TSTP Solution File: LCL210-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL210-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:50:38 EDT 2022
% Result : Unsatisfiable 1.53s 1.72s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of clauses : 63 ( 34 unt; 0 nHn; 26 RR)
% Number of literals : 101 ( 0 equ; 39 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 : 137 ( 14 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(not(p)),or(not(or(p,q)),q))) ).
cnf(refute_0_0,plain,
axiom(or(not(X_569),or(B,X_569))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_569))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(or(not(X_569),or(B,X_569)))
| ~ theorem(or(not(or(B,X_569)),X_571))
| theorem(or(not(X_569),X_571)) ),
inference(subst,[],[rule_3:[bind(X,$fot(X_569)),bind(Y,$fot(or(B,X_569))),bind(Z,$fot(X_571))]]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(not(or(B,X_569)),X_571))
| theorem(or(not(X_569),X_571)) ),
inference(resolve,[$cnf( axiom(or(not(X_569),or(B,X_569))) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ theorem(or(not(or(X_6725,not(X_6724))),or(not(or(X_6724,X_6725)),X_6725)))
| theorem(or(not(not(X_6724)),or(not(or(X_6724,X_6725)),X_6725))) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(X_6725)),bind(X_569,$fot(not(X_6724))),bind(X_571,$fot(or(not(or(X_6724,X_6725)),X_6725)))]]) ).
cnf(refute_0_4,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(not(or(B,A)),X_571))
| theorem(or(not(or(A,B)),X_571)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_571))]]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(not(or(B,A)),X_571))
| theorem(or(not(or(A,B)),X_571)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ theorem(or(not(or(not(X_6346),X_6347)),or(not(or(X_6346,X_6347)),X_6347)))
| theorem(or(not(or(X_6347,not(X_6346))),or(not(or(X_6346,X_6347)),X_6347))) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_6347)),bind(B,$fot(not(X_6346))),bind(X_571,$fot(or(not(or(X_6346,X_6347)),X_6347)))]]) ).
cnf(refute_0_7,plain,
( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(subst,[],[rule_2:[bind(X,$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(not(or(X_6344,X_6345)),or(not(or(not(X_6344),X_6345)),X_6345)))
| theorem(or(not(or(not(X_6344),X_6345)),or(not(or(X_6344,X_6345)),X_6345))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(not(or(X_6344,X_6345)))),bind(B,$fot(not(or(not(X_6344),X_6345)))),bind(C,$fot(X_6345))]]) ).
cnf(refute_0_10,plain,
( ~ theorem(or(not(or(not(X_2838),X_2839)),or(not(or(X_2839,X_2838)),X_2839)))
| theorem(or(not(or(X_2839,X_2838)),or(not(or(not(X_2838),X_2839)),X_2839))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(not(or(not(X_2838),X_2839)))),bind(B,$fot(not(or(X_2839,X_2838)))),bind(C,$fot(X_2839))]]) ).
cnf(refute_0_11,plain,
axiom(or(not(or(X_23,X_23)),X_23)),
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_12,plain,
( ~ axiom(or(not(or(X_23,X_23)),X_23))
| ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_23)),bind(Y,$fot(or(X_23,X_23)))]]) ).
cnf(refute_0_13,plain,
( ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(resolve,[$cnf( axiom(or(not(or(X_23,X_23)),X_23)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ theorem(or(or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836)),or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836))))
| theorem(or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836))) ),
inference(subst,[],[refute_0_13:[bind(X_23,$fot(or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836))))]]) ).
cnf(refute_0_15,plain,
( ~ theorem(or(not(or(not(X_2785),X_2786)),or(X_2787,or(not(or(X_2786,X_2785)),X_2786))))
| theorem(or(X_2787,or(not(or(not(X_2785),X_2786)),or(not(or(X_2786,X_2785)),X_2786)))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(not(or(not(X_2785),X_2786)))),bind(B,$fot(X_2787)),bind(C,$fot(or(not(or(X_2786,X_2785)),X_2786)))]]) ).
cnf(refute_0_16,plain,
axiom(or(not(or(not(A),X_2781)),or(not(or(X_2781,A)),or(X_2781,X_2781)))),
inference(subst,[],[axiom_1_6:[bind(B,$fot(X_2781)),bind(C,$fot(X_2781))]]) ).
cnf(refute_0_17,plain,
axiom(or(not(X_24),or(B,X_24))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_18,plain,
( ~ axiom(or(not(X_24),or(B,X_24)))
| ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_24))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_19,plain,
( ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(resolve,[$cnf( axiom(or(not(X_24),or(B,X_24))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ theorem(or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125)))
| theorem(or(B,or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125)))) ),
inference(subst,[],[refute_0_19:[bind(X_24,$fot(or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125))))]]) ).
