%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP302-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 10:17:26 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.38s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 37
% Syntax : Number of formulae : 247 ( 26 unt; 14 def)
% Number of atoms : 752 ( 240 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 955 ( 450 ~; 491 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c8 = inverse(sk_c1)
| inverse(sk_c5) = sk_c4 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = inverse(sk_c1)
| sk_c4 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f22]) ).
fof(f28,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c4 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f30]) ).
fof(f40,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| sk_c4 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c8 = inverse(sk_c2)
| inverse(sk_c5) = sk_c4 ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c8 = inverse(sk_c2)
| sk_c4 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| multiply(X1,sk_c8) != sk_c6
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X3) != X4
| inverse(X4) != sk_c8
| multiply(X3,sk_c8) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c7 != inverse(sk_c8)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7)
| inverse(X3) != X4
| sk_c8 != inverse(X4)
| multiply(X3,sk_c8) != X4 ),
inference(reorient_equations,[],[f54]) ).
fof(f57,definition,
( spl0_1
<=> ! [X4,X3] :
( inverse(X3) != X4
| multiply(X3,sk_c8) != X4
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ! [X3,X4] :
( inverse(X3) != X4
| multiply(X3,sk_c8) != X4
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_2
<=> ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f61,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_3
<=> sk_c7 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( sk_c7 != inverse(sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_4
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl0_5
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f71,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f55,f70,f60,f67,f63,f60,f57]) ).
fof(f75,definition,
( spl0_6
<=> sk_c4 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f77,plain,
( sk_c4 = multiply(sk_c5,sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f81,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f53,f79,f75]) ).
fof(f84,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f86,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f51,f79,f84]) ).
fof(f89,definition,
( spl0_9
<=> inverse(sk_c5) = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f91,plain,
( inverse(sk_c5) = sk_c4
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f49,f79,f89]) ).
fof(f94,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f96,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f47,f79,f94]) ).
fof(f99,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f101,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f45,f79,f99]) ).
fof(f103,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f43,f79,f63]) ).
fof(f105,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f106,plain,
( sk_c6 != multiply(sk_c2,sk_c8)
| spl0_12 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( sk_c6 = multiply(sk_c2,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f41,f105,f75]) ).
fof(f113,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f31,f105,f63]) ).
fof(f115,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 != multiply(sk_c1,sk_c7)
| spl0_13 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f117,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f29,f115,f75]) ).
fof(f121,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f23,f115,f94]) ).
fof(f122,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f21,f115,f99]) ).
fof(f123,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f19,f115,f63]) ).
fof(f125,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f127,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f17,f125,f75]) ).
fof(f129,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f15,f125,f84]) ).
fof(f130,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f13,f125,f89]) ).
fof(f131,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f11,f125,f94]) ).
fof(f132,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f9,f125,f99]) ).
fof(f133,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f7,f125,f63]) ).
fof(f134,plain,
spl0_5,
inference(avatar_split_clause,[],[f5,f70]) ).
fof(f137,plain,
( inverse(sk_c5) = multiply(sk_c5,sk_c8)
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f91,f77]) ).
fof(f138,plain,
( sk_c8 = multiply(sk_c3,inverse(sk_c8))
| ~ spl0_3
| ~ spl0_10 ),
inference(forward_demodulation,[],[f96,f64]) ).
fof(f139,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c3,sk_c7)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f61,f101]) ).
fof(f143,plain,
( sk_c8 != multiply(sk_c3,sk_c7)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f139]) ).
fof(f146,plain,
( sk_c8 != multiply(sk_c3,inverse(sk_c8))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_11 ),
inference(forward_demodulation,[],[f143,f64]) ).
fof(f157,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f146,f138]) ).
fof(f158,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f157]) ).
fof(f164,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f61,f127]) ).
fof(f165,plain,
( sk_c8 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f164]) ).
fof(f174,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c2,sk_c8)
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[],[f107,f71]) ).
fof(f175,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f165,f117]) ).
fof(f176,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f175]) ).
fof(f177,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f3,f3]) ).
fof(f179,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f127]) ).
fof(f180,plain,
( identity = multiply(multiply(sk_c5,sk_c8),sk_c5)
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f3,f137]) ).
fof(f181,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f81]) ).
fof(f182,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f183,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f182,f4]) ).
fof(f184,plain,
( identity = multiply(sk_c5,multiply(sk_c8,sk_c5))
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f180,f4]) ).
