%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HWC002-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 : Sun Sep 27 07:32:05 AM UTC 2026
% Result : Unsatisfiable 8.43s 4.48s
% Output : Refutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 38
% Syntax : Number of formulae : 77 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 40 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1002 ( 32 ~; 30 |; 0 &; 940 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 198 ( 0 ^; 198 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(circuit_decl,type,
circuit: $i > $i > $i > $o ).
thf(top_decl,type,
top: $i > $i ).
thf(connect_decl,type,
connect: $i > $i > $i ).
thf(table_decl,type,
table: $i > $i > $i > $i > $i ).
thf(n0_decl,type,
n0: $i ).
thf(n1_decl,type,
n1: $i ).
thf(nil_decl,type,
nil: $i ).
thf(bottom_decl,type,
bottom: $i > $i ).
thf(middle_decl,type,
middle: $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ connect ) @ bottom @ ( C @ ( A @ or ) @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_across_middle2) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ connect ) @ bottom @ ( C @ ( A @ or ) @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( nil @ connect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connect_definition1) ).
thf(61,plain,
! [A: $i] :
( ( A @ ( nil @ connect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
( ( n0 @ ( n0 @ or ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition1) ).
thf(53,plain,
( ( n0 @ ( n0 @ or ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ bottom @ ( B @ not @ middle @ ( A @ top @ circuit ) ) )
| ~ ( C @ bottom @ ( B @ middle @ ( A @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invert_middle) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ bottom @ ( B @ not @ middle @ ( A @ top @ circuit ) ) )
| ~ ( C @ bottom @ ( B @ middle @ ( A @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
( ( n1 @ ( n0 @ and ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition2) ).
thf(45,plain,
( ( n1 @ ( n0 @ and ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ not @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ not @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invert_adjacent1) ).
thf(59,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ not @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ not @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
( ( n1 @ ( n0 @ or ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition2) ).
thf(63,plain,
( ( n1 @ ( n0 @ or ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ or ) @ connect ) @ bottom @ ( nil @ ( B @ ( A @ ( C @ or ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',split_and_omit_middle2) ).
thf(67,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ or ) @ connect ) @ bottom @ ( nil @ ( B @ ( A @ ( C @ or ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
( ( n0 @ ( n0 @ ( n0 @ ( n0 @ table ) ) ) )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_table) ).
thf(43,plain,
( ( n0 @ ( n0 @ ( n0 @ ( n0 @ table ) ) ) )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
( ( n0 @ ( n1 @ or ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition3) ).
thf(55,plain,
( ( n0 @ ( n1 @ or ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ table ) ) ) @ not )
= ( D @ not @ ( C @ not @ ( B @ not @ ( A @ not @ table ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_table_definition) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ table ) ) ) @ not )
= ( D @ not @ ( C @ not @ ( B @ not @ ( A @ not @ table ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ and ) @ connect ) @ bottom @ ( nil @ ( B @ ( A @ ( C @ and ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',split_and_omit_middle1) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ and ) @ connect ) @ bottom @ ( nil @ ( B @ ( A @ ( C @ and ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ connect ) @ bottom @ ( C @ ( A @ and ) @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_across_middle1) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ connect ) @ bottom @ ( C @ ( A @ and ) @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ bottom @ ( C @ ( A @ or ) @ middle @ ( B @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_across_empty_middle2) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ bottom @ ( C @ ( A @ or ) @ middle @ ( B @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ or ) @ connect ) @ bottom @ ( D @ middle @ ( C @ ( B @ ( A @ or ) @ connect ) @ top @ circuit ) ) )
| ~ ( G @ ( F @ connect ) @ ( E @ connect ) @ bottom @ ( D @ middle @ ( C @ ( B @ connect ) @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_nearest_middle2) ).
