) ).
fof(f736,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f735,f688]) ).
fof(f737,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f736]) ).
fof(f738,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c6 )
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f57,f688]) ).
fof(f740,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c7) )
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f738,f688]) ).
fof(f743,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f740,f78]) ).
fof(f744,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f743,f688]) ).
fof(f746,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f744,f704]) ).
fof(f747,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f746]) ).
fof(f752,plain,
( sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f531,f688]) ).
fof(f755,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_demodulation,[],[f752,f704]) ).
fof(f760,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f755,f688]) ).
fof(f761,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f760]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f70]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f84]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f89]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f99]) ).
cnf(s7,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f104]) ).
cnf(s8,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f105]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f106]) ).
cnf(s10,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f107]) ).
cnf(s11,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f108]) ).
cnf(s12,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f109]) ).
cnf(s13,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f110]) ).
cnf(s14,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f111]) ).
cnf(s15,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s16,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s17,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f114]) ).
cnf(s18,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f115]) ).
cnf(s19,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f116]) ).
cnf(s20,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f117]) ).
cnf(s21,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f118]) ).
cnf(s22,plain,
spl0_6,
inference(sat_conversion,[],[f119]) ).
cnf(s23,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f485]) ).
cnf(s24,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f490]) ).
cnf(s25,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f498]) ).
cnf(s26,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f504]) ).
cnf(s28,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f536]) ).
cnf(s30,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f562]) ).
cnf(s42,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| spl0_15
| ~ spl0_18 ),
inference(sat_conversion,[],[f692]) ).
cnf(s44,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f698]) ).
cnf(s49,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f737]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(sat_conversion,[],[f747]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_18 ),
inference(sat_conversion,[],[f761]) ).
cnf(s55,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1,s22]) ).
cnf(s56,plain,
spl0_4,
inference(rat,[],[s24,s12,s13,s14,s15,s16,s22]) ).
cnf(s57,plain,
spl0_5,
inference(rat,[],[s23,s17,s18,s19,s20,s21,s22]) ).
cnf(s58,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s25,s3,s4,s5,s6]) ).
cnf(s59,plain,
( ~ spl0_13
| ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s50,s44,s56,s57]) ).
cnf(s60,plain,
( ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s8,s25,s9,s10,s11,s59,s58]) ).
cnf(s61,plain,
~ spl0_3,
inference(rat,[],[s50,s44,s2,s7,s60,s56,s57]) ).
cnf(s62,plain,
( ~ spl0_13
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s54,s44,s56,s57]) ).
cnf(s63,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s28,s10,s11]) ).
cnf(s64,plain,
( ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s28,s5,s6,s62]) ).
cnf(s65,plain,
~ spl0_2,
inference(rat,[],[s64,s63]) ).
cnf(s66,plain,
spl0_1,
inference(rat,[],[s55,s56,s57,s61,s65]) ).
cnf(s67,plain,
( ~ spl0_13
| ~ spl0_18
| ~ spl0_8 ),
inference(rat,[],[s30,s49,s42,s57,s22,s66,s56]) ).
cnf(s68,plain,
( ~ spl0_13
| ~ spl0_8 ),
inference(rat,[],[s67,s44,s57,s56]) ).
cnf(s69,plain,
spl0_13,
inference(rat,[],[s10,s26,s7,s8,s9,s11,s66]) ).
cnf(s70,plain,
~ spl0_8,
inference(rat,[],[s68,s69]) ).
cnf(s71,plain,
spl0_12,
inference(rat,[],[s6,s70]) ).
cnf(s72,plain,
spl0_11,
inference(rat,[],[s5,s70]) ).
cnf(s73,plain,
spl0_10,
inference(rat,[],[s4,s70]) ).
cnf(s74,plain,
spl0_9,
inference(rat,[],[s3,s70]) ).
cnf(s75,plain,
spl0_7,
inference(rat,[],[s2,s70]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s26,s73,s75,s66,s71,s74,s72]) ).
fof(f762,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP304-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:55:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.83/1.05 % (3313559)Input is clausal, will run a generic CNF schedule.