fof(f188,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(multiply(sk_c8,sk_c7),X0)
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f4,f174]) ).
fof(f191,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(sk_c8,multiply(sk_c7,X0))
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[],[f188,f4]) ).
fof(f195,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c1,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f179]) ).
fof(f196,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c1,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f195,f1]) ).
fof(f197,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c2,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f181]) ).
fof(f198,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c2,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f197,f1]) ).
fof(f205,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f196,f117]) ).
fof(f214,plain,
( inverse(sk_c8) != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f65,f205]) ).
fof(f224,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c8,multiply(sk_c7,multiply(sk_c1,X0)))
| ~ spl0_5
| ~ spl0_12
| ~ spl0_14 ),
inference(superposition,[],[f191,f196]) ).
fof(f231,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c8,multiply(multiply(sk_c8,sk_c8),multiply(sk_c1,X0)))
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f224,f205]) ).
fof(f236,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,multiply(sk_c1,X0))))
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f231,f4]) ).
fof(f241,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f236,f196]) ).
fof(f261,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f183,f3]) ).
fof(f262,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f183,f4]) ).
fof(f263,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f183,f183]) ).
fof(f266,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(inverse(sk_c8),X0)
| ~ spl0_7 ),
inference(superposition,[],[f183,f198]) ).
fof(f269,plain,
( multiply(sk_c8,sk_c5) = multiply(inverse(sk_c5),identity)
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f183,f184]) ).
fof(f274,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_14 ),
inference(superposition,[],[f183,f179]) ).
fof(f275,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_7 ),
inference(superposition,[],[f183,f181]) ).
fof(f282,plain,
( multiply(sk_c8,sk_c5) = multiply(multiply(sk_c5,sk_c8),identity)
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f269,f137]) ).
fof(f285,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c8,X0)) = multiply(inverse(sk_c8),X0)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f266,f241]) ).
fof(f287,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f261,f263]) ).
fof(f292,plain,
( multiply(sk_c8,sk_c5) = multiply(sk_c5,multiply(sk_c8,identity))
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f282,f4]) ).
fof(f297,plain,
( multiply(sk_c5,sk_c8) = multiply(sk_c8,sk_c5)
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f292,f287]) ).
fof(f305,plain,
( identity = multiply(sk_c8,multiply(inverse(sk_c8),identity))
| ~ spl0_14 ),
inference(superposition,[],[f179,f274]) ).
fof(f310,plain,
( identity = multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,identity)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f305,f285]) ).
fof(f315,plain,
( identity = multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f310,f287]) ).
fof(f333,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(multiply(sk_c5,sk_c8),sk_c5)
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f177,f137]) ).
fof(f342,plain,
! [X0,X1] : multiply(inverse(inverse(X1)),multiply(inverse(X0),X0)) = X1,
inference(superposition,[],[f183,f177]) ).
fof(f345,plain,
! [X0,X1] : multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(forward_demodulation,[],[f342,f263]) ).
fof(f349,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(sk_c5,multiply(sk_c8,sk_c5))
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f333,f4]) ).
fof(f562,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c3,X0)) = X0
| ~ spl0_11 ),
inference(superposition,[],[f183,f101]) ).
fof(f591,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f562,f96]) ).
fof(f784,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f183,f345]) ).
fof(f1019,plain,
( sk_c5 = multiply(inverse(multiply(sk_c5,sk_c8)),identity)
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f262,f184]) ).
fof(f1052,plain,
( sk_c5 = inverse(multiply(sk_c5,sk_c8))
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1019,f287]) ).
fof(f1142,plain,
( sk_c5 = inverse(multiply(sk_c8,sk_c5))
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1052,f297]) ).
fof(f1271,plain,
( inverse(sk_c8) = multiply(sk_c8,multiply(sk_c8,identity))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f285,f287]) ).
fof(f1284,plain,
( ! [X0] : inverse(sk_c8) = multiply(sk_c8,multiply(sk_c8,multiply(inverse(X0),X0)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f345,f285]) ).
fof(f1287,plain,
( inverse(sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1284,f345]) ).
fof(f1295,plain,
( inverse(sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1271,f287]) ).
fof(f1303,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1295,f214]) ).
fof(f1304,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1303]) ).
fof(f1305,plain,
( inverse(sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f64,f205]) ).
