%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP278-1 : 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 : n010.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 10:17:22 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 40
% Syntax : Number of formulae : 270 ( 22 unt; 16 def)
% Number of atoms : 828 ( 243 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1057 ( 499 ~; 542 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/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_c1,sk_c6) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c6 = inverse(sk_c1)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c5 = inverse(sk_c4)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c5 = inverse(sk_c4)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c5 = inverse(sk_c4)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c5 = inverse(sk_c3) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| sk_c5 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
! [X2,X0,X1] :
( multiply(X0,sk_c6) != sk_c5
| inverse(X0) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(sk_c6,sk_c4) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| inverse(X2) != sk_c5
| multiply(X2,sk_c4) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
! [X2,X0,X1] :
( sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c5 != inverse(sk_c4)
| sk_c5 != multiply(sk_c6,sk_c4)
| multiply(sk_c5,sk_c6) != sk_c4
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c4) ),
inference(reorient_equations,[],[f44]) ).
fof(f47,definition,
( spl0_1
<=> ! [X2] :
( sk_c5 != inverse(X2)
| sk_c5 != multiply(X2,sk_c4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f48,plain,
( ! [X2] :
( sk_c5 != multiply(X2,sk_c4)
| sk_c5 != inverse(X2) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,definition,
( spl0_2
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f51,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_3
<=> multiply(sk_c5,sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c6) != sk_c4
| spl0_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl0_4
<=> sk_c5 = multiply(sk_c6,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f58,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( sk_c5 != multiply(sk_c6,sk_c4)
| spl0_4 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl0_5
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f62,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( sk_c5 != inverse(sk_c4)
| spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f65,definition,
( spl0_6
<=> ! [X0] :
( sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f66,plain,
( ! [X0] :
( sk_c5 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f67,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f45,f65,f61,f57,f53,f50,f47]) ).
fof(f69,definition,
( spl0_7
<=> sk_c5 = multiply(sk_c3,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f71,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f43,f57,f69]) ).
fof(f74,definition,
( spl0_8
<=> sk_c5 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f76,plain,
( sk_c5 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f41,f57,f74]) ).
fof(f79,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f39,f57,f79]) ).
fof(f84,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f86,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f37,f57,f84]) ).
fof(f88,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f35,f57,f53]) ).
fof(f89,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f33,f61,f69]) ).
fof(f90,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f31,f61,f74]) ).
fof(f91,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f29,f61,f79]) ).
fof(f92,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f27,f61,f84]) ).
fof(f93,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f25,f61,f53]) ).
fof(f95,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f97,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f23,f95,f69]) ).
fof(f99,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f21,f95,f74]) ).
fof(f100,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f19,f95,f79]) ).
fof(f101,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f17,f95,f84]) ).
fof(f102,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f15,f95,f53]) ).
fof(f104,definition,
( spl0_12
<=> multiply(sk_c1,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f106,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f13,f104,f69]) ).
fof(f108,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f11,f104,f74]) ).
fof(f109,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f9,f104,f79]) ).
fof(f110,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f7,f104,f84]) ).
fof(f111,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f5,f104,f53]) ).
fof(f112,plain,
( identity = multiply(sk_c5,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f76]) ).
fof(f113,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_10 ),
inference(superposition,[],[f3,f86]) ).
fof(f116,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f117,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(sk_c4,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f54]) ).
fof(f118,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c3,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f112]) ).
fof(f120,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c3,multiply(sk_c4,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f71]) ).
fof(f121,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c3,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f118,f1]) ).
fof(f122,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f116,f1]) ).
fof(f125,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c2,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f113]) ).
fof(f126,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c2,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f125,f1]) ).
fof(f127,plain,
( multiply(sk_c4,sk_c2) = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f117,f113]) ).
fof(f131,plain,
( sk_c4 = multiply(sk_c5,sk_c5)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f121,f71]) ).
fof(f156,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f122,f3]) ).
fof(f157,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f122,f122]) ).
fof(f158,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f122,f113]) ).
fof(f159,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(inverse(sk_c6),X0)
| ~ spl0_10 ),
inference(superposition,[],[f122,f126]) ).