% 1.83/1.05 % (3313564)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=403281117:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.83/1.05 % (3313568)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4226149111:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.83/1.05 % (3313565)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=88388065:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.83/1.05 % (3313570)dis-21_1_sil=8000:lcm=predicate:random_seed=3959944037: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)
% 1.83/1.05 % (3313569)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3454941600:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.83/1.05 % (3313567)lrs+10_1_sil=8000:sp=occurrence:random_seed=957032965:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.83/1.05 % (3313566)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1572822790:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.83/1.05 % (3313570)Refutation not found, incomplete strategy
% 1.83/1.05 % (3313570)------------------------------
% 1.83/1.05 % (3313570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.83/1.05 % (3313570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/1.05 % (3313570)CaDiCaL version: 2.1.3
% 1.83/1.05 % (3313570)Termination reason: Refutation not found, incomplete strategy
% 1.83/1.05 % (3313570)Time elapsed: 0.003 s
% 1.83/1.05 % (3313570)Peak memory usage: 88 MB
% 1.83/1.05 % (3313570)Instructions burned: 1 (million)
% 1.83/1.05 % (3313567)Refutation not found, incomplete strategy
% 1.83/1.05 % (3313567)------------------------------
% 1.83/1.05 % (3313567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.83/1.05 % (3313567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/1.05 % (3313567)CaDiCaL version: 2.1.3
% 1.83/1.05 % (3313567)Termination reason: Refutation not found, incomplete strategy
% 1.83/1.05 % (3313567)Time elapsed: 0.003 s
% 1.83/1.05 % (3313567)Peak memory usage: 88 MB
% 1.83/1.05 % (3313567)Instructions burned: 4 (million)
% 1.83/1.05 % (3313569)First to succeed.
% 1.83/1.05 % (3313569)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3313559"
% 1.83/1.05 % (3313568)Instruction limit reached!
% 1.83/1.05 % (3313568)------------------------------
% 1.83/1.05 % (3313568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.83/1.05 % (3313568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/1.05 % (3313568)CaDiCaL version: 2.1.3
% 1.83/1.05 % (3313568)Termination reason: Instruction limit
% 1.83/1.05 % (3313568)Termination phase: Saturation
% 1.83/1.05 % (3313568)Time elapsed: 0.067 s
% 1.83/1.05 % (3313568)Peak memory usage: 89 MB
% 1.83/1.05 % (3313568)Instructions burned: 115 (million)
% 1.83/1.05 % (3313567)------------------------------
% 1.83/1.05 % (3313567)------------------------------
% 1.83/1.05 % (3313570)------------------------------
% 1.83/1.05 % (3313570)------------------------------
% 1.83/1.05 % (3313578)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=1164115897:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.83/1.05 % (3313578)Refutation not found, incomplete strategy
% 1.83/1.05 % (3313578)------------------------------
% 1.83/1.05 % (3313578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.83/1.05 % (3313578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/1.05 % (3313578)CaDiCaL version: 2.1.3
% 1.83/1.05 % (3313578)Termination reason: Refutation not found, incomplete strategy
% 1.83/1.05 % (3313578)Time elapsed: 0.006 s
% 1.83/1.05 % (3313578)Peak memory usage: 88 MB
% 1.83/1.05 % (3313578)Instructions burned: 9 (million)
% 1.83/1.05 % (3313569)Refutation found. Thanks to Tanya!
% 1.83/1.05 % SZS status Unsatisfiable for theBenchmark
% 1.83/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.26 % (3313569)------------------------------
% 3.50/1.26 % (3313569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.26 % (3313569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.26 % (3313569)CaDiCaL version: 2.1.3
% 3.50/1.26 % (3313569)Termination reason: Refutation
% 3.50/1.26 % (3313569)Time elapsed: 0.017 s
% 3.50/1.26 % (3313569)Peak memory usage: 89 MB
% 3.50/1.26 % (3313569)Instructions burned: 26 (million)
% 3.50/1.26 % (3313569)------------------------------
% 3.50/1.26 % (3313569)------------------------------
% 3.50/1.26 % (3313559)Success in time 0.442 s
% 3.50/1.26 % Vampire exiting
%------------------------------------------------------------------------------