fof(f1330,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c8)
| sk_c8 != inverse(inverse(X0)) )
| ~ spl0_1 ),
inference(equality_resolution,[],[f58]) ).
fof(f1333,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c8)
| sk_c8 != X0 )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1330,f784]) ).
fof(f1354,plain,
( multiply(sk_c8,sk_c8) != multiply(sk_c8,sk_c8)
| sk_c8 != sk_c8
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f1333,f1287]) ).
fof(f1358,plain,
( multiply(sk_c5,sk_c8) != multiply(sk_c5,sk_c8)
| sk_c8 != sk_c5
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f1333,f137]) ).
fof(f1365,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f1354]) ).
fof(f1366,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1365]) ).
fof(f1398,plain,
( ! [X1] :
( multiply(sk_c8,sk_c7) != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f68,f71]) ).
fof(f1399,plain,
( ! [X1] :
( multiply(X1,sk_c8) != multiply(sk_c8,multiply(sk_c8,sk_c8))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1398,f205]) ).
fof(f1400,plain,
( ! [X1] :
( identity != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1399,f315]) ).
fof(f1401,plain,
( identity != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f1400,f174]) ).
fof(f1429,plain,
( identity != multiply(sk_c8,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1401,f81]) ).
fof(f1441,plain,
( identity != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1429,f205]) ).
fof(f1457,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1441,f315]) ).
fof(f1458,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1457]) ).
fof(f1459,plain,
( sk_c8 != sk_c5
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f1358]) ).
fof(f1476,plain,
( sk_c8 = inverse(multiply(sk_c5,sk_c8))
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f86,f77]) ).
fof(f1477,plain,
( sk_c6 != multiply(multiply(inverse(sk_c8),identity),sk_c8)
| ~ spl0_7
| spl0_12 ),
inference(forward_demodulation,[],[f106,f275]) ).
fof(f1519,plain,
( sk_c8 = inverse(multiply(sk_c8,sk_c5))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1476,f297]) ).
fof(f1520,plain,
( sk_c6 != multiply(inverse(sk_c8),multiply(identity,sk_c8))
| ~ spl0_7
| spl0_12 ),
inference(forward_demodulation,[],[f1477,f4]) ).
fof(f1541,plain,
( sk_c6 != multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| spl0_12 ),
inference(forward_demodulation,[],[f1520,f1]) ).
fof(f1551,plain,
( identity != sk_c6
| ~ spl0_7
| spl0_12 ),
inference(forward_demodulation,[],[f1541,f3]) ).
fof(f1554,plain,
( identity != multiply(sk_c8,sk_c7)
| ~ spl0_5
| ~ spl0_7
| spl0_12 ),
inference(forward_demodulation,[],[f1551,f71]) ).
fof(f1556,plain,
( identity != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_5
| ~ spl0_7
| spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1554,f205]) ).
fof(f1560,plain,
( identity = multiply(multiply(sk_c8,sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f3,f1305]) ).
fof(f1570,plain,
( identity = multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1560,f4]) ).
fof(f1572,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1570,f1556]) ).
fof(f1573,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1572]) ).
fof(f1575,plain,
( sk_c8 != multiply(multiply(inverse(sk_c8),identity),sk_c7)
| spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f116,f274]) ).
fof(f1584,plain,
( sk_c8 != multiply(inverse(sk_c8),multiply(identity,sk_c7))
| spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1575,f4]) ).
fof(f1589,plain,
( sk_c8 != multiply(inverse(sk_c8),sk_c7)
| spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1584,f1]) ).
fof(f1591,plain,
( sk_c8 != multiply(inverse(sk_c8),multiply(sk_c8,sk_c8))
| ~ spl0_10
| ~ spl0_11
| spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1589,f591]) ).
fof(f1592,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1591,f183]) ).
fof(f1593,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1592]) ).
fof(f1601,plain,
( sk_c8 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f1519,f1142]) ).
fof(f1602,plain,
( sk_c8 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f1142,f1519]) ).
fof(f1618,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f1601,f1459]) ).
fof(f1619,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1618]) ).
fof(f1622,plain,
( ! [X1] :
( multiply(sk_c8,sk_c7) != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f68,f71]) ).
fof(f1623,plain,
( ! [X1] :
( multiply(X1,sk_c8) != multiply(sk_c8,multiply(sk_c8,sk_c8))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1622,f591]) ).
