%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP309-1 : 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 : n012.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 10:13:36 AM UTC 2026
% Result : Unsatisfiable 0.42s 0.84s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 41
% Syntax : Number of formulae : 276 ( 23 unt; 16 def)
% Number of atoms : 926 ( 258 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1239 ( 589 ~; 634 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 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 : 41 ( 0 sgn 41 !; 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
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = inverse(sk_c7)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
multiply(sk_c5,sk_c6) = sk_c7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
sk_c7 = multiply(sk_c5,sk_c6),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,X0) != sk_c6
| multiply(X1,sk_c7) != X0
| inverse(X1) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X3,sk_c6) != sk_c5
| inverse(X3) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c5 != inverse(sk_c7)
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c6 != multiply(sk_c7,X0)
| multiply(X1,sk_c7) != X0
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,plain,
! [X2,X3,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c5 != inverse(sk_c7)
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ),
inference(equality_resolution,[],[f48]) ).
fof(f51,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f52,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl0_2
<=> ! [X2] :
( sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f55,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c6 != multiply(X2,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,definition,
( spl0_3
<=> ! [X1] :
( sk_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f58,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,multiply(X1,sk_c7)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_4
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f61,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f64,definition,
( spl0_5
<=> sk_c5 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f65,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( sk_c5 != inverse(sk_c7)
| spl0_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_6
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f69,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f70,plain,
( multiply(sk_c7,sk_c6) != sk_c5
| spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f49,f68,f64,f60,f57,f54,f51]) ).
fof(f73,definition,
( spl0_7
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f75,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f79,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f46,f77,f73]) ).
fof(f82,definition,
( spl0_9
<=> sk_c5 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f84,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f44,f77,f82]) ).
fof(f87,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f89,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f42,f77,f87]) ).
fof(f92,definition,
( spl0_11
<=> sk_c6 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f94,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f40,f77,f92]) ).
fof(f97,definition,
( spl0_12
<=> sk_c2 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f99,plain,
( sk_c2 = multiply(sk_c1,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f38,f97,f73]) ).
fof(f101,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f97,f82]) ).
fof(f102,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f34,f97,f87]) ).
fof(f103,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f32,f97,f92]) ).
fof(f105,definition,
( spl0_13
<=> sk_c6 = multiply(sk_c7,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f107,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f30,f105,f73]) ).
fof(f109,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f28,f105,f82]) ).
fof(f110,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f26,f105,f87]) ).
fof(f111,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f24,f105,f92]) ).
fof(f112,plain,
spl0_4,
inference(avatar_split_clause,[],[f22,f60]) ).
fof(f113,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f20,f64,f73]) ).
fof(f114,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f64,f82]) ).
fof(f115,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f64,f87]) ).
fof(f116,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f64,f92]) ).
fof(f117,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f68,f73]) ).
fof(f118,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f68,f82]) ).
fof(f119,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f68,f87]) ).
fof(f120,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f68,f92]) ).
fof(f121,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f3,f75]) ).
fof(f122,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f89]) ).
fof(f124,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f126,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_11 ),
inference(superposition,[],[f4,f94]) ).
fof(f127,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f61]) ).
fof(f129,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f121]) ).
fof(f130,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f129,f1]) ).
fof(f132,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f124,f1]) ).
fof(f134,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f122]) ).
fof(f135,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f134,f1]) ).
fof(f140,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f130,f84]) ).
fof(f144,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c5,identity)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f127,f121]) ).
fof(f172,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f132,f94]) ).
fof(f173,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_4 ),
inference(superposition,[],[f132,f61]) ).
fof(f175,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f132,f140]) ).
fof(f177,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_10 ),
inference(superposition,[],[f132,f122]) ).
fof(f178,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_7 ),
inference(superposition,[],[f132,f121]) ).
fof(f182,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f175,f3]) ).
fof(f184,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f172,f89]) ).
fof(f188,plain,
( sk_c7 != sk_c5
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f70,f184]) ).
fof(f189,plain,
( multiply(sk_c3,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f126,f184]) ).
fof(f190,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f132,f184]) ).
fof(f192,plain,
( identity = sk_c6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f190,f3]) ).
fof(f193,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f189,f94]) ).
fof(f196,plain,
( sk_c6 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f192,f182]) ).
