%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL403+2 : TPTP v9.2.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 04:40:16 PM UTC 2026
% Result : Theorem 54.31s 36.19s
% Output : CNFRefutation 54.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 60 ( 31 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 35 ~; 33 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 230 ( 50 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X1,X2] :
( ( is_a_theorem(implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17] : is_a_theorem(implies(implies(implies(implies(implies(X3,implies(X4,X3)),implies(implies(X5,implies(X6,implies(X7,X6))),X8)),X8),implies(implies(implies(implies(implies(implies(implies(X9,X10),implies(implies(X10,X11),implies(X9,X11))),implies(implies(implies(n(X12),X12),X12),X13)),X13),implies(implies(X14,implies(n(X14),X15)),X16)),X16),X17)),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f2) ).
fof(f3,conjecture,
is_a_theorem(implies(x,implies(n(y),n(implies(x,y))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f3) ).
fof(c_0_3,plain,
! [X35,X36] :
( ~ is_a_theorem(implies(X35,X36))
| ~ is_a_theorem(X35)
| is_a_theorem(X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[condensed_detachment])]) ).
fof(c_0_4,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] : is_a_theorem(implies(implies(implies(implies(implies(X37,implies(X38,X37)),implies(implies(X39,implies(X40,implies(X41,X40))),X42)),X42),implies(implies(implies(implies(implies(implies(implies(X43,X44),implies(implies(X44,X45),implies(X43,X45))),implies(implies(implies(n(X46),X46),X46),X47)),X47),implies(implies(X48,implies(n(X48),X49)),X50)),X50),X51)),X51)),
inference(variable_rename,[status(thm)],[f2]) ).
cnf(c_0_5,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6),implies(implies(implies(implies(implies(implies(implies(X7,X8),implies(implies(X8,X9),implies(X7,X9))),implies(implies(implies(n(X10),X10),X10),X11)),X11),implies(implies(X12,implies(n(X12),X13)),X14)),X14),X15)),X15)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(implies(X2,implies(X3,X2)),implies(implies(X4,implies(X5,implies(X6,X5))),X7)),X7),implies(implies(implies(implies(implies(implies(implies(X8,X9),implies(implies(X9,X10),implies(X8,X10))),implies(implies(implies(n(X11),X11),X11),X12)),X12),implies(implies(X13,implies(n(X13),X14)),X15)),X15),X1))) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,implies(X3,X2)),implies(implies(X4,implies(X5,implies(X6,X5))),X1))) ),
inference(spm,[status(thm)],[c_0_5,c_0_9]) ).
cnf(c_0_11,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_12,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_13,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,implies(X3,implies(X4,X3))),X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X9)),X9))),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_15,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X8)),X8)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X1))) ),
inference(spm,[status(thm)],[c_0_5,c_0_15]) ).
cnf(c_0_17,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5)),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_18,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),implies(X4,X3))),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_19,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_20,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X1))) ),
inference(spm,[status(thm)],[c_0_5,c_0_17]) ).
cnf(c_0_21,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_5,c_0_19]) ).
cnf(c_0_22,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,implies(n(X2),X3)),X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_23,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_24,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_5,c_0_21]) ).
cnf(c_0_25,plain,
is_a_theorem(implies(implies(implies(n(X1),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_26,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_23]) ).
cnf(c_0_27,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(n(X2),X2),X2),X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_28,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,implies(implies(n(X2),X4),X3))) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_30,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(n(X2),X2))) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(n(X1),implies(X1,implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
is_a_theorem(implies(n(n(implies(X1,X2))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(implies(n(X2),X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_34,plain,
is_a_theorem(implies(n(n(implies(n(X1),X1))),X1)),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_35,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(n(X1),X3),X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_25]) ).
cnf(c_0_36,plain,
is_a_theorem(implies(implies(X1,n(implies(n(X1),X1))),n(implies(n(X1),X1)))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_29]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,n(X1))) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(X1,n(implies(n(n(X1)),n(X1))))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(implies(n(n(X1)),n(X1)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(implies(X1,implies(n(X2),X2)),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_40]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(implies(implies(X1,n(X2)),X2),X2)),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_44,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,implies(implies(X4,X2),X3))) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(n(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_46,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X9)),X9),X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_47,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,implies(n(X1),X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_42]) ).
cnf(c_0_48,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(implies(X3,n(X2)),X2))) ),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(n(implies(X1,X2)),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(implies(implies(X1,implies(n(X1),X2)),X3),X3)),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_51,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(n(X1),X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_21]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(n(implies(X1,implies(X2,n(X3)))),X3)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(implies(X3,implies(n(X3),X4)),X2))) ),
inference(spm,[status(thm)],[c_0_24,c_0_50]) ).
fof(c_0_54,negated_conjecture,
~ is_a_theorem(implies(x,implies(n(y),n(implies(x,y))))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[f3])]) ).
cnf(c_0_55,plain,
( is_a_theorem(implies(X1,implies(X2,n(X3))))
| ~ is_a_theorem(implies(X3,implies(X1,implies(X2,n(X3))))) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(n(X2),X3)))),
inference(spm,[status(thm)],[c_0_53,c_0_19]) ).
cnf(c_0_57,negated_conjecture,
~ is_a_theorem(implies(x,implies(n(y),n(implies(x,y))))),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(X1,implies(n(X2),n(implies(X1,X2))))),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.22 % Problem : LCL403+2 : TPTP v9.2.1. Released v9.1.0.
% 0.03/0.22 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.46 % Computer : n027.cluster.edu
% 0.12/0.46 % Model : x86_64 x86_64
% 0.12/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.46 % Memory : 8042.1875MB
% 0.12/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.46 % CPULimit : 300
% 0.12/0.46 % WCLimit : 300
% 0.12/0.46 % DateTime : Mon May 4 22:32:05 EDT 2026
% 0.12/0.46 % CPUTime :
% 0.12/0.46 % start to proof: theBenchmark
% 54.31/36.19 % Version : CSE_E---1.7
% 54.31/36.19 % Problem : theBenchmark.p
% 54.31/36.19 % SZS status Theorem for theBenchmark.p
% 54.31/36.19 % SZS output start CNFRefutation
% See solution above
% 54.49/36.39 % Total time : 28.613s
%------------------------------------------------------------------------------