cnf(refute_0_21,plain,
( ~ axiom(or(not(or(A,A)),A))
| theorem(or(not(or(A,A)),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(A,A)),A)))]]) ).
cnf(refute_0_22,plain,
theorem(or(not(or(A,A)),A)),
inference(resolve,[$cnf( axiom(or(not(or(A,A)),A)) )],[axiom_1_2,refute_0_21]) ).
cnf(refute_0_23,plain,
theorem(or(not(or(X_123,X_123)),X_123)),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_123))]]) ).
cnf(refute_0_24,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_25,plain,
( ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ theorem(or(not(or(X_123,X_123)),X_123))
| theorem(or(not(or(X_124,or(X_123,X_123))),or(X_124,X_123))) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(or(X_123,X_123))),bind(B,$fot(X_123)),bind(C,$fot(X_124))]]) ).
cnf(refute_0_27,plain,
theorem(or(not(or(X_124,or(X_123,X_123))),or(X_124,X_123))),
inference(resolve,[$cnf( theorem(or(not(or(X_123,X_123)),X_123)) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
theorem(or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125))),
inference(subst,[],[refute_0_27:[bind(X_123,$fot(X_125)),bind(X_124,$fot(X_126))]]) ).
cnf(refute_0_29,plain,
theorem(or(B,or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125)))),
inference(resolve,[$cnf( theorem(or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125))) )],[refute_0_28,refute_0_20]) ).
cnf(refute_0_30,plain,
theorem(or(X_160,or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125)))),
inference(subst,[],[refute_0_29:[bind(B,$fot(X_160))]]) ).
cnf(refute_0_31,plain,
( ~ theorem(or(X_160,or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125))))
| theorem(or(not(or(X_126,or(X_125,X_125))),or(X_160,or(X_126,X_125)))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_160)),bind(B,$fot(not(or(X_126,or(X_125,X_125))))),bind(C,$fot(or(X_126,X_125)))]]) ).
cnf(refute_0_32,plain,
theorem(or(not(or(X_126,or(X_125,X_125))),or(X_160,or(X_126,X_125)))),
inference(resolve,[$cnf( theorem(or(X_160,or(not(or(X_126,or(X_125,X_125))),or(X_126,X_125)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ axiom(or(not(X_569),or(X_126,or(X_125,X_125))))
| ~ theorem(or(not(or(X_126,or(X_125,X_125))),or(X_160,or(X_126,X_125))))
| theorem(or(not(X_569),or(X_160,or(X_126,X_125)))) ),
inference(subst,[],[rule_3:[bind(X,$fot(X_569)),bind(Y,$fot(or(X_126,or(X_125,X_125)))),bind(Z,$fot(or(X_160,or(X_126,X_125))))]]) ).
cnf(refute_0_34,plain,
( ~ axiom(or(not(X_569),or(X_126,or(X_125,X_125))))
| theorem(or(not(X_569),or(X_160,or(X_126,X_125)))) ),
inference(resolve,[$cnf( theorem(or(not(or(X_126,or(X_125,X_125))),or(X_160,or(X_126,X_125)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ axiom(or(not(or(not(A),X_2781)),or(not(or(X_2781,A)),or(X_2781,X_2781))))
| theorem(or(not(or(not(A),X_2781)),or(X_2783,or(not(or(X_2781,A)),X_2781)))) ),
inference(subst,[],[refute_0_34:[bind(X_125,$fot(X_2781)),bind(X_126,$fot(not(or(X_2781,A)))),bind(X_160,$fot(X_2783)),bind(X_569,$fot(or(not(A),X_2781)))]]) ).
cnf(refute_0_36,plain,
theorem(or(not(or(not(A),X_2781)),or(X_2783,or(not(or(X_2781,A)),X_2781)))),
inference(resolve,[$cnf( axiom(or(not(or(not(A),X_2781)),or(not(or(X_2781,A)),or(X_2781,X_2781)))) )],[refute_0_16,refute_0_35]) ).
cnf(refute_0_37,plain,
theorem(or(not(or(not(X_2785),X_2786)),or(X_2787,or(not(or(X_2786,X_2785)),X_2786)))),
inference(subst,[],[refute_0_36:[bind(A,$fot(X_2785)),bind(X_2781,$fot(X_2786)),bind(X_2783,$fot(X_2787))]]) ).
cnf(refute_0_38,plain,
theorem(or(X_2787,or(not(or(not(X_2785),X_2786)),or(not(or(X_2786,X_2785)),X_2786)))),
inference(resolve,[$cnf( theorem(or(not(or(not(X_2785),X_2786)),or(X_2787,or(not(or(X_2786,X_2785)),X_2786)))) )],[refute_0_37,refute_0_15]) ).
