%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL401-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:06:32 PM UTC 2026
% Result : Unsatisfiable 73.76s 19.62s
% Output : CNFRefutation 73.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 5
% Syntax : Number of formulae : 150 ( 75 unt; 0 def)
% Number of atoms : 238 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 178 ( 90 ~; 88 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 462 ( 0 sgn 462 !; 0 ?; 454 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
fof(f3,axiom,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
fof(f4,axiom,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(not(implies(x,y)),not(y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_67) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(cnf_transformation,[],[f2]) ).
tcf(c_56,plain,
! [X0: $i] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_58,negated_conjecture,
~ is_a_theorem(implies(not(implies(x,y)),not(y))),
inference(cnf_transformation,[],[f5]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_112,c_54]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(implies(X2,X0),X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)) ),
inference(superposition,[status(thm)],[c_55,c_116]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_56,c_116]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(superposition,[status(thm)],[c_57,c_116]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(superposition,[status(thm)],[c_159,c_54]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(implies(X1,X2),implies(not(X0),X2)))),
inference(superposition,[status(thm)],[c_55,c_160]) ).
tcf(c_215,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_56,c_160]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(not(implies(not(X0),X1)),X2))),
inference(superposition,[status(thm)],[c_57,c_160]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_143,c_160]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_56,c_116]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(superposition,[status(thm)],[c_57,c_116]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(not(X2),X1)),X3)) ),
inference(superposition,[status(thm)],[c_214,c_116]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_214,c_54]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_498,c_430]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(superposition,[status(thm)],[c_529,c_116]) ).
tcf(c_3568,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_3826,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_429,c_630]) ).
tcf(c_3933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X3,implies(X0,X2)))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_3568,c_3826]) ).
tcf(c_3934,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(superposition,[status(thm)],[c_429,c_3826]) ).
tcf(c_4256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X3,implies(X0,X2)))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(superposition,[status(thm)],[c_57,c_3933]) ).
tcf(c_4315,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_56,c_4256]) ).
tcf(c_4347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X2,implies(X3,X1)))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_4315,c_3933]) ).
tcf(c_4357,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(X1,implies(X2,X2)))),
inference(superposition,[status(thm)],[c_4315,c_4256]) ).
tcf(c_4721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X1)),X2)) ),
inference(superposition,[status(thm)],[c_4357,c_3934]) ).
tcf(c_4723,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X1)),X2)) ),
inference(superposition,[status(thm)],[c_4357,c_208]) ).
tcf(c_5269,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(superposition,[status(thm)],[c_55,c_4723]) ).
tcf(c_5495,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,X1)))),
inference(superposition,[status(thm)],[c_5269,c_158]) ).
tcf(c_5499,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(superposition,[status(thm)],[c_5269,c_433]) ).
tcf(c_5517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : is_a_theorem(implies(X0,implies(X1,implies(X2,implies(not(implies(X3,X3)),X4))))),
inference(superposition,[status(thm)],[c_5499,c_4347]) ).
tcf(c_5536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(X0,implies(X1,implies(X2,implies(not(X1),X3))))),
inference(superposition,[status(thm)],[c_5495,c_4256]) ).
tcf(c_5802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : is_a_theorem(implies(X0,implies(X1,implies(X2,implies(X3,implies(not(X2),X4)))))),
inference(superposition,[status(thm)],[c_5536,c_4347]) ).
tcf(c_6464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : is_a_theorem(implies(X0,implies(not(implies(not(implies(X1,implies(X2,X2))),X3)),X4))),
inference(superposition,[status(thm)],[c_216,c_4721]) ).
tcf(c_17381,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(superposition,[status(thm)],[c_56,c_54]) ).
tcf(c_17384,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_17461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( is_a_theorem(X4)
| ~ is_a_theorem(implies(implies(X0,implies(X1,implies(not(implies(X2,X2)),X3))),X4)) ),
inference(superposition,[status(thm)],[c_5517,c_208]) ).
tcf(c_17466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : is_a_theorem(implies(implies(implies(X0,implies(not(implies(X1,X1)),X2)),X3),implies(X4,X3))),
inference(superposition,[status(thm)],[c_55,c_17461]) ).
