%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP353-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:43 AM UTC 2026
% Result : Unsatisfiable 2.78s 1.28s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 42
% Syntax : Number of formulae : 246 ( 18 unt; 15 def)
% Number of atoms : 783 ( 229 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 998 ( 461 ~; 522 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c1)
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,X3) != sk_c6
| inverse(X2) != X3
| multiply(X3,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(sk_c7,sk_c5)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != multiply(X2,X3)
| inverse(X2) != X3
| sk_c6 != multiply(X3,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
! [X2,X0,X1] :
( multiply(sk_c6,sk_c5) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(sk_c7,sk_c5)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != multiply(X2,inverse(X2))
| sk_c6 != multiply(inverse(X2),sk_c7) ),
inference(equality_resolution,[],[f54]) ).
fof(f57,definition,
( spl0_1
<=> ! [X2] :
( sk_c6 != multiply(X2,inverse(X2))
| sk_c6 != multiply(inverse(X2),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ! [X2] :
( sk_c6 != multiply(inverse(X2),sk_c7)
| sk_c6 != multiply(X2,inverse(X2)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_2
<=> ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f61,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_4
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_5
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f72,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_6
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c5) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f55,f74,f71,f67,f63,f60,f57]) ).
fof(f79,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f52,f67,f79]) ).
fof(f84,definition,
( spl0_8
<=> sk_c4 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f86,plain,
( sk_c4 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f50,f67,f84]) ).
fof(f89,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c3,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f91,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f48,f67,f89]) ).
fof(f94,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f96,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f46,f67,f94]) ).
fof(f99,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f44,f67,f99]) ).
fof(f105,definition,
( spl0_12
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f107,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f40,f105,f79]) ).
fof(f109,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f38,f105,f84]) ).
fof(f110,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f105,f89]) ).
fof(f111,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f34,f105,f94]) ).
fof(f112,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f32,f105,f99]) ).
fof(f113,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f30,f105,f63]) ).
fof(f115,definition,
( spl0_13
<=> sk_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f117,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f28,f115,f79]) ).
fof(f119,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f26,f115,f84]) ).
fof(f120,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f24,f115,f89]) ).
fof(f121,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f22,f115,f94]) ).
fof(f122,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f20,f115,f99]) ).
fof(f123,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f18,f115,f63]) ).
fof(f124,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f74,f79]) ).
fof(f125,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f74,f84]) ).
fof(f126,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f74,f89]) ).
fof(f127,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f74,f94]) ).
fof(f128,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f74,f99]) ).
fof(f129,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f74,f63]) ).
fof(f130,plain,
( identity = multiply(sk_c4,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f86]) ).
fof(f131,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_11 ),
inference(superposition,[],[f3,f101]) ).
fof(f133,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f137,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c7,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f81]) ).
fof(f140,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f133,f1]) ).
fof(f142,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c4,multiply(sk_c3,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f130]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c3,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f142,f1]) ).
fof(f144,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c2,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f131]) ).
fof(f145,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c2,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f144,f1]) ).
fof(f146,plain,
( sk_c4 = multiply(sk_c4,sk_c6)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f143,f91]) ).
fof(f160,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f145,f96]) ).
fof(f169,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c6)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f137,f160]) ).
fof(f172,plain,
( multiply(sk_c6,sk_c7) = sk_c4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f169,f146]) ).
fof(f173,plain,
( sk_c5 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f172,f64]) ).
fof(f187,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f91,f173]) ).
fof(f206,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c4)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f140,f146]) ).
fof(f207,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3 ),
inference(superposition,[],[f140,f64]) ).
fof(f208,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_7 ),
inference(superposition,[],[f140,f81]) ).
fof(f211,plain,
( sk_c3 = multiply(inverse(sk_c4),identity)
| ~ spl0_8 ),
inference(superposition,[],[f140,f130]) ).
fof(f216,plain,
( sk_c3 = multiply(inverse(sk_c5),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f211,f173]) ).
fof(f217,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f208,f173]) ).
fof(f218,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f206,f3]) ).
fof(f242,plain,
( sk_c3 = multiply(inverse(sk_c5),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f216,f218]) ).
fof(f256,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f242,f217]) ).
fof(f263,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f187,f256]) ).
fof(f273,plain,
( spl0_4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f263,f99,f94,f89,f84,f79,f63,f67]) ).
fof(f274,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c4,sk_c6)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f137,f68]) ).
fof(f279,plain,
( multiply(sk_c6,sk_c5) = sk_c4
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f274,f146]) ).
fof(f280,plain,
( sk_c5 = multiply(sk_c6,sk_c5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f279,f173]) ).
fof(f285,plain,
( sk_c5 != sk_c7
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f76,f280]) ).
fof(f287,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f140,f280]) ).
