%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL368+1 : TPTP v9.2.1. Released v9.1.0.
% 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 : n020.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 04:40:06 PM UTC 2026
% Result : Theorem 15.24s 9.63s
% Output : CNFRefutation 15.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 28 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 83 ( 43 ~; 38 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 132 ( 25 sgn 16 !; 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/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(cn_1,axiom,
! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
fof(cn_2,axiom,
! [X1] : is_a_theorem(implies(implies(not(X1),X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
fof(cn_3,axiom,
! [X1,X2] : is_a_theorem(implies(X1,implies(not(X1),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
fof(prove_cn_23,conjecture,
is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_23) ).
fof(c_0_5,plain,
! [X12,X13] :
( ~ is_a_theorem(implies(X12,X13))
| ~ is_a_theorem(X12)
| is_a_theorem(X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[condensed_detachment])]) ).
fof(c_0_6,plain,
! [X14,X15,X16] : is_a_theorem(implies(implies(X14,X15),implies(implies(X15,X16),implies(X14,X16)))),
inference(variable_rename,[status(thm)],[cn_1]) ).
cnf(c_0_7,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_10,plain,
! [X17] : is_a_theorem(implies(implies(not(X17),X17),X17)),
inference(variable_rename,[status(thm)],[cn_2]) ).
cnf(c_0_11,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_7,c_0_9]) ).
fof(c_0_12,plain,
! [X18,X19] : is_a_theorem(implies(X18,implies(not(X18),X19))),
inference(variable_rename,[status(thm)],[cn_3]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,implies(X4,X3)))
| ~ is_a_theorem(implies(X2,X4)) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_15,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(not(X2),X2))) ),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_17,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X2),not(X1))) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_15]) ).
cnf(c_0_20,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,X4))
| ~ is_a_theorem(implies(X4,X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_22,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_23,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3))))
| ~ is_a_theorem(implies(X1,implies(X4,X2))) ),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_24,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X4,X3))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_25,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_26,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(not(implies(implies(X1,X2),implies(X3,X2))),implies(X3,X1))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_30,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_11,c_0_29]) ).
cnf(c_0_31,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_32,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_9]) ).
cnf(c_0_33,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(implies(not(X2),X4),X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_34,plain,
is_a_theorem(implies(implies(not(implies(not(X1),X1)),implies(not(X1),X1)),X1)),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_35,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(implies(X1,X4))
| ~ is_a_theorem(implies(X4,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
cnf(c_0_36,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_13]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(X3),X4)))
| ~ is_a_theorem(implies(implies(implies(X2,X5),implies(X1,X5)),X3)) ),
inference(spm,[status(thm)],[c_0_35,c_0_8]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(not(implies(X1,X2)),X3))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_16,c_0_40]) ).
fof(c_0_43,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),u))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_cn_23])]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_26,c_0_41]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(implies(X2,X1),X1)),X3))),
inference(spm,[status(thm)],[c_0_38,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(y,z)),u),implies(implies(y,implies(x,z)),u))),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(not(X1),X3),X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_44]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_16,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
~ is_a_theorem(implies(implies(y,implies(x,z)),implies(x,implies(y,z)))),
inference(spm,[status(thm)],[c_0_46,c_0_9]) ).
cnf(c_0_50,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X1,X4))))
| ~ is_a_theorem(implies(X3,implies(X2,X4))) ),
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(X1,implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
~ is_a_theorem(implies(x,implies(implies(x,z),z))),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),X3)))
| ~ is_a_theorem(implies(X1,implies(not(X3),X2))) ),
inference(spm,[status(thm)],[c_0_11,c_0_48]) ).
cnf(c_0_54,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(implies(X2,implies(X3,X1))) ),
inference(spm,[status(thm)],[c_0_14,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
~ is_a_theorem(implies(x,implies(not(z),x))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_54,c_0_15]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL368+1 : TPTP v9.2.1. Released v9.1.0.
% 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 22:26:50 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 15.24/9.63 % Version : CSE_E---1.7
% 15.24/9.63 % Problem : theBenchmark.p
% 15.24/9.63 % SZS status Theorem for theBenchmark.p
% 15.24/9.63 % SZS output start CNFRefutation
% See solution above
% 15.24/9.68 % Total time : 7.383s
%------------------------------------------------------------------------------