tcf(c_17467,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(superposition,[status(thm)],[c_56,c_17461]) ).
tcf(c_17480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( is_a_theorem(implies(X4,X3))
| ~ is_a_theorem(implies(implies(X0,implies(not(implies(X1,X1)),X2)),X3)) ),
inference(superposition,[status(thm)],[c_17466,c_54]) ).
tcf(c_17484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : is_a_theorem(implies(X0,implies(implies(implies(not(implies(X1,X1)),X2),X3),implies(X4,X3)))),
inference(superposition,[status(thm)],[c_55,c_17480]) ).
tcf(c_17499,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(not(implies(X0,X0)),X1),X2)) ),
inference(superposition,[status(thm)],[c_17467,c_208]) ).
tcf(c_17503,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(superposition,[status(thm)],[c_17467,c_17461]) ).
tcf(c_17505,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_17503,c_208]) ).
tcf(c_17516,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,not(implies(X1,X1)))) ),
inference(superposition,[status(thm)],[c_217,c_17505]) ).
tcf(c_17553,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(not(not(implies(X0,X0))),not(implies(X0,X0))),X1)),
inference(superposition,[status(thm)],[c_56,c_17516]) ).
tcf(c_17683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(X0,implies(X1,implies(X2,implies(not(X1),X3))))),
inference(superposition,[status(thm)],[c_5802,c_17461]) ).
tcf(c_17687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(X0,implies(X1,implies(not(X0),X2))),X3)) ),
inference(superposition,[status(thm)],[c_17683,c_208]) ).
tcf(c_17694,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(superposition,[status(thm)],[c_17683,c_17461]) ).
tcf(c_17701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(X0,implies(not(implies(not(implies(X1,X1)),X2)),X3))),
inference(superposition,[status(thm)],[c_17694,c_17499]) ).
tcf(c_17716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(not(implies(not(implies(X0,X0)),X1)),X2),X3)) ),
inference(superposition,[status(thm)],[c_17701,c_208]) ).
tcf(c_17761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(implies(implies(not(implies(X0,X0)),X1),X2),implies(X3,X2))),
inference(superposition,[status(thm)],[c_17484,c_17461]) ).
tcf(c_17920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(implies(X0,not(implies(X1,X1))),implies(X2,implies(X0,X3)))),
inference(superposition,[status(thm)],[c_17761,c_158]) ).
tcf(c_17984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X2,implies(X0,X3)))
| ~ is_a_theorem(implies(X0,not(implies(X1,X1)))) ),
inference(superposition,[status(thm)],[c_17920,c_54]) ).
tcf(c_18000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(not(implies(not(implies(X0,implies(X1,X1))),X2)),X3)),
inference(superposition,[status(thm)],[c_6464,c_17461]) ).
tcf(c_18006,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(not(implies(X0,implies(X1,X1))),X2)),
inference(superposition,[status(thm)],[c_18000,c_17381]) ).
tcf(c_18013,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X1)),X2)) ),
inference(superposition,[status(thm)],[c_18006,c_208]) ).
tcf(c_18036,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(superposition,[status(thm)],[c_55,c_18013]) ).
tcf(c_18074,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,X1)))),
inference(superposition,[status(thm)],[c_18036,c_158]) ).
tcf(c_18104,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(implies(not(not(implies(X1,X1))),not(implies(X1,X1))),X2))),
inference(superposition,[status(thm)],[c_17553,c_17984]) ).
tcf(c_18191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_18074,c_116]) ).
tcf(c_18664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X1),X2),implies(X3,X2)))),
inference(superposition,[status(thm)],[c_55,c_18191]) ).
tcf(c_18892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_18664,c_54]) ).
tcf(c_18926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(implies(X2,X0),implies(X3,implies(X2,X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_18892,c_158]) ).
tcf(c_19317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X0,implies(X2,implies(not(X1),X3))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_17384,c_17687]) ).
tcf(c_20092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X2,implies(not(X1),X3)))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_19317,c_17505]) ).