fof(f1628,plain,
( ! [X0] : multiply(inverse(X0),X0) = multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f349,f1602]) ).
fof(f1660,plain,
( ! [X0] :
( multiply(inverse(X0),X0) != multiply(sk_c8,multiply(sk_c8,sk_c8))
| sk_c8 != inverse(inverse(sk_c8)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1623,f177]) ).
fof(f1669,plain,
( ! [X0] : multiply(inverse(X0),X0) != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1660,f784]) ).
fof(f1676,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1669,f1628]) ).
fof(f1677,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1676]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f73]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f82]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f87]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f92]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f97]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s8,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f103]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s14,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s15,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s18,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s19,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s20,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s21,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s22,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s23,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s24,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f131]) ).
cnf(s25,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s26,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s27,plain,
spl0_5,
inference(sat_conversion,[],[f134]) ).
cnf(s29,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f158]) ).
cnf(s32,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f176]) ).
cnf(s40,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f1304]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s51,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f1458]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f1573]) ).
cnf(s56,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f1593]) ).
cnf(s58,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f1619]) ).
cnf(s61,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f1677]) ).
cnf(s62,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(rat,[],[s2,s27]) ).
cnf(s63,plain,
spl0_3,
inference(rat,[],[s40,s8,s14,s20,s26,s27]) ).
cnf(s64,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s51,s3,s9,s15,s21,s27]) ).
cnf(s65,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s61,s22,s23,s24,s25,s64,s27]) ).
cnf(s66,plain,
( spl0_13
| ~ spl0_14 ),
inference(rat,[],[s56,s18,s19]) ).
cnf(s67,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s51,s55,s66,s65,s27,s63]) ).
cnf(s68,plain,
~ spl0_4,
inference(rat,[],[s61,s4,s5,s6,s7,s67,s64,s27]) ).
cnf(s69,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s29,s24,s25,s63]) ).
cnf(s70,plain,
~ spl0_2,
inference(rat,[],[s32,s66,s69]) ).
cnf(s71,plain,
spl0_1,
inference(rat,[],[s62,s63,s68,s70]) ).
cnf(s72,plain,
spl0_14,
inference(rat,[],[s58,s21,s22,s23,s71]) ).
cnf(s73,plain,
( ~ spl0_7
| ~ spl0_13 ),
inference(rat,[],[s55,s41,s71,s72,s63,s27]) ).
cnf(s74,plain,
spl0_7,
inference(rat,[],[s58,s3,s4,s5,s71]) ).
cnf(s75,plain,
spl0_13,
inference(rat,[],[s66,s72]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s73,s75,s74]) ).
fof(f1681,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP302-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 09:48:50 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.38 % (2125321)Will run a generic schedule for satisfiability detection.
% 0.07/0.38 % (2125327)% WARNING: option uhcvi not known.
% 0.07/0.38 % (2125330)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=15215108:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.38 % (2125332)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2236237634:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.38 % (2125327)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4136530295:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.38 % (2125326)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3667284880_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.38 % (2125328)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2459138741:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.38 % (2125329)dis+10_1_sil=32000:sp=arity:random_seed=1673017734:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.38 % (2125331)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3697879702:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.38 % TRYING [1]
% 0.07/0.38 % TRYING [2]
% 0.07/0.38 % TRYING [3]
% 0.07/0.38 % TRYING [4]
% 0.07/0.38 % TRYING [5]
% 0.07/0.38 % (2125331) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2125321-2125331"...
% 0.07/0.38 % (2125330) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2125321-2125330"...
% 0.07/0.38 % (2125331)...printing done.
% 0.07/0.38 % (2125330)...printing done.
% 0.07/0.38 % (2125331)Refutation found. Thanks to Tanya!
% 0.07/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.38 % (2125331)------------------------------
% 0.07/0.38 % (2125331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.38 % (2125331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.38 % (2125331)CaDiCaL version: 2.1.3
% 0.07/0.38 % (2125331)Termination reason: Refutation
% 0.07/0.38 % (2125331)Time elapsed: 0.016 s
% 0.07/0.38 % (2125331)Peak memory usage: 13 MB
% 0.07/0.38 % (2125331)Instructions burned: 49 (million)
% 0.07/0.38 % (2125321)Success in time 0.044 s
% 0.07/0.38 % Vampire exiting
%------------------------------------------------------------------------------