fof(f161,plain,
( ! [X0] : multiply(sk_c3,X0) = multiply(inverse(sk_c5),X0)
| ~ spl0_8 ),
inference(superposition,[],[f122,f121]) ).
fof(f162,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c4)
| ~ spl0_3 ),
inference(superposition,[],[f122,f54]) ).
fof(f163,plain,
( sk_c5 = multiply(inverse(sk_c5),sk_c4)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f122,f131]) ).
fof(f175,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f162,f163]) ).
fof(f177,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_10 ),
inference(forward_demodulation,[],[f158,f159]) ).
fof(f178,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f156,f157]) ).
fof(f182,plain,
( identity = multiply(sk_c5,sk_c2)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f113,f175]) ).
fof(f183,plain,
( sk_c5 != multiply(sk_c5,sk_c4)
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f59,f175]) ).
fof(f200,plain,
( sk_c2 = multiply(inverse(sk_c5),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f122,f182]) ).
fof(f203,plain,
( sk_c2 = multiply(sk_c3,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f200,f161]) ).
fof(f205,plain,
( sk_c2 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f203,f178]) ).
fof(f207,plain,
( multiply(sk_c5,sk_c2) = multiply(sk_c3,multiply(sk_c5,identity))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f120,f127]) ).
fof(f212,plain,
( multiply(sk_c5,sk_c2) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f207,f178]) ).
fof(f214,plain,
( multiply(sk_c2,sk_c5) = multiply(sk_c5,sk_c2)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f212,f205]) ).
fof(f215,plain,
( identity = multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f214,f182]) ).
fof(f216,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f215,f81]) ).
fof(f217,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f216,f175]) ).
fof(f219,plain,
( sk_c2 = multiply(sk_c2,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f177,f217]) ).
fof(f220,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f1,f217]) ).
fof(f221,plain,
( sk_c6 = sk_c2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f219,f81]) ).
fof(f223,plain,
( sk_c5 = sk_c2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f221,f175]) ).
fof(f237,plain,
( sk_c5 = multiply(sk_c2,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f71,f205]) ).
fof(f238,plain,
( sk_c5 = inverse(sk_c2)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f76,f205]) ).
fof(f239,plain,
( sk_c5 = inverse(sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f238,f223]) ).
fof(f240,plain,
( sk_c5 = multiply(sk_c5,sk_c4)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f237,f223]) ).
fof(f242,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f240,f183]) ).
fof(f243,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f246,plain,
( sk_c5 = multiply(sk_c5,sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f58,f175]) ).
fof(f247,plain,
( sk_c5 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f240,f220]) ).
fof(f302,plain,
( sk_c5 != inverse(sk_c5)
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f63,f247]) ).
fof(f311,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f302,f239]) ).
fof(f312,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f317,plain,
( ! [X1] :
( sk_c5 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f51,f175]) ).
fof(f319,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f317,f175]) ).
fof(f322,plain,
( identity != sk_c5
| sk_c5 != inverse(inverse(sk_c5))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f319,f3]) ).
fof(f328,plain,
( sk_c5 != inverse(inverse(sk_c5))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f322,f217]) ).
fof(f333,plain,
( sk_c5 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f328,f239]) ).
fof(f338,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f333,f239]) ).
fof(f339,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f340,plain,
( ! [X0] :
( sk_c5 != multiply(X0,sk_c5)
| inverse(X0) != sk_c6 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f66,f175]) ).
fof(f341,plain,
( ! [X0] :
( sk_c5 != multiply(X0,sk_c5)
| inverse(X0) != sk_c5 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f340,f175]) ).
fof(f353,plain,
( identity != sk_c5
| sk_c5 != inverse(inverse(sk_c5))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f341,f3]) ).
fof(f359,plain,
( sk_c5 != inverse(inverse(sk_c5))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f353,f217]) ).
fof(f364,plain,
( sk_c5 != inverse(sk_c5)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f359,f239]) ).
fof(f369,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f364,f239]) ).
fof(f370,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f369]) ).