tcf(c_25630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(X0,implies(not(implies(implies(not(not(implies(X1,X1))),not(implies(X1,X1))),X2)),X3))),
inference(superposition,[status(thm)],[c_18104,c_20092]) ).
tcf(c_26440,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(not(implies(implies(not(not(implies(X0,X0))),not(implies(X0,X0))),X1)),X2)),
inference(superposition,[status(thm)],[c_25630,c_17716]) ).
tcf(c_28880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X3,implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_18926,c_54]) ).
tcf(c_29193,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,implies(X0,X1)))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(superposition,[status(thm)],[c_56,c_28880]) ).
tcf(c_29754,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(implies(not(implies(not(X1),X1)),implies(not(X1),X1)),X1))),
inference(superposition,[status(thm)],[c_56,c_29193]) ).
tcf(c_31356,plain,
! [X0: $i] : is_a_theorem(implies(implies(not(implies(not(X0),X0)),implies(not(X0),X0)),X0)),
inference(superposition,[status(thm)],[c_29754,c_17716]) ).
tcf(c_38657,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(not(implies(not(X0),X0)),implies(not(X0),X0))) ),
inference(superposition,[status(thm)],[c_31356,c_54]) ).
tcf(c_38707,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(implies(not(not(implies(X0,X0))),not(implies(X0,X0))),X1),X2)) ),
inference(superposition,[status(thm)],[c_26440,c_208]) ).
tcf(c_38772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(X0,implies(X1,implies(not(implies(X2,X2)),X3)))),
inference(superposition,[status(thm)],[c_5517,c_38707]) ).
tcf(c_38774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(X0,implies(not(implies(X1,X1)),X2)),X3)) ),
inference(superposition,[status(thm)],[c_38772,c_208]) ).
tcf(c_38948,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(superposition,[status(thm)],[c_5802,c_38657]) ).
tcf(c_38952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(implies(X0,implies(not(X1),X2)),X3)) ),
inference(superposition,[status(thm)],[c_38948,c_116]) ).
tcf(c_40370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(X0,implies(implies(implies(not(X0),X1),X2),implies(X3,X2)))),
inference(superposition,[status(thm)],[c_55,c_38952]) ).
tcf(c_40372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(X0,implies(not(implies(X1,implies(not(X0),X2))),X3))),
inference(superposition,[status(thm)],[c_57,c_38952]) ).
tcf(c_40487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : is_a_theorem(implies(implies(implies(not(implies(X0,implies(not(implies(X1,X1)),X2))),X3),X4),implies(X5,X4))),
inference(superposition,[status(thm)],[c_40370,c_38774]) ).
tcf(c_40666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( is_a_theorem(implies(X5,X4))
| ~ is_a_theorem(implies(implies(not(implies(X0,implies(not(implies(X1,X1)),X2))),X3),X4)) ),
inference(superposition,[status(thm)],[c_40487,c_54]) ).
tcf(c_41185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : is_a_theorem(implies(X0,implies(not(implies(X1,implies(not(implies(not(implies(X2,implies(not(implies(X3,X3)),X4))),X5)),X6))),X7))),
inference(superposition,[status(thm)],[c_40372,c_40666]) ).
tcf(c_41671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : is_a_theorem(implies(not(implies(X0,implies(not(implies(not(implies(X1,implies(not(implies(X2,X2)),X3))),X4)),X5))),X6)),
inference(superposition,[status(thm)],[c_41185,c_38707]) ).
tcf(c_88558,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(superposition,[status(thm)],[c_56,c_54]) ).
tcf(c_88561,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_88573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : is_a_theorem(implies(X0,implies(not(implies(not(implies(X1,implies(not(implies(X2,X2)),X3))),X4)),X5))),
inference(superposition,[status(thm)],[c_41671,c_88558]) ).
tcf(c_88575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : is_a_theorem(implies(not(implies(not(implies(X0,implies(not(implies(X1,X1)),X2))),X3)),X4)),
inference(superposition,[status(thm)],[c_88573,c_88558]) ).
