%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP309-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:27 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 37
% Syntax : Number of formulae : 245 ( 23 unt; 18 def)
% Number of atoms : 898 ( 245 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1286 ( 633 ~; 635 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
sk_c7 = multiply(sk_c5,sk_c6),
inference(reorient_equations,[],[f21]) ).
fof(f27,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/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/sandbox/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(f35,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c2
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/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/sandbox/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(f43,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ 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_c6 != multiply(sk_c7,multiply(X1,sk_c7))
| sk_c7 != inverse(X1) )
| ~ 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(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(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(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(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(f124,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
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(f140,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f130,f84]) ).
fof(f172,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f132,f94]) ).
fof(f175,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f132,f140]) ).
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(f190,plain,
( sk_c7 = multiply(identity,sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f61,f182]) ).
fof(f191,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f190,f1]) ).
fof(f193,plain,
( sk_c7 != sk_c5
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f70,f184]) ).
fof(f195,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f132,f184]) ).
fof(f197,plain,
( identity = sk_c6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f195,f3]) ).
fof(f199,plain,
( identity != sk_c7
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f193,f182]) ).
fof(f200,plain,
( sk_c7 = multiply(sk_c5,identity)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f61,f197]) ).
fof(f203,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f121,f197]) ).
fof(f213,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f203,f1]) ).
fof(f216,plain,
( sk_c7 = multiply(identity,identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f200,f182]) ).
fof(f219,plain,
( identity = sk_c7
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f216,f1]) ).
fof(f231,plain,
( sk_c6 = inverse(identity)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f75,f213]) ).
fof(f232,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f231,f197]) ).
fof(f242,plain,
( $false
| ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f219,f199]) ).
fof(f243,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f244,plain,
( identity != inverse(sk_c7)
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f66,f182]) ).
fof(f253,plain,
( identity != inverse(identity)
| ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f244,f219]) ).
fof(f288,plain,
( $false
| ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f253,f232]) ).
fof(f289,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f288]) ).
fof(f351,plain,
( identity = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f65,f182]) ).
fof(f365,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_8 ),
inference(superposition,[],[f3,f79]) ).
fof(f367,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f3,f351]) ).
fof(f368,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f367,f1]) ).
fof(f373,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f351,f368]) ).
fof(f399,plain,
( ! [X2] :
( sk_c6 != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f55,f368]) ).
fof(f400,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f399,f191]) ).
fof(f401,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f400,f368]) ).
fof(f402,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f401,f368]) ).
fof(f408,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f402,f3]) ).
fof(f410,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f408]) ).
fof(f413,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f410,f373]) ).
fof(f417,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f413,f373]) ).
fof(f418,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f421,plain,
( ! [X1] :
( sk_c6 != multiply(identity,multiply(X1,identity))
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f58,f368]) ).
fof(f422,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f421,f1]) ).
fof(f423,plain,
( ! [X1] :
( sk_c7 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f422,f191]) ).
fof(f424,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f423,f368]) ).
fof(f425,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f424,f368]) ).
fof(f429,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f425,f3]) ).
fof(f431,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f429]) ).
fof(f434,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f431,f373]) ).
fof(f438,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f434,f373]) ).
fof(f439,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f442,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c7)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f52,f191]) ).
fof(f443,plain,
( ! [X3] :
( sk_c5 != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f442,f368]) ).
fof(f444,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f443,f182]) ).
fof(f445,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| identity != multiply(X3,identity) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f444,f191]) ).
fof(f446,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f445,f368]) ).
fof(f451,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f446,f3]) ).
fof(f453,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f451]) ).
fof(f456,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f453,f373]) ).
fof(f460,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f456,f373]) ).
fof(f461,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f460]) ).
fof(f470,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_12 ),
inference(superposition,[],[f132,f99]) ).
fof(f472,plain,
( sk_c7 = multiply(sk_c7,sk_c2)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f470,f79]) ).
fof(f474,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_13 ),
inference(superposition,[],[f132,f107]) ).