fof(f413,definition,
( spl0_14
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f414,plain,
( identity = sk_c5
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f415,plain,
( identity != sk_c5
| spl0_14 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f418,definition,
( spl0_15
<=> sk_c5 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f419,plain,
( sk_c5 = inverse(sk_c5)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f420,plain,
( sk_c5 != inverse(sk_c5)
| spl0_15 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f422,definition,
( spl0_16
<=> sk_c5 = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f423,plain,
( sk_c5 = sk_c4
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f424,plain,
( sk_c5 != sk_c4
| spl0_16 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f437,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_5 ),
inference(superposition,[],[f3,f62]) ).
fof(f438,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f437,f246]) ).
fof(f439,plain,
( spl0_14
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f438,f74,f69,f61,f57,f53,f413]) ).
fof(f442,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_14 ),
inference(superposition,[],[f1,f414]) ).
fof(f500,plain,
( sk_c5 != sk_c4
| sk_c5 != inverse(identity)
| ~ spl0_1 ),
inference(superposition,[],[f48,f1]) ).
fof(f514,plain,
( sk_c5 != inverse(identity)
| ~ spl0_1
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f500,f423]) ).
fof(f516,plain,
( sk_c5 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f514,f414]) ).
fof(f519,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f516,f419]) ).
fof(f520,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f535,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[],[f162,f423]) ).
fof(f537,plain,
( sk_c5 = multiply(sk_c6,sk_c5)
| ~ spl0_4
| ~ spl0_16 ),
inference(forward_demodulation,[],[f58,f423]) ).
fof(f538,plain,
( identity = sk_c4
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_demodulation,[],[f437,f442]) ).
fof(f541,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[],[f535,f3]) ).
fof(f545,plain,
( sk_c6 = sk_c5
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f541,f414]) ).
fof(f553,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_11 ),
inference(superposition,[],[f3,f97]) ).
fof(f558,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f122,f106]) ).
fof(f561,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f558,f97]) ).
fof(f563,plain,
( sk_c6 = sk_c5
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f561,f537]) ).
fof(f582,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[],[f66,f106]) ).
fof(f584,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f582]) ).
fof(f586,plain,
( $false
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f584,f97]) ).
fof(f587,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f603,plain,
( ! [X1] :
( sk_c5 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f51,f545]) ).
fof(f604,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f603,f545]) ).
fof(f620,plain,
( identity != sk_c5
| sk_c5 != inverse(inverse(sk_c5))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f604,f3]) ).
fof(f629,plain,
( sk_c5 != inverse(inverse(sk_c5))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f620,f414]) ).
fof(f633,plain,
( sk_c5 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f629,f419]) ).
fof(f636,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f633,f419]) ).
fof(f637,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f636]) ).
fof(f667,definition,
( spl0_18
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f668,plain,
( sk_c6 = sk_c5
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f669,plain,
( sk_c6 != sk_c5
| spl0_18 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f677,plain,
( sk_c4 = multiply(inverse(sk_c5),identity)
| ~ spl0_5 ),
inference(superposition,[],[f122,f437]) ).
fof(f680,plain,
( sk_c4 = inverse(sk_c5)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f677,f178]) ).
fof(f692,plain,
( sk_c5 != sk_c4
| ~ spl0_5
| spl0_15 ),
inference(superposition,[],[f420,f680]) ).
fof(f694,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f122,f553]) ).
fof(f697,plain,
( sk_c1 = inverse(sk_c6)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f694,f178]) ).
fof(f700,plain,
( identity = multiply(sk_c1,sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f3,f697]) ).
fof(f701,plain,
( identity = sk_c5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f700,f106]) ).
fof(f702,plain,
( $false
| ~ spl0_11
| ~ spl0_12
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f701,f415]) ).
fof(f703,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f702]) ).
fof(f727,plain,
( sk_c4 != multiply(sk_c5,sk_c5)
| spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f55,f668]) ).
fof(f730,plain,
( sk_c5 = multiply(sk_c5,sk_c5)
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f537,f668]) ).
fof(f732,plain,
( sk_c5 != multiply(sk_c5,sk_c5)
| spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f727,f423]) ).
fof(f733,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f732,f730]) ).
fof(f734,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f733]) ).
fof(f737,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f563,f669]) ).
fof(f738,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f737]) ).
fof(f742,plain,
( ~ spl0_16
| ~ spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f692,f418,f61,f422]) ).