thf(88,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ or ) @ connect ) @ bottom @ ( D @ middle @ ( C @ ( B @ ( A @ or ) @ connect ) @ top @ circuit ) ) )
| ~ ( G @ ( F @ connect ) @ ( E @ connect ) @ bottom @ ( D @ middle @ ( C @ ( B @ connect ) @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ not @ connect ) @ bottom @ ( nil @ ( B @ ( A @ not @ connect ) @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invert_adjacent2) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ not @ connect ) @ bottom @ ( nil @ ( B @ ( A @ not @ connect ) @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ ( E @ table ) ) ) @ ( D @ ( C @ ( B @ ( A @ table ) ) ) @ and ) )
= ( H @ ( D @ and ) @ ( G @ ( C @ and ) @ ( F @ ( B @ and ) @ ( E @ ( A @ and ) @ table ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_table_definition) ).
thf(102,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ ( E @ table ) ) ) @ ( D @ ( C @ ( B @ ( A @ table ) ) ) @ and ) )
= ( H @ ( D @ and ) @ ( G @ ( C @ and ) @ ( F @ ( B @ and ) @ ( E @ ( A @ and ) @ table ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
( ( n1 @ not )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition2) ).
thf(92,plain,
( ( n1 @ not )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( nil @ or ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition5) ).
thf(65,plain,
! [A: $i] :
( ( A @ ( nil @ or ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(37,axiom,
( ( n0 @ ( n1 @ and ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition3) ).
thf(109,plain,
( ( n0 @ ( n1 @ and ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(20,axiom,
( ( n0 @ not )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition1) ).
thf(77,plain,
( ( n0 @ not )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,axiom,
( ( n0 @ ( n0 @ and ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition1) ).
thf(96,plain,
( ( n0 @ ( n0 @ and ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ or ) @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ ( C @ or ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',split_and_keep_middle2) ).
thf(73,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ or ) @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ ( C @ or ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ bottom @ ( C @ ( A @ and ) @ middle @ ( B @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_across_empty_middle1) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ bottom @ ( C @ ( A @ and ) @ middle @ ( B @ top @ circuit ) ) )
| ~ ( D @ ( C @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(17,axiom,
( ( nil @ not )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition3) ).
thf(71,plain,
( ( nil @ not )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ and ) @ connect ) @ bottom @ ( D @ middle @ ( C @ ( B @ ( A @ and ) @ connect ) @ top @ circuit ) ) )
| ~ ( G @ ( F @ connect ) @ ( E @ connect ) @ bottom @ ( D @ middle @ ( C @ ( B @ connect ) @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_nearest_middle1) ).
thf(49,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( E @ and ) @ connect ) @ bottom @ ( D @ middle @ ( C @ ( B @ ( A @ and ) @ connect ) @ top @ circuit ) ) )
| ~ ( G @ ( F @ connect ) @ ( E @ connect ) @ bottom @ ( D @ middle @ ( C @ ( B @ connect ) @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( nil @ and ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition5) ).
thf(81,plain,
! [A: $i] :
( ( A @ ( nil @ and ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,negated_conjecture,
~ ( nil @ ( n1 @ ( n1 @ ( n0 @ ( n0 @ table ) ) ) @ connect ) @ bottom @ ( nil @ ( nil @ ( n1 @ ( n0 @ ( n1 @ ( n0 @ table ) ) ) @ connect ) @ top @ circuit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_output_configuration) ).
thf(39,plain,
~ ( nil @ ( n1 @ ( n1 @ ( n0 @ ( n0 @ table ) ) ) @ connect ) @ bottom @ ( nil @ ( nil @ ( n1 @ ( n0 @ ( n1 @ ( n0 @ table ) ) ) @ connect ) @ top @ circuit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(31,axiom,
( ( n1 @ ( n1 @ ( n1 @ ( n1 @ table ) ) ) )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',full_table) ).
thf(98,plain,
( ( n1 @ ( n1 @ ( n1 @ ( n1 @ table ) ) ) )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [B: $i,A: $i] : ( A @ bottom @ ( B @ ( A @ top @ circuit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsume_symmetric) ).