fof(f476,plain,
( multiply(sk_c5,sk_c6) = sk_c2
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f474,f65]) ).
fof(f477,plain,
( sk_c7 = sk_c2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f476,f61]) ).
fof(f479,plain,
( sk_c6 != sk_c2
| sk_c7 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f55,f99]) ).
fof(f494,plain,
( sk_c6 != sk_c2
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f479,f79]) ).
fof(f496,definition,
( spl0_16
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f497,plain,
( identity = sk_c6
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f508,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_8 ),
inference(superposition,[],[f132,f365]) ).
fof(f511,plain,
( sk_c1 = multiply(sk_c5,identity)
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f508,f65]) ).
fof(f525,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f472,f477]) ).
fof(f541,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f132,f525]) ).
fof(f543,plain,
( identity = sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f541,f3]) ).
fof(f567,plain,
( sk_c6 = multiply(identity,sk_c2)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f107,f543]) ).
fof(f580,plain,
( sk_c6 = sk_c2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f567,f1]) ).
fof(f584,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f580,f494]) ).
fof(f585,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f584]) ).
fof(f587,plain,
( sk_c7 = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f580,f477]) ).
fof(f591,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f587,f543]) ).
fof(f593,plain,
( spl0_16
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f591,f105,f97,f77,f64,f60,f496]) ).
fof(f596,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f52,f69]) ).
fof(f600,plain,
( sk_c6 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f596]) ).
fof(f607,definition,
( spl0_19
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f608,plain,
( identity = sk_c5
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f616,definition,
( spl0_21
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f618,plain,
( sk_c6 != sk_c5
| spl0_21 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f620,plain,
( sk_c6 != sk_c5
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f600,f65]) ).
fof(f622,plain,
( ~ spl0_21
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f620,f68,f64,f51,f616]) ).
fof(f630,plain,
( sk_c5 = multiply(sk_c7,identity)
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f69,f497]) ).
fof(f638,plain,
( sk_c5 = multiply(identity,identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f630,f543]) ).
fof(f642,plain,
( identity = sk_c5
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f638,f1]) ).
fof(f645,plain,
( spl0_19
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f642,f496,f105,f97,f77,f68,f64,f60,f607]) ).
fof(f653,plain,
( sk_c1 = multiply(identity,identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_19 ),
inference(superposition,[],[f511,f608]) ).
fof(f654,plain,
( identity = sk_c1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_19 ),
inference(forward_demodulation,[],[f653,f1]) ).
fof(f661,plain,
( identity != sk_c6
| ~ spl0_19
| spl0_21 ),
inference(forward_demodulation,[],[f618,f608]) ).
fof(f662,plain,
( $false
| ~ spl0_16
| ~ spl0_19
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f661,f497]) ).
fof(f663,plain,
( ~ spl0_16
| ~ spl0_19
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f662]) ).
fof(f664,plain,
( ! [X1] :
( sk_c6 != multiply(identity,multiply(X1,identity))
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f58,f543]) ).
fof(f666,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f664,f1]) ).
fof(f667,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f666,f497]) ).
fof(f668,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f667,f543]) ).
fof(f669,plain,
( identity != sk_c1
| identity != inverse(sk_c5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f668,f511]) ).
fof(f675,plain,
( identity != inverse(identity)
| identity != sk_c1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f669,f608]) ).
fof(f677,definition,
( spl0_23
<=> identity = sk_c1 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f678,plain,
( identity = sk_c1
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f681,definition,
( spl0_24
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f684,plain,
( ~ spl0_23
| ~ spl0_24
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f675,f607,f496,f105,f97,f77,f64,f60,f57,f681,f677]) ).
fof(f685,plain,
( spl0_23
| ~ spl0_5
| ~ spl0_8
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f654,f607,f77,f64,f677]) ).
fof(f691,plain,
( sk_c7 = inverse(identity)
| ~ spl0_8
| ~ spl0_23 ),
inference(superposition,[],[f79,f678]) ).
fof(f698,plain,
( identity = inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f691,f543]) ).
fof(f701,plain,
( spl0_24
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f698,f677,f105,f97,f77,f64,f60,f681]) ).
