%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PUZ016-2.005 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 02:32:42 PM UTC 2026
% Result : Unsatisfiable 0.42s 6.29s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 52
% Syntax : Number of formulae : 105 ( 5 unt; 0 def)
% Number of atoms : 231 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 282 ( 156 ~; 126 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 38 ( 37 usr; 38 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,negated_conjecture,
~ vertical_1_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uncovered2_1_2) ).
fof(f5,negated_conjecture,
~ horizontal_1_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uncovered3_1_2) ).
fof(f7,negated_conjecture,
( vertical_1_1
| horizontal_1_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_1_1) ).
fof(f9,negated_conjecture,
( horizontal_1_4
| vertical_1_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_1_5) ).
fof(f11,negated_conjecture,
( vertical_1_2
| horizontal_2_1
| vertical_2_2
| horizontal_2_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_2_2) ).
fof(f13,negated_conjecture,
( vertical_1_4
| horizontal_2_3
| vertical_2_4
| horizontal_2_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_2_4) ).
fof(f15,negated_conjecture,
( vertical_2_1
| vertical_3_1
| horizontal_3_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_3_1) ).
fof(f17,negated_conjecture,
( vertical_2_3
| horizontal_3_2
| vertical_3_3
| horizontal_3_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_3_3) ).
fof(f19,negated_conjecture,
( vertical_2_5
| horizontal_3_4
| vertical_3_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_3_5) ).
fof(f21,negated_conjecture,
( vertical_3_2
| horizontal_4_1
| vertical_4_2
| horizontal_4_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_4_2) ).
fof(f23,negated_conjecture,
( vertical_3_4
| horizontal_4_3
| vertical_4_4
| horizontal_4_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_4_4) ).
fof(f25,negated_conjecture,
( vertical_4_1
| horizontal_5_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_5_1) ).
fof(f27,negated_conjecture,
( vertical_4_3
| horizontal_5_2
| horizontal_5_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_5_3) ).
fof(f29,negated_conjecture,
( vertical_4_5
| horizontal_5_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',covered_5_5) ).
fof(f31,negated_conjecture,
( ~ vertical_1_4
| ~ horizontal_1_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover1_1_4) ).
fof(f36,negated_conjecture,
( ~ vertical_1_1
| ~ horizontal_2_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover3_2_1) ).
fof(f37,negated_conjecture,
( ~ vertical_1_1
| ~ vertical_2_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover5_2_1) ).
fof(f44,negated_conjecture,
( ~ vertical_2_3
| ~ horizontal_2_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover1_2_3) ).
fof(f45,negated_conjecture,
( ~ horizontal_2_2
| ~ horizontal_2_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover2_2_3) ).
fof(f47,negated_conjecture,
( ~ horizontal_2_2
| ~ vertical_2_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover4_2_3) ).
fof(f56,negated_conjecture,
( ~ horizontal_2_4
| ~ vertical_2_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover4_2_5) ).
fof(f57,negated_conjecture,
( ~ vertical_1_5
| ~ vertical_2_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover5_2_5) ).
fof(f62,negated_conjecture,
( ~ vertical_3_2
| ~ horizontal_3_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover1_3_2) ).
fof(f63,negated_conjecture,
( ~ horizontal_3_1
| ~ horizontal_3_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover2_3_2) ).
fof(f64,negated_conjecture,
( ~ vertical_2_2
| ~ horizontal_3_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover3_3_2) ).
fof(f65,negated_conjecture,
( ~ horizontal_3_1
| ~ vertical_3_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover4_3_2) ).
fof(f66,negated_conjecture,
( ~ vertical_2_2
| ~ vertical_3_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover5_3_2) ).
fof(f67,negated_conjecture,
( ~ vertical_2_2
| ~ horizontal_3_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover6_3_2) ).
fof(f74,negated_conjecture,
( ~ vertical_3_4
| ~ horizontal_3_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover1_3_4) ).
fof(f75,negated_conjecture,
( ~ horizontal_3_3
| ~ horizontal_3_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover2_3_4) ).
fof(f77,negated_conjecture,
( ~ horizontal_3_3
| ~ vertical_3_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover4_3_4) ).
fof(f78,negated_conjecture,
( ~ vertical_2_4
| ~ vertical_3_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover5_3_4) ).
fof(f79,negated_conjecture,
( ~ vertical_2_4
| ~ horizontal_3_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover6_3_4) ).
