TSTP Solution File: LCL198-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL198-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:50:30 EDT 2022
% Result : Unsatisfiable 1.82s 2.01s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of clauses : 55 ( 29 unt; 0 nHn; 25 RR)
% Number of literals : 90 ( 0 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 129 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(or(not(or(A,A)),A)) ).
cnf(axiom_1_3,axiom,
axiom(or(not(A),or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(or(not(or(A,B)),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) ) ).
cnf(rule_3,axiom,
( theorem(or(not(X),Z))
| ~ axiom(or(not(X),Y))
| ~ theorem(or(not(Y),Z)) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(or(not(or(not(p),or(not(p),q))),or(not(p),q))) ).
cnf(refute_0_0,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(not(or(B,A)),X_687))
| theorem(or(not(or(A,B)),X_687)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_687))]]) ).
cnf(refute_0_1,plain,
( ~ theorem(or(not(or(B,A)),X_687))
| theorem(or(not(or(A,B)),X_687)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(not(or(or(X_6232,X_6231),X_6232)),or(X_6232,X_6231)))
| theorem(or(not(or(X_6232,or(X_6232,X_6231))),or(X_6232,X_6231))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_6232)),bind(B,$fot(or(X_6232,X_6231))),bind(X_687,$fot(or(X_6232,X_6231)))]]) ).
cnf(refute_0_3,plain,
axiom(or(not(or(X_23,X_23)),X_23)),
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_4,plain,
( ~ axiom(or(not(or(X_23,X_23)),X_23))
| ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_23)),bind(Y,$fot(or(X_23,X_23)))]]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(resolve,[$cnf( axiom(or(not(or(X_23,X_23)),X_23)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ theorem(or(or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651)),or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651))))
| theorem(or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651))) ),
inference(subst,[],[refute_0_5:[bind(X_23,$fot(or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651))))]]) ).
cnf(refute_0_7,plain,
( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,or(A,C)))),bind(Y,$fot(or(A,or(B,C))))]]) ).
cnf(refute_0_8,plain,
( ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ theorem(or(X_2747,or(or(not(or(X_2748,X_2750)),or(X_2750,X_2749)),X_2748)))
| theorem(or(or(not(or(X_2748,X_2750)),or(X_2750,X_2749)),or(X_2747,X_2748))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_2747)),bind(B,$fot(or(not(or(X_2748,X_2750)),or(X_2750,X_2749)))),bind(C,$fot(X_2748))]]) ).
cnf(refute_0_10,plain,
axiom(or(not(X_24),or(B,X_24))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_11,plain,
( ~ axiom(or(not(X_24),or(B,X_24)))
| ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_24))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_12,plain,
( ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(resolve,[$cnf( axiom(or(not(X_24),or(B,X_24))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ theorem(or(or(not(or(X_2516,X_2518)),or(X_2518,X_2517)),X_2516))
| theorem(or(B,or(or(not(or(X_2516,X_2518)),or(X_2518,X_2517)),X_2516))) ),
inference(subst,[],[refute_0_12:[bind(X_24,$fot(or(or(not(or(X_2516,X_2518)),or(X_2518,X_2517)),X_2516)))]]) ).
cnf(refute_0_14,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(A,B))
| theorem(or(B,A)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,A))),bind(Y,$fot(or(A,B)))]]) ).
cnf(refute_0_15,plain,
( ~ theorem(or(A,B))
| theorem(or(B,A)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ theorem(or(X_1325,or(not(or(X_1325,X_1327)),or(X_1327,X_1326))))
| theorem(or(or(not(or(X_1325,X_1327)),or(X_1327,X_1326)),X_1325)) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_1325)),bind(B,$fot(or(not(or(X_1325,X_1327)),or(X_1327,X_1326))))]]) ).