cnf(refute_0_39,plain,
theorem(or(or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836)),or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836)))),
inference(subst,[],[refute_0_38:[bind(X_2785,$fot(X_2835)),bind(X_2786,$fot(X_2836)),bind(X_2787,$fot(or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836))))]]) ).
cnf(refute_0_40,plain,
theorem(or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836))),
inference(resolve,[$cnf( theorem(or(or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836)),or(not(or(not(X_2835),X_2836)),or(not(or(X_2836,X_2835)),X_2836)))) )],[refute_0_39,refute_0_14]) ).
cnf(refute_0_41,plain,
theorem(or(not(or(not(X_2838),X_2839)),or(not(or(X_2839,X_2838)),X_2839))),
inference(subst,[],[refute_0_40:[bind(X_2835,$fot(X_2838)),bind(X_2836,$fot(X_2839))]]) ).
cnf(refute_0_42,plain,
theorem(or(not(or(X_2839,X_2838)),or(not(or(not(X_2838),X_2839)),X_2839))),
inference(resolve,[$cnf( theorem(or(not(or(not(X_2838),X_2839)),or(not(or(X_2839,X_2838)),X_2839))) )],[refute_0_41,refute_0_10]) ).
cnf(refute_0_43,plain,
theorem(or(not(or(X_6220,X_6219)),or(not(or(not(X_6219),X_6220)),X_6220))),
inference(subst,[],[refute_0_42:[bind(X_2838,$fot(X_6219)),bind(X_2839,$fot(X_6220))]]) ).
cnf(refute_0_44,plain,
( ~ theorem(or(not(or(X_6220,X_6219)),or(not(or(not(X_6219),X_6220)),X_6220)))
| theorem(or(not(or(X_6219,X_6220)),or(not(or(not(X_6219),X_6220)),X_6220))) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_6219)),bind(B,$fot(X_6220)),bind(X_571,$fot(or(not(or(not(X_6219),X_6220)),X_6220)))]]) ).
cnf(refute_0_45,plain,
theorem(or(not(or(X_6219,X_6220)),or(not(or(not(X_6219),X_6220)),X_6220))),
inference(resolve,[$cnf( theorem(or(not(or(X_6220,X_6219)),or(not(or(not(X_6219),X_6220)),X_6220))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
theorem(or(not(or(X_6344,X_6345)),or(not(or(not(X_6344),X_6345)),X_6345))),
inference(subst,[],[refute_0_45:[bind(X_6219,$fot(X_6344)),bind(X_6220,$fot(X_6345))]]) ).
cnf(refute_0_47,plain,
theorem(or(not(or(not(X_6344),X_6345)),or(not(or(X_6344,X_6345)),X_6345))),
inference(resolve,[$cnf( theorem(or(not(or(X_6344,X_6345)),or(not(or(not(X_6344),X_6345)),X_6345))) )],[refute_0_46,refute_0_9]) ).
cnf(refute_0_48,plain,
theorem(or(not(or(not(X_6346),X_6347)),or(not(or(X_6346,X_6347)),X_6347))),
inference(subst,[],[refute_0_47:[bind(X_6344,$fot(X_6346)),bind(X_6345,$fot(X_6347))]]) ).
cnf(refute_0_49,plain,
theorem(or(not(or(X_6347,not(X_6346))),or(not(or(X_6346,X_6347)),X_6347))),
inference(resolve,[$cnf( theorem(or(not(or(not(X_6346),X_6347)),or(not(or(X_6346,X_6347)),X_6347))) )],[refute_0_48,refute_0_6]) ).
cnf(refute_0_50,plain,
theorem(or(not(or(X_6725,not(X_6724))),or(not(or(X_6724,X_6725)),X_6725))),
inference(subst,[],[refute_0_49:[bind(X_6346,$fot(X_6724)),bind(X_6347,$fot(X_6725))]]) ).
cnf(refute_0_51,plain,
theorem(or(not(not(X_6724)),or(not(or(X_6724,X_6725)),X_6725))),
inference(resolve,[$cnf( theorem(or(not(or(X_6725,not(X_6724))),or(not(or(X_6724,X_6725)),X_6725))) )],[refute_0_50,refute_0_3]) ).
cnf(refute_0_52,plain,
theorem(or(not(not(p)),or(not(or(p,q)),q))),
inference(subst,[],[refute_0_51:[bind(X_6724,$fot(p)),bind(X_6725,$fot(q))]]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(not(p)),or(not(or(p,q)),q))) )],[refute_0_52,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL210-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 19:35:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.53/1.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.53/1.72
% 1.53/1.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.53/1.73
%------------------------------------------------------------------------------