fof(f289,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f287,f207]) ).
fof(f304,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f289,f285]) ).
fof(f305,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f304]) ).
fof(f307,plain,
( sk_c5 = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f280,f75]) ).
fof(f324,plain,
( sk_c6 != multiply(sk_c4,sk_c7)
| sk_c6 != multiply(sk_c3,sk_c4)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f58,f86]) ).
fof(f331,plain,
( sk_c6 != multiply(sk_c3,sk_c4)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f324,f81]) ).
fof(f335,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f331,f91]) ).
fof(f336,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f340,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f61,f101]) ).
fof(f342,plain,
( sk_c7 != multiply(sk_c2,sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f340]) ).
fof(f353,plain,
( sk_c7 = sk_c4
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f279,f75]) ).
fof(f354,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f342,f99,f60,f94]) ).
fof(f357,definition,
( spl0_14
<=> sk_c7 = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f358,plain,
( sk_c7 = sk_c4
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f361,definition,
( spl0_15
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f362,plain,
( sk_c5 = sk_c7
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f365,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f61,f107]) ).
fof(f368,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f365]) ).
fof(f373,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_13 ),
inference(superposition,[],[f140,f117]) ).
fof(f374,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f117]) ).
fof(f375,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f373,f107]) ).
fof(f390,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f140,f375]) ).
fof(f392,plain,
( identity = sk_c6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f390,f3]) ).
fof(f398,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f374,f68]) ).
fof(f405,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f398,f75]) ).
fof(f409,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f405,f368]) ).
fof(f410,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f409]) ).
fof(f411,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1,f392]) ).
fof(f412,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f140,f405]) ).
fof(f414,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f412,f107]) ).
fof(f434,plain,
( sk_c5 = sk_c7
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f75,f411]) ).
fof(f435,plain,
( sk_c5 != sk_c7
| spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f65,f411]) ).
fof(f438,plain,
( ~ spl0_15
| spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f435,f115,f105,f63,f361]) ).
fof(f439,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f434,f115,f105,f74,f361]) ).
fof(f442,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f72,f107]) ).
fof(f445,plain,
( sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f442]) ).
fof(f446,plain,
( $false
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f445,f117]) ).
fof(f447,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f446]) ).
fof(f450,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f68,f362]) ).
fof(f455,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f58,f107]) ).
fof(f460,plain,
( sk_c6 != multiply(sk_c1,sk_c7)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f455,f414]) ).
fof(f461,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f460,f117]) ).
fof(f462,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f461]) ).
fof(f481,plain,
( spl0_14
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f353,f89,f84,f79,f74,f67,f357]) ).
fof(f494,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f86,f358]) ).
fof(f503,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f494,f256]) ).
fof(f516,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f72,f503]) ).
fof(f517,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f516]) ).
fof(f519,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f450,f517]) ).
fof(f520,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f521,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f307,f99,f94,f89,f84,f79,f74,f67,f63,f361]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f82]) ).
cnf(s3,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f92]) ).
cnf(s5,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f97]) ).
cnf(s6,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s8,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s9,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s10,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s11,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s12,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s13,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s14,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s15,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s16,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s17,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s18,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s19,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s20,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f124]) ).
cnf(s21,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f125]) ).
cnf(s22,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f126]) ).
cnf(s23,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f127]) ).
cnf(s24,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f128]) ).
cnf(s25,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f129]) ).
cnf(s28,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f273]) ).
cnf(s30,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f305]) ).
cnf(s32,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f336]) ).
cnf(s36,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f354]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f410]) ).
cnf(s40,plain,
( spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f438]) ).
cnf(s41,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f439]) ).
cnf(s44,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f447]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f462]) ).
cnf(s46,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f481]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f520]) ).
cnf(s51,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f521]) ).
cnf(s57,plain,
spl0_3,
inference(rat,[],[s40,s41,s13,s19,s25]) ).
cnf(s58,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s30,s20,s21,s22,s23,s24,s57]) ).
cnf(s59,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_7
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s51,s50,s46,s58,s57]) ).
cnf(s60,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s44,s12,s18]) ).
cnf(s61,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s44,s11,s17]) ).
cnf(s62,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s44,s10,s16]) ).
cnf(s63,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s44,s9,s15]) ).
cnf(s64,plain,
( ~ spl0_8
| ~ spl0_4
| ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s44,s8,s14,s59]) ).
cnf(s65,plain,
( ~ spl0_6
| ~ spl0_4
| spl0_1
| spl0_2 ),
inference(rat,[],[s64,s63,s62,s61,s60,s1,s57]) ).
cnf(s66,plain,
( ~ spl0_4
| spl0_2
| spl0_1 ),
inference(rat,[],[s65,s58]) ).
