%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL039-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 : 300s
% DateTime : Tue May 5 04:39:14 PM UTC 2026
% Result : Unsatisfiable 20.28s 12.76s
% Output : CNFRefutation 20.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of clauses : 48 ( 19 unt; 0 nHn; 32 RR)
% Number of literals : 89 ( 0 equ; 52 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 86 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(necessitation1,axiom,
is_a_theorem(implies(necessary(implies(X1,X2)),implies(necessary(X1),necessary(X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation1) ).
cnf(axiom_of_necessitation,axiom,
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_of_necessitation) ).
cnf(cn_35,axiom,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_35) ).
cnf(cn_18,axiom,
is_a_theorem(implies(X1,implies(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_18) ).
cnf(necessitation2,axiom,
is_a_theorem(implies(necessary(X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation2) ).
cnf(prove_this,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(cn_49,axiom,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_49) ).
cnf(c_0_8,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
condensed_detachment ).
cnf(c_0_9,axiom,
is_a_theorem(implies(necessary(implies(X1,X2)),implies(necessary(X1),necessary(X2)))),
necessitation1 ).
cnf(c_0_10,plain,
( is_a_theorem(implies(necessary(X1),necessary(X2)))
| ~ is_a_theorem(necessary(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(necessary(implies(X2,X1)))
| ~ is_a_theorem(necessary(X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_12,axiom,
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(X1) ),
axiom_of_necessitation ).
cnf(c_0_13,axiom,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
cn_35 ).
cnf(c_0_14,plain,
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(necessary(implies(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))
| ~ is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_16,axiom,
is_a_theorem(implies(X1,implies(X2,X1))),
cn_18 ).
cnf(c_0_17,plain,
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_18,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
cnf(c_0_19,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_20,plain,
( is_a_theorem(necessary(implies(X1,X2)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,axiom,
is_a_theorem(implies(necessary(X1),X1)),
necessitation2 ).
cnf(c_0_22,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(necessary(implies(implies(X2,X3),X1)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_24,plain,
( is_a_theorem(implies(necessary(X1),X2))
| ~ is_a_theorem(implies(necessary(X1),implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_25,plain,
( is_a_theorem(implies(necessary(implies(X1,X2)),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,plain,
( is_a_theorem(necessary(X1))
| ~ is_a_theorem(implies(implies(X2,X3),X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_27,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
prove_this ).
cnf(c_0_28,plain,
( is_a_theorem(implies(necessary(X1),X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_29,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessary(implies(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_25]) ).
cnf(c_0_30,plain,
( is_a_theorem(necessary(implies(implies(X1,X2),implies(X1,X3))))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_31,negated_conjecture,
~ is_a_theorem(implies(a,not(necessary(not(a))))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( ~ is_a_theorem(implies(X1,not(necessary(not(a)))))
| ~ is_a_theorem(implies(a,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
~ is_a_theorem(implies(implies(X1,a),not(necessary(not(a))))),
inference(spm,[status(thm)],[c_0_33,c_0_16]) ).
cnf(c_0_35,plain,
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_36,negated_conjecture,
( ~ is_a_theorem(implies(X1,implies(a,not(necessary(not(a))))))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,axiom,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
cn_49 ).
cnf(c_0_38,negated_conjecture,
~ is_a_theorem(implies(not(not(necessary(not(a)))),not(a))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( ~ is_a_theorem(implies(not(not(necessary(not(a)))),X1))
| ~ is_a_theorem(implies(X1,not(a))) ),
inference(spm,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(implies(X3,X1),X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_41,negated_conjecture,
~ is_a_theorem(implies(not(not(necessary(not(a)))),necessary(not(a)))),
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( ~ is_a_theorem(implies(not(not(necessary(not(a)))),X1))
| ~ is_a_theorem(implies(X1,necessary(not(a)))) ),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_44,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_46,negated_conjecture,
~ is_a_theorem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_47,plain,
$false,
inference(sr,[status(thm)],[c_0_21,c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL039-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n021.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 21:55:10 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 20.28/12.76 % Version : CSE_E---1.7
% 20.28/12.76 % Problem : theBenchmark.p
% 20.28/12.76 % SZS status Unsatisfiable for theBenchmark.p
% 20.28/12.76 % SZS output start CNFRefutation
% See solution above
% 20.38/12.84 % Total time : 9.382s
%------------------------------------------------------------------------------