cnf(refute_0_17,plain,
( ~ theorem(or(not(or(X_1322,X_1324)),or(X_1322,or(X_1324,X_1323))))
| theorem(or(X_1322,or(not(or(X_1322,X_1324)),or(X_1324,X_1323)))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(not(or(X_1322,X_1324)))),bind(B,$fot(X_1322)),bind(C,$fot(or(X_1324,X_1323)))]]) ).
cnf(refute_0_18,plain,
( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
| ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(not(or(C,A)),or(C,B)))),bind(Y,$fot(or(not(A),B)))]]) ).
cnf(refute_0_19,plain,
( ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ theorem(or(not(X_1187),or(X_1187,X_1186)))
| theorem(or(not(or(C,X_1187)),or(C,or(X_1187,X_1186)))) ),
inference(subst,[],[refute_0_19:[bind(A,$fot(X_1187)),bind(B,$fot(or(X_1187,X_1186)))]]) ).
cnf(refute_0_21,plain,
( ~ axiom(or(not(or(X_7,X_8)),or(X_8,X_7)))
| theorem(or(not(or(X_7,X_8)),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(X_7,X_8)),or(X_8,X_7))))]]) ).
cnf(refute_0_22,plain,
axiom(or(not(or(X_7,X_8)),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_23,plain,
theorem(or(not(or(X_7,X_8)),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(or(not(or(X_7,X_8)),or(X_8,X_7))) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
theorem(or(not(or(X_1181,X_1182)),or(X_1182,X_1181))),
inference(subst,[],[refute_0_23:[bind(X_7,$fot(X_1181)),bind(X_8,$fot(X_1182))]]) ).
cnf(refute_0_25,plain,
axiom(or(not(X_685),or(B,X_685))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_685))]]) ).
cnf(refute_0_26,plain,
( ~ axiom(or(not(X_685),or(B,X_685)))
| ~ theorem(or(not(or(B,X_685)),X_687))
| theorem(or(not(X_685),X_687)) ),
inference(subst,[],[rule_3:[bind(X,$fot(X_685)),bind(Y,$fot(or(B,X_685))),bind(Z,$fot(X_687))]]) ).
cnf(refute_0_27,plain,
( ~ theorem(or(not(or(B,X_685)),X_687))
| theorem(or(not(X_685),X_687)) ),
inference(resolve,[$cnf( axiom(or(not(X_685),or(B,X_685))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ theorem(or(not(or(X_1181,X_1182)),or(X_1182,X_1181)))
| theorem(or(not(X_1182),or(X_1182,X_1181))) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(X_1181)),bind(X_685,$fot(X_1182)),bind(X_687,$fot(or(X_1182,X_1181)))]]) ).
cnf(refute_0_29,plain,
theorem(or(not(X_1182),or(X_1182,X_1181))),
inference(resolve,[$cnf( theorem(or(not(or(X_1181,X_1182)),or(X_1182,X_1181))) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
theorem(or(not(X_1187),or(X_1187,X_1186))),
inference(subst,[],[refute_0_29:[bind(X_1181,$fot(X_1186)),bind(X_1182,$fot(X_1187))]]) ).
cnf(refute_0_31,plain,
theorem(or(not(or(C,X_1187)),or(C,or(X_1187,X_1186)))),
inference(resolve,[$cnf( theorem(or(not(X_1187),or(X_1187,X_1186))) )],[refute_0_30,refute_0_20]) ).
cnf(refute_0_32,plain,
theorem(or(not(or(X_1322,X_1324)),or(X_1322,or(X_1324,X_1323)))),
inference(subst,[],[refute_0_31:[bind(C,$fot(X_1322)),bind(X_1186,$fot(X_1323)),bind(X_1187,$fot(X_1324))]]) ).
cnf(refute_0_33,plain,
theorem(or(X_1322,or(not(or(X_1322,X_1324)),or(X_1324,X_1323)))),
inference(resolve,[$cnf( theorem(or(not(or(X_1322,X_1324)),or(X_1322,or(X_1324,X_1323)))) )],[refute_0_32,refute_0_17]) ).