fof(f199,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f177,f182]) ).
fof(f200,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f178,f182]) ).
fof(f206,plain,
( sk_c7 != sk_c6
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f188,f196]) ).
fof(f207,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f199,f196]) ).
fof(f208,plain,
( sk_c4 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f200,f196]) ).
fof(f209,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f208,f3]) ).
fof(f210,plain,
( sk_c5 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f209,f182]) ).
fof(f211,plain,
( sk_c6 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f210,f196]) ).
fof(f243,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c5,sk_c5)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f144,f182]) ).
fof(f244,plain,
( multiply(sk_c7,sk_c4) = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f243,f196]) ).
fof(f245,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f244,f193]) ).
fof(f246,plain,
( sk_c6 = multiply(sk_c7,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f245,f211]) ).
fof(f247,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f246,f184]) ).
fof(f248,plain,
( $false
| ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f247,f206]) ).
fof(f249,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f250,plain,
( sk_c6 != inverse(sk_c7)
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f66,f196]) ).
fof(f251,plain,
( sk_c6 = multiply(sk_c7,sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f69,f196]) ).
fof(f252,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f251,f184]) ).
fof(f262,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f207,f252]) ).
fof(f264,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f262,f3]) ).
fof(f271,plain,
( sk_c5 = sk_c3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f264,f182]) ).
fof(f278,plain,
( sk_c6 = sk_c3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f271,f196]) ).
fof(f281,plain,
( sk_c7 = sk_c3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f278,f252]) ).
fof(f284,plain,
( sk_c7 != inverse(sk_c7)
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f250,f252]) ).
fof(f300,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f89,f281]) ).
fof(f301,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f300,f284]) ).
fof(f302,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f306,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c7)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f52,f252]) ).
fof(f308,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f306,f196]) ).
fof(f310,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f308,f252]) ).
fof(f311,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c7) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f310,f252]) ).
fof(f329,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f311,f89]) ).
fof(f331,plain,
( sk_c7 != multiply(sk_c3,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f329]) ).
fof(f334,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f331,f94]) ).
fof(f339,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f334,f252]) ).
fof(f340,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f368,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(sk_c7,multiply(X1,sk_c7)) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f58,f252]) ).
fof(f371,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c7,multiply(sk_c3,sk_c7))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f368,f89]) ).
fof(f373,plain,
( sk_c7 != multiply(sk_c7,multiply(sk_c3,sk_c7))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f371]) ).
fof(f376,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f373,f135]) ).
fof(f377,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f376]) ).
fof(f392,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_5 ),
inference(superposition,[],[f3,f65]) ).
fof(f393,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f392,f182]) ).
fof(f401,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_12 ),
inference(superposition,[],[f132,f99]) ).
fof(f403,plain,
( sk_c7 = multiply(sk_c7,sk_c2)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f401,f79]) ).
fof(f405,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_13 ),
inference(superposition,[],[f132,f107]) ).
fof(f407,plain,
( multiply(sk_c5,sk_c6) = sk_c2
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f405,f65]) ).
fof(f408,plain,
( sk_c7 = sk_c2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f407,f61]) ).
fof(f409,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f107,f408]) ).
fof(f410,plain,
( sk_c7 != sk_c5
| sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f55,f65]) ).
fof(f420,definition,
( spl0_15
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f421,plain,
( sk_c7 = sk_c6
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f425,definition,
( spl0_16
<=> sk_c6 = multiply(sk_c7,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f427,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| spl0_16 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f429,definition,
( spl0_17
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f430,plain,
( sk_c7 = sk_c5
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f431,plain,
( sk_c7 != sk_c5
| spl0_17 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f435,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f132,f393]) ).
fof(f437,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f435,f3]) ).
fof(f442,plain,
( sk_c7 = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f437,f182]) ).
fof(f447,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f442,f431]) ).
fof(f448,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f454,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f173,f430]) ).
fof(f456,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f454,f3]) ).
fof(f457,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f456,f437]) ).
fof(f460,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f52,f430]) ).
fof(f461,plain,
( spl0_15
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f457,f429,f82,f73,f64,f60,f420]) ).
fof(f463,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_15 ),
inference(superposition,[],[f69,f421]) ).
fof(f477,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f460,f421]) ).
fof(f478,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c7) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f477,f421]) ).