tcf(c_88577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(not(implies(X0,implies(not(implies(X1,X1)),X2))),X3)),
inference(superposition,[status(thm)],[c_88575,c_88558]) ).
tcf(c_88604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X1,implies(X0,X3)))
| ~ is_a_theorem(implies(X0,not(implies(not(X1),X2)))) ),
inference(superposition,[status(thm)],[c_217,c_430]) ).
tcf(c_88608,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(superposition,[status(thm)],[c_88577,c_88558]) ).
tcf(c_88620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( is_a_theorem(X4)
| ~ is_a_theorem(implies(implies(not(implies(X0,implies(not(implies(X1,X1)),X2))),X3),X4)) ),
inference(superposition,[status(thm)],[c_88575,c_208]) ).
tcf(c_88674,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(superposition,[status(thm)],[c_88608,c_88620]) ).
tcf(c_88676,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_88674,c_208]) ).
tcf(c_88860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(X0,implies(X1,implies(X2,implies(not(X1),X3))))),
inference(superposition,[status(thm)],[c_5802,c_88676]) ).
tcf(c_88870,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(superposition,[status(thm)],[c_88860,c_88676]) ).
tcf(c_88874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(implies(X0,implies(not(X1),X2)),X3)) ),
inference(superposition,[status(thm)],[c_88870,c_116]) ).
tcf(c_88985,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(not(implies(not(X0),X0)),implies(not(X0),X0))) ),
inference(superposition,[status(thm)],[c_31356,c_54]) ).
tcf(c_89323,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(not(implies(X0,implies(X1,X1))),X2)),
inference(superposition,[status(thm)],[c_6464,c_88985]) ).
tcf(c_89332,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X1)),X2)) ),
inference(superposition,[status(thm)],[c_89323,c_208]) ).
tcf(c_89344,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(superposition,[status(thm)],[c_55,c_89332]) ).
tcf(c_89379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(implies(implies(X3,X3),X1),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_89344,c_116]) ).
tcf(c_91557,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_56,c_630]) ).
tcf(c_91560,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_429,c_630]) ).
tcf(c_91982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X2,implies(X3,X1)))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_89344,c_91560]) ).
tcf(c_92185,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,implies(X2,X0)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_91557,c_91982]) ).
tcf(c_92271,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_92185,c_208]) ).
tcf(c_92372,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_55,c_92271]) ).
tcf(c_92495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(implies(X2,X0),implies(X3,implies(X2,X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_92372,c_158]) ).
tcf(c_94885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(implies(X1,X2),implies(X3,X2)))),
inference(superposition,[status(thm)],[c_55,c_89379]) ).
tcf(c_94889,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(implies(X2,X2),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_429,c_89379]) ).
tcf(c_95513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_94885,c_54]) ).
tcf(c_96064,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_94889,c_54]) ).
tcf(c_100257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X3,implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_92495,c_54]) ).
tcf(c_100585,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,implies(X0,X1)))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(superposition,[status(thm)],[c_56,c_100257]) ).
tcf(c_100853,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(superposition,[status(thm)],[c_215,c_100585]) ).
tcf(c_100897,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(X0,implies(X1,implies(not(X1),X2)))),
inference(superposition,[status(thm)],[c_88870,c_100585]) ).
tcf(c_101367,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)) ),
inference(superposition,[status(thm)],[c_100853,c_96064]) ).
tcf(c_101369,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),implies(X2,X1))),
inference(superposition,[status(thm)],[c_100853,c_95513]) ).
tcf(c_101420,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)) ),
inference(superposition,[status(thm)],[c_100897,c_96064]) ).
tcf(c_103986,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(superposition,[status(thm)],[c_88561,c_101367]) ).
tcf(c_105170,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(superposition,[status(thm)],[c_55,c_101420]) ).
tcf(c_105428,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,not(X1)),implies(X1,implies(X0,X2)))),
inference(superposition,[status(thm)],[c_105170,c_158]) ).
tcf(c_106856,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),not(X1))) ),
inference(superposition,[status(thm)],[c_217,c_103986]) ).
tcf(c_106920,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,not(not(implies(X0,X1)))),implies(X0,X1))),
inference(superposition,[status(thm)],[c_105428,c_103986]) ).