fof(f743,plain,
( sk_c5 = sk_c4
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_demodulation,[],[f538,f414]) ).
fof(f744,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f743,f424]) ).
fof(f745,plain,
( ~ spl0_5
| ~ spl0_14
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f744]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s2,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f72]) ).
cnf(s3,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f77]) ).
cnf(s4,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f82]) ).
cnf(s5,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f87]) ).
cnf(s6,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f88]) ).
cnf(s7,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f89]) ).
cnf(s8,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f90]) ).
cnf(s9,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s10,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f92]) ).
cnf(s11,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f93]) ).
cnf(s12,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f98]) ).
cnf(s13,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f99]) ).
cnf(s14,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f100]) ).
cnf(s15,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s16,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s17,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s18,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s19,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s20,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s21,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s22,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f243]) ).
cnf(s23,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f312]) ).
cnf(s27,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f339]) ).
cnf(s31,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f370]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f439]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f520]) ).
cnf(s50,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f587]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f637]) ).
cnf(s62,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f703]) ).
cnf(s68,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f734]) ).
cnf(s69,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f738]) ).
cnf(s71,plain,
( ~ spl0_5
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f742]) ).
cnf(s72,plain,
( ~ spl0_5
| ~ spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f745]) ).
cnf(s73,plain,
spl0_3,
inference(rat,[],[s69,s68,s72,s62,s6,s11,s16,s21]) ).
cnf(s74,plain,
( spl0_7
| ~ spl0_6 ),
inference(rat,[],[s50,s12,s17]) ).
cnf(s75,plain,
( spl0_12
| ~ spl0_6 ),
inference(rat,[],[s31,s18,s19,s20,s74,s73]) ).
cnf(s76,plain,
~ spl0_6,
inference(rat,[],[s31,s13,s14,s15,s50,s75,s74,s73]) ).
cnf(s77,plain,
spl0_5,
inference(rat,[],[s23,s7,s8,s9,s10,s73]) ).
cnf(s78,plain,
spl0_4,
inference(rat,[],[s22,s2,s3,s4,s5,s73]) ).
cnf(s79,plain,
( spl0_12
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s27,s18,s19,s20,s73]) ).
cnf(s80,plain,
( ~ spl0_14
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s71,s57,s73,s77]) ).
cnf(s81,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s80,s72,s77]) ).
cnf(s82,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s13,s39,s62,s79,s81,s73,s78,s77]) ).
cnf(s83,plain,
~ spl0_2,
inference(rat,[],[s62,s12,s17,s82,s81]) ).
cnf(s84,plain,
spl0_1,
inference(rat,[],[s1,s76,s77,s73,s78,s83]) ).
cnf(s85,plain,
( ~ spl0_14
| ~ spl0_16 ),
inference(rat,[],[s71,s45,s84,s77]) ).
cnf(s86,plain,
~ spl0_14,
inference(rat,[],[s85,s72,s77]) ).
cnf(s87,plain,
spl0_8,
inference(rat,[],[s62,s13,s18,s86]) ).
cnf(s88,plain,
~ spl0_7,
inference(rat,[],[s39,s77,s86,s78,s73,s87]) ).
cnf(s89,plain,
spl0_12,
inference(rat,[],[s17,s88]) ).
cnf(s90,plain,
spl0_11,
inference(rat,[],[s12,s88]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s62,s86,s89,s90]) ).
fof(f746,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP278-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n010.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 09:44:46 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.18/0.48 % (707500)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (707509)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1234400277:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (707506)% WARNING: option uhcvi not known.
% 0.18/0.48 % (707507)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2047365868:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (707505)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1711793225_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (707506)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4231888442:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (707510)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3523878861:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (707509) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-707500-707509"...
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % (707509)...printing done.
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % (707509)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (707509)------------------------------
% 0.18/0.49 % (707509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (707509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (707509)CaDiCaL version: 2.1.3
% 0.18/0.49 % (707509)Termination reason: Refutation
% 0.18/0.49 % (707509)Time elapsed: 0.009 s
% 0.18/0.49 % (707509)Peak memory usage: 12 MB
% 0.18/0.49 % (707509)Instructions burned: 23 (million)
% 0.18/0.49 % (707500)Success in time 0.042 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------