fof(f482,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f478,f79]) ).
fof(f483,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_15
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f482]) ).
fof(f484,plain,
( sk_c7 != sk_c2
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f483,f99]) ).
fof(f487,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f484,f408]) ).
fof(f488,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f487]) ).
fof(f502,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f392,f430]) ).
fof(f506,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c7,multiply(sk_c1,sk_c7))
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f58,f79]) ).
fof(f507,plain,
( sk_c6 != multiply(sk_c7,multiply(sk_c1,sk_c7))
| ~ spl0_3
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f506]) ).
fof(f508,plain,
( sk_c6 != multiply(sk_c7,sk_c2)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f507,f99]) ).
fof(f510,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f508,f107]) ).
fof(f511,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f513,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f410,f430]) ).
fof(f517,plain,
( ~ spl0_16
| ~ spl0_2
| ~ spl0_5
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f513,f429,f64,f54,f425]) ).
fof(f534,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f502,f456]) ).
fof(f535,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f534,f427]) ).
fof(f536,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f535]) ).
fof(f556,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f403,f408]) ).
fof(f617,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f409,f556]) ).
fof(f622,plain,
( sk_c7 = sk_c5
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f463,f556]) ).
fof(f624,plain,
( spl0_15
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f617,f105,f97,f77,f64,f60,f420]) ).
fof(f625,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f622,f431]) ).
fof(f626,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f625]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f71]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f80]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f85]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f90]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f95]) ).
cnf(s6,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f100]) ).
cnf(s7,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f101]) ).
cnf(s8,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f102]) ).
cnf(s9,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f103]) ).
cnf(s10,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f108]) ).
cnf(s11,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f109]) ).
cnf(s12,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f110]) ).
cnf(s13,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f111]) ).
cnf(s14,plain,
spl0_4,
inference(sat_conversion,[],[f112]) ).
cnf(s15,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f113]) ).
cnf(s16,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f114]) ).
cnf(s17,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f115]) ).
cnf(s18,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f116]) ).
cnf(s19,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f117]) ).
cnf(s20,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f118]) ).
cnf(s21,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f119]) ).
cnf(s22,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f120]) ).
cnf(s23,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f249]) ).
cnf(s24,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f302]) ).
cnf(s26,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f340]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f377]) ).
cnf(s41,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f448]) ).
cnf(s45,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f461]) ).
cnf(s46,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f488]) ).
cnf(s48,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f511]) ).
cnf(s49,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f517]) ).
cnf(s50,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f536]) ).
cnf(s55,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f624]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f626]) ).
cnf(s57,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1,s14]) ).
cnf(s58,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(rat,[],[s23,s24,s14]) ).
cnf(s59,plain,
spl0_5,
inference(rat,[],[s58,s15,s16,s17,s18]) ).
cnf(s60,plain,
spl0_6,
inference(rat,[],[s23,s19,s20,s21,s22,s14]) ).
cnf(s61,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s48,s5,s9,s13]) ).
cnf(s62,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s48,s4,s8,s12]) ).
cnf(s63,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s48,s3,s7,s11]) ).
cnf(s64,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_3 ),
inference(rat,[],[s48,s2,s6,s10,s33,s60]) ).
cnf(s65,plain,
~ spl0_3,
inference(rat,[],[s64,s63,s62,s61]) ).
cnf(s66,plain,
( ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s49,s50,s59,s14]) ).
cnf(s67,plain,
( spl0_9
| spl0_17 ),
inference(rat,[],[s56,s55,s3,s7,s11,s14,s59,s60]) ).
cnf(s68,plain,
( ~ spl0_9
| spl0_17 ),
inference(rat,[],[s56,s55,s2,s6,s10,s41,s60,s59,s14]) ).
cnf(s69,plain,
spl0_17,
inference(rat,[],[s68,s67]) ).
cnf(s71,plain,
~ spl0_2,
inference(rat,[],[s66,s69]) ).
cnf(s72,plain,
spl0_1,
inference(rat,[],[s57,s59,s60,s65,s71]) ).
cnf(s73,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s26,s12,s13,s60,s72]) ).
cnf(s74,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s26,s8,s9,s60,s72]) ).
cnf(s75,plain,
( ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s26,s4,s5,s46,s74,s73,s45,s69,s59,s14,s72,s60]) ).