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(s6,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f100]) ).
cnf(s7,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f101]) ).
cnf(s10,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f108]) ).
cnf(s11,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f109]) ).
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,[],[f243]) ).
cnf(s24,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f289]) ).
cnf(s35,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f418]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f439]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f461]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f585]) ).
cnf(s49,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f593]) ).
cnf(s52,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_21 ),
inference(sat_conversion,[],[f622]) ).
cnf(s54,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f645]) ).
cnf(s55,plain,
( ~ spl0_16
| ~ spl0_19
| spl0_21 ),
inference(sat_conversion,[],[f663]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_19
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f684]) ).
cnf(s57,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_19
| spl0_23 ),
inference(sat_conversion,[],[f685]) ).
cnf(s62,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f701]) ).
cnf(s63,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1,s14]) ).
cnf(s64,plain,
spl0_5,
inference(rat,[],[s24,s15,s16,s17,s18,s14]) ).
cnf(s65,plain,
spl0_6,
inference(rat,[],[s23,s19,s20,s21,s22,s14]) ).
cnf(s66,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s56,s62,s57,s54,s49,s3,s7,s11,s14,s64,s65]) ).
cnf(s67,plain,
( ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s56,s62,s57,s54,s49,s2,s6,s10,s38,s65,s64,s14]) ).
cnf(s68,plain,
~ spl0_3,
inference(rat,[],[s67,s66]) ).
cnf(s69,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s46,s3,s7,s11,s14,s64]) ).
cnf(s70,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s46,s2,s6,s10,s35,s64,s14]) ).
cnf(s71,plain,
~ spl0_2,
inference(rat,[],[s70,s69]) ).
cnf(s72,plain,
spl0_1,
inference(rat,[],[s63,s64,s65,s68,s71]) ).
cnf(s73,plain,
~ spl0_21,
inference(rat,[],[s52,s64,s65,s72]) ).
cnf(s74,plain,
( ~ spl0_8
| ~ spl0_16
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s55,s54,s65,s64,s14,s73]) ).
cnf(s75,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s74,s49,s64,s14]) ).
cnf(s76,plain,
spl0_9,
inference(rat,[],[s75,s3,s7,s11]) ).
cnf(s77,plain,
~ spl0_7,
inference(rat,[],[s41,s64,s72,s14,s76]) ).
cnf(s78,plain,
spl0_13,
inference(rat,[],[s10,s77]) ).
cnf(s79,plain,
spl0_12,
inference(rat,[],[s6,s77]) ).
cnf(s80,plain,
spl0_8,
inference(rat,[],[s2,s77]) ).
cnf(s81,plain,
$false,
inference(rat,[],[s75,s78,s79,s80]) ).
fof(f702,plain,
$false,
inference(avatar_sat_refutation,[],[s81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP309-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:53:15 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % (1416493)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1416500)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3822166705:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (1416499)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1416498)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2688406590_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (1416499)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3952816427:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1416501)dis+10_1_sil=32000:sp=arity:random_seed=4081617625:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1416503)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1509016250:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1416502)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2228041866:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (1416504)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1761637110:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (1416503) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1416493-1416503"...
% 0.17/0.47 % (1416502) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1416493-1416502"...
% 0.17/0.47 % (1416501) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1416493-1416501"...
% 0.17/0.47 % TRYING [5]
% 0.17/0.47 % (1416501)...printing done.
% 0.17/0.47 % (1416502)...printing done.
% 0.17/0.47 % (1416503)...printing done.
% 0.17/0.47 % (1416501)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1416501)------------------------------
% 0.17/0.47 % (1416501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1416501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1416501)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1416501)Termination reason: Refutation
% 0.17/0.47 % (1416501)Time elapsed: 0.015 s
% 0.17/0.47 % (1416501)Peak memory usage: 12 MB
% 0.17/0.47 % (1416501)Instructions burned: 23 (million)
% 0.17/0.47 % (1416493)Success in time 0.048 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------