fof(f83,negated_conjecture,
( ~ vertical_4_1
| ~ horizontal_4_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover1_4_1) ).
fof(f84,negated_conjecture,
( ~ vertical_3_1
| ~ horizontal_4_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover3_4_1) ).
fof(f85,negated_conjecture,
( ~ vertical_3_1
| ~ vertical_4_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover5_4_1) ).
fof(f92,negated_conjecture,
( ~ vertical_4_3
| ~ horizontal_4_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover1_4_3) ).
fof(f93,negated_conjecture,
( ~ horizontal_4_2
| ~ horizontal_4_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover2_4_3) ).
fof(f94,negated_conjecture,
( ~ vertical_3_3
| ~ horizontal_4_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover3_4_3) ).
fof(f95,negated_conjecture,
( ~ horizontal_4_2
| ~ vertical_4_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover4_4_3) ).
fof(f96,negated_conjecture,
( ~ vertical_3_3
| ~ vertical_4_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover5_4_3) ).
fof(f97,negated_conjecture,
( ~ vertical_3_3
| ~ horizontal_4_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover6_4_3) ).
fof(f104,negated_conjecture,
( ~ horizontal_4_4
| ~ vertical_4_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover4_4_5) ).
fof(f105,negated_conjecture,
( ~ vertical_3_5
| ~ vertical_4_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover5_4_5) ).
fof(f106,negated_conjecture,
( ~ vertical_3_5
| ~ horizontal_4_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover6_4_5) ).
fof(f108,negated_conjecture,
( ~ horizontal_5_1
| ~ horizontal_5_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover2_5_2) ).
fof(f109,negated_conjecture,
( ~ vertical_4_2
| ~ horizontal_5_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover3_5_2) ).
fof(f110,negated_conjecture,
( ~ vertical_4_2
| ~ horizontal_5_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover6_5_2) ).
fof(f111,negated_conjecture,
( ~ horizontal_5_2
| ~ horizontal_5_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover2_5_3) ).
fof(f114,negated_conjecture,
( ~ horizontal_5_3
| ~ horizontal_5_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover2_5_4) ).
fof(f115,negated_conjecture,
( ~ vertical_4_4
| ~ horizontal_5_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover3_5_4) ).
fof(f116,negated_conjecture,
( ~ vertical_4_4
| ~ horizontal_5_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_cover6_5_4) ).
tcf(c_167,negated_conjecture,
~ vertical_1_2,
inference(cnf_transformation,[],[f3]) ).
tcf(c_169,negated_conjecture,
~ horizontal_1_1,
inference(cnf_transformation,[],[f5]) ).
tcf(c_170,negated_conjecture,
( vertical_1_1
| horizontal_1_1 ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_172,negated_conjecture,
( vertical_1_5
| horizontal_1_4 ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_174,negated_conjecture,
( vertical_2_2
| horizontal_2_2
| horizontal_2_1
| vertical_1_2 ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_176,negated_conjecture,
( vertical_2_4
| horizontal_2_4
| horizontal_2_3
| vertical_1_4 ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_178,negated_conjecture,
( vertical_3_1
| horizontal_3_1
| vertical_2_1 ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_180,negated_conjecture,
( vertical_3_3
| horizontal_3_3
| horizontal_3_2
| vertical_2_3 ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_182,negated_conjecture,
( vertical_3_5
| horizontal_3_4
| vertical_2_5 ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_184,negated_conjecture,
( vertical_4_2
| horizontal_4_2
| horizontal_4_1
| vertical_3_2 ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_186,negated_conjecture,
( vertical_4_4
| horizontal_4_4
| horizontal_4_3
| vertical_3_4 ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_188,negated_conjecture,
( horizontal_5_1
| vertical_4_1 ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_190,negated_conjecture,
( horizontal_5_3
| horizontal_5_2
| vertical_4_3 ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_192,negated_conjecture,
( horizontal_5_4
| vertical_4_5 ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_194,negated_conjecture,
( ~ vertical_1_4
| ~ horizontal_1_4 ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_199,negated_conjecture,
( ~ horizontal_2_1
| ~ vertical_1_1 ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_200,negated_conjecture,
( ~ vertical_2_1
| ~ vertical_1_1 ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_207,negated_conjecture,
( ~ vertical_2_3
| ~ horizontal_2_3 ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_208,negated_conjecture,
( ~ horizontal_2_3
| ~ horizontal_2_2 ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_210,negated_conjecture,
( ~ vertical_2_3
| ~ horizontal_2_2 ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_219,negated_conjecture,
( ~ vertical_2_5
| ~ horizontal_2_4 ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_220,negated_conjecture,