cnf(s67,plain,
spl0_4,
inference(rat,[],[s28,s2,s3,s4,s5,s6,s57]) ).
cnf(s68,plain,
spl0_6,
inference(rat,[],[s58,s67]) ).
cnf(s70,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s39,s12,s18,s67,s68]) ).
cnf(s71,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s39,s11,s17,s36,s68,s67]) ).
cnf(s72,plain,
~ spl0_2,
inference(rat,[],[s71,s70]) ).
cnf(s73,plain,
spl0_1,
inference(rat,[],[s66,s67,s72]) ).
cnf(s75,plain,
spl0_7,
inference(rat,[],[s45,s8,s14,s73,s67,s68]) ).
cnf(s76,plain,
spl0_9,
inference(rat,[],[s45,s10,s16,s73,s67,s68]) ).
cnf(s77,plain,
~ spl0_8,
inference(rat,[],[s32,s73,s75,s76]) ).
cnf(s78,plain,
spl0_13,
inference(rat,[],[s15,s77]) ).
cnf(s79,plain,
spl0_12,
inference(rat,[],[s9,s77]) ).
cnf(s81,plain,
$false,
inference(rat,[],[s45,s68,s67,s73,s78,s79]) ).
fof(f531,plain,
$false,
inference(avatar_sat_refutation,[],[s81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP353-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:57:23 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.78/1.28 % (2090089)Input is clausal, will run a generic CNF schedule.
% 2.78/1.28 % (2090094)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=788300437:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.78/1.28 % (2090100)dis-21_1_sil=8000:lcm=predicate:random_seed=3968556834:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.78/1.28 % (2090097)lrs+10_1_sil=8000:sp=occurrence:random_seed=3219586843:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.78/1.28 % (2090099)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3237185376:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.78/1.28 % (2090096)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1665996686:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.78/1.28 % (2090098)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2575697141:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.78/1.28 % (2090095)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2048174715:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.78/1.28 % (2090100)Refutation not found, incomplete strategy
% 2.78/1.28 % (2090100)------------------------------
% 2.78/1.28 % (2090100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.28 % (2090100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.28 % (2090100)CaDiCaL version: 2.1.3
% 2.78/1.28 % (2090100)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.28 % (2090100)Time elapsed: 0.002 s
% 2.78/1.28 % (2090100)Peak memory usage: 88 MB
% 2.78/1.28 % (2090100)Instructions burned: 1 (million)
% 2.78/1.28 % (2090097)Refutation not found, incomplete strategy
% 2.78/1.28 % (2090097)------------------------------
% 2.78/1.28 % (2090097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.28 % (2090097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.28 % (2090097)CaDiCaL version: 2.1.3
% 2.78/1.28 % (2090097)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.28 % (2090097)Time elapsed: 0.003 s
% 2.78/1.28 % (2090097)Peak memory usage: 88 MB
% 2.78/1.28 % (2090097)Instructions burned: 4 (million)
% 2.78/1.28 % (2090099)First to succeed.
% 2.78/1.28 % (2090099)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2090089"
% 2.78/1.28 % (2090098)Instruction limit reached!
% 2.78/1.28 % (2090098)------------------------------
% 2.78/1.28 % (2090098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.28 % (2090098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.28 % (2090098)CaDiCaL version: 2.1.3
% 2.78/1.28 % (2090098)Termination reason: Instruction limit
% 2.78/1.28 % (2090098)Termination phase: Saturation
% 2.78/1.28 % (2090098)Time elapsed: 0.068 s
% 2.78/1.28 % (2090098)Peak memory usage: 89 MB
% 2.78/1.28 % (2090098)Instructions burned: 115 (million)
% 2.78/1.28 % (2090108)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=4035345432:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.78/1.28 % (2090097)------------------------------
% 2.78/1.28 % (2090097)------------------------------
% 2.78/1.28 % (2090100)------------------------------
% 2.78/1.28 % (2090100)------------------------------
% 2.78/1.28 % (2090108)Also succeeded, but the first one will report.
% 2.78/1.28 % (2090099)Refutation found. Thanks to Tanya!
% 2.78/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.48 % (2090099)------------------------------
% 3.67/1.48 % (2090099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.48 % (2090099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.48 % (2090099)CaDiCaL version: 2.1.3
% 3.67/1.48 % (2090099)Termination reason: Refutation
% 3.67/1.48 % (2090099)Time elapsed: 0.016 s
% 3.67/1.48 % (2090099)Peak memory usage: 89 MB
% 3.67/1.48 % (2090099)Instructions burned: 23 (million)
% 3.67/1.48 % (2090099)------------------------------
% 3.67/1.48 % (2090099)------------------------------
% 3.67/1.48 % (2090089)Success in time 0.437 s
% 3.67/1.48 % Vampire exiting
%------------------------------------------------------------------------------