cnf(s76,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s46,s55,s69,s72,s59,s14]) ).
cnf(s77,plain,
spl0_9,
inference(rat,[],[s76,s3,s7,s11]) ).
cnf(s78,plain,
~ spl0_7,
inference(rat,[],[s75,s77]) ).
cnf(s79,plain,
spl0_13,
inference(rat,[],[s10,s78]) ).
cnf(s80,plain,
spl0_12,
inference(rat,[],[s6,s78]) ).
cnf(s81,plain,
spl0_8,
inference(rat,[],[s2,s78]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s76,s79,s80,s81]) ).
fof(f627,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP309-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 09:49:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.42/0.84 % (2125741)Input is clausal, will run a generic CNF schedule.
% 0.42/0.84 % (2125751)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1282117108:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.42/0.84 % (2125747)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1275960666:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.42/0.84 % (2125752)dis-21_1_sil=8000:lcm=predicate:random_seed=3924243793: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)
% 0.42/0.84 % (2125749)lrs+10_1_sil=8000:sp=occurrence:random_seed=4261082509:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.42/0.84 % (2125746)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=295439249:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.42/0.84 % (2125750)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3972147185:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.42/0.84 % (2125748)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1523670310:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.42/0.84 % (2125752)Refutation not found, incomplete strategy
% 0.42/0.84 % (2125752)------------------------------
% 0.42/0.84 % (2125752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.84 % (2125752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.84 % (2125752)CaDiCaL version: 2.1.3
% 0.42/0.84 % (2125752)Termination reason: Refutation not found, incomplete strategy
% 0.42/0.84 % (2125752)Time elapsed: 0.001 s
% 0.42/0.84 % (2125752)Peak memory usage: 88 MB
% 0.42/0.84 % (2125752)Instructions burned: 1 (million)
% 0.42/0.84 % (2125749)Refutation not found, incomplete strategy
% 0.42/0.84 % (2125749)------------------------------
% 0.42/0.84 % (2125749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.84 % (2125749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.84 % (2125749)CaDiCaL version: 2.1.3
% 0.42/0.84 % (2125749)Termination reason: Refutation not found, incomplete strategy
% 0.42/0.84 % (2125749)Time elapsed: 0.001 s
% 0.42/0.84 % (2125749)Peak memory usage: 88 MB
% 0.42/0.84 % (2125749)Instructions burned: 2 (million)
% 0.42/0.84 % (2125751)First to succeed.
% 0.42/0.84 % (2125751)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2125741"
% 0.42/0.84 % (2125750)Instruction limit reached!
% 0.42/0.84 % (2125750)------------------------------
% 0.42/0.84 % (2125750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.84 % (2125750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.84 % (2125750)CaDiCaL version: 2.1.3
% 0.42/0.84 % (2125750)Termination reason: Instruction limit
% 0.42/0.84 % (2125750)Termination phase: Saturation
% 0.42/0.84 % (2125750)Time elapsed: 0.036 s
% 0.42/0.84 % (2125750)Peak memory usage: 89 MB
% 0.42/0.84 % (2125750)Instructions burned: 115 (million)
% 0.42/0.84 % (2125749)------------------------------
% 0.42/0.84 % (2125749)------------------------------
% 0.42/0.84 % (2125752)------------------------------
% 0.42/0.84 % (2125752)------------------------------
% 0.42/0.84 % (2125751)Refutation found. Thanks to Tanya!
% 0.42/0.84 % SZS status Unsatisfiable for theBenchmark
% 0.42/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.93 % (2125751)------------------------------
% 2.35/0.93 % (2125751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.93 % (2125751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.93 % (2125751)CaDiCaL version: 2.1.3
% 2.35/0.93 % (2125751)Termination reason: Refutation
% 2.35/0.93 % (2125751)Time elapsed: 0.009 s
% 2.35/0.93 % (2125751)Peak memory usage: 89 MB
% 2.35/0.93 % (2125751)Instructions burned: 23 (million)
% 2.35/0.93 % (2125751)------------------------------
% 2.35/0.93 % (2125751)------------------------------
% 2.35/0.93 % (2125741)Success in time 0.301 s
% 2.35/0.93 % Vampire exiting
%------------------------------------------------------------------------------