( ~ vertical_2_5
| ~ vertical_1_5 ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_225,negated_conjecture,
( ~ vertical_3_2
| ~ horizontal_3_2 ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_226,negated_conjecture,
( ~ horizontal_3_2
| ~ horizontal_3_1 ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_227,negated_conjecture,
( ~ horizontal_3_2
| ~ vertical_2_2 ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_228,negated_conjecture,
( ~ vertical_3_2
| ~ horizontal_3_1 ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_229,negated_conjecture,
( ~ vertical_3_2
| ~ vertical_2_2 ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_230,negated_conjecture,
( ~ horizontal_3_1
| ~ vertical_2_2 ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_237,negated_conjecture,
( ~ vertical_3_4
| ~ horizontal_3_4 ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_238,negated_conjecture,
( ~ horizontal_3_4
| ~ horizontal_3_3 ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_240,negated_conjecture,
( ~ vertical_3_4
| ~ horizontal_3_3 ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_241,negated_conjecture,
( ~ vertical_3_4
| ~ vertical_2_4 ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_242,negated_conjecture,
( ~ horizontal_3_3
| ~ vertical_2_4 ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_246,negated_conjecture,
( ~ vertical_4_1
| ~ horizontal_4_1 ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_247,negated_conjecture,
( ~ horizontal_4_1
| ~ vertical_3_1 ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_248,negated_conjecture,
( ~ vertical_4_1
| ~ vertical_3_1 ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_255,negated_conjecture,
( ~ vertical_4_3
| ~ horizontal_4_3 ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_256,negated_conjecture,
( ~ horizontal_4_3
| ~ horizontal_4_2 ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_257,negated_conjecture,
( ~ horizontal_4_3
| ~ vertical_3_3 ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_258,negated_conjecture,
( ~ vertical_4_3
| ~ horizontal_4_2 ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_259,negated_conjecture,
( ~ vertical_4_3
| ~ vertical_3_3 ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_260,negated_conjecture,
( ~ horizontal_4_2
| ~ vertical_3_3 ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_267,negated_conjecture,
( ~ vertical_4_5
| ~ horizontal_4_4 ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_268,negated_conjecture,
( ~ vertical_4_5
| ~ vertical_3_5 ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_269,negated_conjecture,
( ~ horizontal_4_4
| ~ vertical_3_5 ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_271,negated_conjecture,
( ~ horizontal_5_2
| ~ horizontal_5_1 ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_272,negated_conjecture,
( ~ horizontal_5_2
| ~ vertical_4_2 ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_273,negated_conjecture,
( ~ horizontal_5_1
| ~ vertical_4_2 ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_274,negated_conjecture,
( ~ horizontal_5_3
| ~ horizontal_5_2 ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_277,negated_conjecture,
( ~ horizontal_5_4
| ~ horizontal_5_3 ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_278,negated_conjecture,
( ~ horizontal_5_4
| ~ vertical_4_4 ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_279,negated_conjecture,
( ~ horizontal_5_3
| ~ vertical_4_4 ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_281,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_174,c_176,c_180,c_184,c_186,c_194,c_199,c_200,c_207,c_208,c_210,c_219,c_220,c_225,c_226,c_227,c_228,c_229,c_230,c_237,c_238,c_240,c_241,c_242,c_246,c_247,c_248,c_255,c_256,c_257,c_258,c_259,c_260,c_267,c_268,c_269,c_271,c_272,c_273,c_274,c_277,c_278,c_279,c_178,c_182,c_190,c_167,c_169,c_170,c_172,c_188,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ016-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n020.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 06:39:24 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 0.42/6.29 % SZS status Started for theBenchmark.p
% 0.42/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.42/6.29
% 0.42/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.42/6.29
% 0.42/6.29 % ------ iProver source info
% 0.42/6.29
% 0.42/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.42/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.42/6.29 % git: non_committed_changes: false
% 0.42/6.29
% 0.42/6.29 % ------ Parsing...% successful
% 0.42/6.29
% 0.42/6.29
% 0.42/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.42/6.29 %
% 0.42/6.29
% 0.42/6.29 % ------ Preprocessing...%
% 0.42/6.29
% 0.42/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.42/6.29
% 0.42/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.42/6.29
% 0.42/6.29
%------------------------------------------------------------------------------