%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:06:33 PM UTC 2026
% Result : Theorem 1.65s 1.28s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 14 unt; 1 def)
% Number of atoms : 70 ( 1 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 72 ( 33 ~; 19 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 73 !; 4 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ( ? [X3] : ~ a_truth(implies(X3,X3))
& ! [X0,X1] : a_truth(implies(implies(not(X0),not(X1)),implies(X1,X0)))
& ! [X0,X1,X2] : a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2))))
& ! [X0,X1] : a_truth(implies(X0,implies(X1,X0)))
& ! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm147) ).
fof(f2,negated_conjecture,
~ ~ ( ? [X3] : ~ a_truth(implies(X3,X3))
& ! [X0,X1] : a_truth(implies(implies(not(X0),not(X1)),implies(X1,X0)))
& ! [X0,X1,X2] : a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2))))
& ! [X0,X1] : a_truth(implies(X0,implies(X1,X0)))
& ! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ( ? [X9] : ~ a_truth(implies(X9,X9))
& ! [X7,X8] : a_truth(implies(implies(not(X7),not(X8)),implies(X8,X7)))
& ! [X4,X5,X6] : a_truth(implies(implies(X4,implies(X5,X6)),implies(implies(X4,X5),implies(X4,X6))))
& ! [X2,X3] : a_truth(implies(X2,implies(X3,X2)))
& ! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X9] : ~ a_truth(implies(X9,X9))
& ! [X7,X8] : a_truth(implies(implies(not(X7),not(X8)),implies(X8,X7)))
& ! [X4,X5,X6] : a_truth(implies(implies(X4,implies(X5,X6)),implies(implies(X4,X5),implies(X4,X6))))
& ! [X2,X3] : a_truth(implies(X2,implies(X3,X2)))
& ! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( ~ a_truth(implies(sK0,sK0))
& ! [X7,X8] : a_truth(implies(implies(not(X7),not(X8)),implies(X8,X7)))
& ! [X4,X5,X6] : a_truth(implies(implies(X4,implies(X5,X6)),implies(implies(X4,X5),implies(X4,X6))))
& ! [X2,X3] : a_truth(implies(X2,implies(X3,X2)))
& ! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X9,sK0)],[f4]) ).
fof(f6,plain,
~ a_truth(implies(sK0,sK0)),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
! [X6,X4,X5] : a_truth(implies(implies(X4,implies(X5,X6)),implies(implies(X4,X5),implies(X4,X6)))),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X2,X3] : a_truth(implies(X2,implies(X3,X2))),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] : a_truth(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[],[f9]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[],[f8]) ).
tcf(c_53,negated_conjecture,
~ a_truth(implies(sK0,sK0)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_71,definition,
iPr_def_10 = implies(sK0,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_72,negated_conjecture,
~ a_truth(iPr_def_10),
inference(demodulation,[status(thm)],[c_53,c_71]) ).
tcf(c_74,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_75,negated_conjecture,
! [X0: $i,X1: $i] : a_truth(implies(X0,implies(X1,X0))),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_76,negated_conjecture,
! [X0: $i,X1: $i] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( a_truth(implies(implies(X0,X1),implies(X0,X2)))
| ~ a_truth(implies(X0,implies(X1,X2))) ),
inference(superposition,[status(thm)],[c_74,c_76]) ).
tcf(c_213,plain,
a_truth(implies(sK0,iPr_def_10)),
inference(superposition,[status(thm)],[c_71,c_75]) ).
tcf(c_215,plain,
! [X0: $i] :
( a_truth(implies(implies(sK0,X0),iPr_def_10))
| ~ a_truth(implies(sK0,implies(X0,sK0))) ),
inference(superposition,[status(thm)],[c_71,c_170]) ).
tcf(c_219,plain,
! [X0: $i] : a_truth(implies(implies(sK0,X0),iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_215,c_75]) ).
tcf(c_241,plain,
! [X0: $i] :
( a_truth(iPr_def_10)
| ~ a_truth(implies(sK0,X0)) ),
inference(superposition,[status(thm)],[c_219,c_76]) ).
tcf(c_242,plain,
! [X0: $i] : ~ a_truth(implies(sK0,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_241,c_72]) ).
tcf(c_243,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_213,c_242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 23:12:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.65/1.28 % SZS status Started for theBenchmark.p
% 1.65/1.28 % SZS status Theorem for theBenchmark.p
% 1.65/1.28
% 1.65/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.65/1.28
% 1.65/1.28 % ------ iProver source info
% 1.65/1.28
% 1.65/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.65/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.65/1.28 % git: non_committed_changes: false
% 1.65/1.28
% 1.65/1.28 % ------ Parsing...
% 1.65/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.65/1.28
% 1.65/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.65/1.28
% 1.65/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.65/1.28
% 1.65/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.65/1.28 % ------ Proving...
% 1.65/1.28 % ------ Problem Properties
% 1.65/1.28
% 1.65/1.28 %
% 1.65/1.28 % clauses 6
% 1.65/1.28 % conjectures 5
% 1.65/1.28 % EPR 1
% 1.65/1.28 % Horn 6
% 1.65/1.28 % unary 5
% 1.65/1.28 % binary 0
% 1.65/1.28 % lits 8
% 1.65/1.28 % lits eq 1
% 1.65/1.28 % fd_pure 0
% 1.65/1.28 % fd_pseudo 0
% 1.65/1.28 % fd_cond 0
% 1.65/1.28 % fd_pseudo_cond 0
% 1.65/1.28 % AC symbols 0
% 1.65/1.28
% 1.65/1.28 % ------ Schedule dynamic 5 is on
% 1.65/1.28
% 1.65/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.65/1.28
% 1.65/1.28
% 1.65/1.28 % ------
% 1.65/1.28 % Current options:
% 1.65/1.28 % ------
% 1.65/1.28
% 1.65/1.28
% 1.65/1.28 %
% 1.65/1.28
% 1.65/1.28 % ------ Proving...
% 1.65/1.28 %
% 1.65/1.28
% 1.65/1.28 % SZS status Theorem for theBenchmark.p
% 1.65/1.28
% 1.65/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.65/1.28
% 1.65/1.28
%------------------------------------------------------------------------------