tcf(c_109555,plain,
! [X0: $i] : is_a_theorem(implies(implies(not(X0),not(not(implies(not(X0),X0)))),X0)),
inference(superposition,[status(thm)],[c_106920,c_103986]) ).
tcf(c_111002,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(superposition,[status(thm)],[c_101369,c_103986]) ).
tcf(c_111041,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(superposition,[status(thm)],[c_111002,c_158]) ).
tcf(c_111124,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[c_111041,c_88874]) ).
tcf(c_111144,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_111124,c_116]) ).
tcf(c_111731,plain,
! [X0: $i] : is_a_theorem(implies(not(not(implies(not(X0),X0))),X0)),
inference(superposition,[status(thm)],[c_109555,c_111144]) ).
tcf(c_112338,plain,
! [X0: $i] : is_a_theorem(implies(X0,not(implies(not(not(X0)),not(X0))))),
inference(superposition,[status(thm)],[c_111731,c_106856]) ).
tcf(c_113355,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(superposition,[status(thm)],[c_112338,c_88604]) ).
tcf(c_113405,plain,
! [X0: $i] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[c_113355,c_103986]) ).
tcf(c_113413,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(not(not(X0)),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_113405,c_116]) ).
tcf(c_113424,plain,
! [X0: $i] : is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[status(thm)],[c_113405,c_106856]) ).
tcf(c_114158,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,not(not(implies(X1,X0))))),
inference(superposition,[status(thm)],[c_113424,c_111144]) ).
tcf(c_118934,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,not(X0)))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_113413,c_106856]) ).
tcf(c_161800,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(not(implies(X0,X1)),not(X1))),
inference(superposition,[status(thm)],[c_114158,c_118934]) ).
tcf(c_161853,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_161800]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL401-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 23:10:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.46
% 0.16/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.46
% 0.16/0.47 % Detected problem language: tptp
% 0.16/0.48 % Proving...
% 73.76/19.62 % SZS status Started for theBenchmark.p
% 73.76/19.62 % SZS status Unsatisfiable for theBenchmark.p
% 73.76/19.62
% 73.76/19.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 73.76/19.62
% 73.76/19.62 % ------ iProver source info
% 73.76/19.62
% 73.76/19.62 % git: date: 2026-07-19 20:42:38 +0200
% 73.76/19.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 73.76/19.62 % git: non_committed_changes: false
% 73.76/19.62
% 73.76/19.62 % ------ Parsing...% successful
% 73.76/19.62
% 73.76/19.62
% 73.76/19.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 73.76/19.62
% 73.76/19.62 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 73.76/19.62
% 73.76/19.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 73.76/19.62 % ------ Proving...
% 73.76/19.62 % ------ Problem Properties
% 73.76/19.62
% 73.76/19.62 %
% 73.76/19.62 % clauses 5
% 73.76/19.62 % conjectures 1
% 73.76/19.62 % EPR 0
% 73.76/19.62 % Horn 5
% 73.76/19.62 % unary 4
% 73.76/19.62 % binary 0
% 73.76/19.62 % lits 7
% 73.76/19.62 % lits eq 0
% 73.76/19.62 % fd_pure 0
% 73.76/19.62 % fd_pseudo 0
% 73.76/19.62 % fd_cond 0
% 73.76/19.62 % fd_pseudo_cond 0
% 73.76/19.62 % AC symbols 0
% 73.76/19.62
% 73.76/19.62 % ------ Input Options Time Limit: Unbounded
% 73.76/19.62
% 73.76/19.62
% 73.76/19.62 % ------
% 73.76/19.62 % Current options:
% 73.76/19.62 % ------
% 73.76/19.62
% 73.76/19.62
% 73.76/19.62 %
% 73.76/19.62
% 73.76/19.62 % ------ Proving...
% 73.76/19.62 %
% 73.76/19.62
% 73.76/19.62 % SZS status Unsatisfiable for theBenchmark.p
% 73.76/19.62
% 73.76/19.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 73.76/19.63
%------------------------------------------------------------------------------