cnf(refute_0_34,plain,
theorem(or(X_1325,or(not(or(X_1325,X_1327)),or(X_1327,X_1326)))),
inference(subst,[],[refute_0_33:[bind(X_1322,$fot(X_1325)),bind(X_1323,$fot(X_1326)),bind(X_1324,$fot(X_1327))]]) ).
cnf(refute_0_35,plain,
theorem(or(or(not(or(X_1325,X_1327)),or(X_1327,X_1326)),X_1325)),
inference(resolve,[$cnf( theorem(or(X_1325,or(not(or(X_1325,X_1327)),or(X_1327,X_1326)))) )],[refute_0_34,refute_0_16]) ).
cnf(refute_0_36,plain,
theorem(or(or(not(or(X_2516,X_2518)),or(X_2518,X_2517)),X_2516)),
inference(subst,[],[refute_0_35:[bind(X_1325,$fot(X_2516)),bind(X_1326,$fot(X_2517)),bind(X_1327,$fot(X_2518))]]) ).
cnf(refute_0_37,plain,
theorem(or(B,or(or(not(or(X_2516,X_2518)),or(X_2518,X_2517)),X_2516))),
inference(resolve,[$cnf( theorem(or(or(not(or(X_2516,X_2518)),or(X_2518,X_2517)),X_2516)) )],[refute_0_36,refute_0_13]) ).
cnf(refute_0_38,plain,
theorem(or(X_2747,or(or(not(or(X_2748,X_2750)),or(X_2750,X_2749)),X_2748))),
inference(subst,[],[refute_0_37:[bind(B,$fot(X_2747)),bind(X_2516,$fot(X_2748)),bind(X_2517,$fot(X_2749)),bind(X_2518,$fot(X_2750))]]) ).
cnf(refute_0_39,plain,
theorem(or(or(not(or(X_2748,X_2750)),or(X_2750,X_2749)),or(X_2747,X_2748))),
inference(resolve,[$cnf( theorem(or(X_2747,or(or(not(or(X_2748,X_2750)),or(X_2750,X_2749)),X_2748))) )],[refute_0_38,refute_0_9]) ).
cnf(refute_0_40,plain,
theorem(or(or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651)),or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651)))),
inference(subst,[],[refute_0_39:[bind(X_2747,$fot(not(or(or(X_3652,X_3651),X_3652)))),bind(X_2748,$fot(or(X_3652,X_3651))),bind(X_2749,$fot(X_3651)),bind(X_2750,$fot(X_3652))]]) ).
cnf(refute_0_41,plain,
theorem(or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651))),
inference(resolve,[$cnf( theorem(or(or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651)),or(not(or(or(X_3652,X_3651),X_3652)),or(X_3652,X_3651)))) )],[refute_0_40,refute_0_6]) ).
cnf(refute_0_42,plain,
theorem(or(not(or(or(X_6232,X_6231),X_6232)),or(X_6232,X_6231))),
inference(subst,[],[refute_0_41:[bind(X_3651,$fot(X_6231)),bind(X_3652,$fot(X_6232))]]) ).
cnf(refute_0_43,plain,
theorem(or(not(or(X_6232,or(X_6232,X_6231))),or(X_6232,X_6231))),
inference(resolve,[$cnf( theorem(or(not(or(or(X_6232,X_6231),X_6232)),or(X_6232,X_6231))) )],[refute_0_42,refute_0_2]) ).
cnf(refute_0_44,plain,
theorem(or(not(or(not(p),or(not(p),q))),or(not(p),q))),
inference(subst,[],[refute_0_43:[bind(X_6231,$fot(q)),bind(X_6232,$fot(not(p)))]]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(or(not(p),or(not(p),q))),or(not(p),q))) )],[refute_0_44,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL198-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 02:18:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.82/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.82/2.01
% 1.82/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.82/2.01
%------------------------------------------------------------------------------