thf(87,plain,
! [B: $i,A: $i] : ( A @ bottom @ ( B @ ( A @ top @ circuit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(34,axiom,
nil @ ( n1 @ ( n0 @ ( n1 @ ( n0 @ table ) ) ) @ connect ) @ bottom @ ( nil @ ( nil @ ( n1 @ ( n1 @ ( n0 @ ( n0 @ table ) ) ) @ connect ) @ top @ circuit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',input_configuration) ).
thf(104,plain,
nil @ ( n1 @ ( n0 @ ( n1 @ ( n0 @ table ) ) ) @ connect ) @ bottom @ ( nil @ ( nil @ ( n1 @ ( n1 @ ( n0 @ ( n0 @ table ) ) ) @ connect ) @ top @ circuit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ connect ) @ ( D @ ( C @ and ) @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ ( A @ ( C @ and ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_to_middle1) ).
thf(107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ connect ) @ ( D @ ( C @ and ) @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ ( A @ ( C @ and ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,axiom,
( ( n1 @ ( n1 @ and ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition4) ).
thf(79,plain,
( ( n1 @ ( n1 @ and ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ and ) @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ ( C @ and ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',split_and_keep_middle1) ).
thf(94,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ and ) @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ ( C @ and ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ connect ) @ ( A @ connect ) )
= ( B @ ( A @ connect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connect_definition2) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ connect ) @ ( A @ connect ) )
= ( B @ ( A @ connect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(32,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ connect ) @ ( D @ ( C @ or ) @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ ( A @ ( C @ or ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_to_middle2) ).
thf(100,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ connect ) @ ( D @ ( C @ or ) @ connect ) @ bottom @ ( nil @ ( B @ ( A @ connect ) @ ( A @ ( C @ or ) @ connect ) @ top @ circuit ) ) )
| ~ ( E @ ( D @ connect ) @ bottom @ ( C @ middle @ ( B @ ( A @ connect ) @ top @ circuit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(27,axiom,
( ( n1 @ ( n1 @ or ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition4) ).
thf(90,plain,
( ( n1 @ ( n1 @ or ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(38,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ ( E @ table ) ) ) @ ( D @ ( C @ ( B @ ( A @ table ) ) ) @ or ) )
= ( H @ ( D @ or ) @ ( G @ ( C @ or ) @ ( F @ ( B @ or ) @ ( E @ ( A @ or ) @ table ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_table_definition) ).
thf(111,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ ( E @ table ) ) ) @ ( D @ ( C @ ( B @ ( A @ table ) ) ) @ or ) )
= ( H @ ( D @ or ) @ ( G @ ( C @ or ) @ ( F @ ( B @ or ) @ ( E @ ( A @ or ) @ table ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(186,plain,
$false,
inference(e,[status(thm)],[57,61,53,41,45,59,63,67,43,55,75,51,47,69,88,85,102,92,65,109,77,96,73,105,71,49,81,39,98,87,104,107,79,94,83,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HWC002-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/0.71 % Computer : n015.cluster.edu
% 0.24/0.71 % Model : x86_64 x86_64
% 0.24/0.71 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.71 % Memory : 8046.5625MB
% 0.24/0.71 % OS : Linux 6.8.0-71-generic
% 0.24/0.71 % CPULimit : 300
% 0.24/0.72 % WCLimit : 300
% 0.24/0.72 % DateTime : Fri Sep 25 16:01:43 UTC 2026
% 0.24/0.72 % CPUTime :
% 0.24/0.72 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.42/1.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.04/1.83 % [INFO] Parsing done (323ms).
% 2.04/1.85 % [INFO] Running in sequential loop mode.
% 3.17/2.48 % [INFO] eprover registered as external prover.
% 3.39/2.50 % [INFO] Scanning for conjecture ...
% 3.61/2.67 % [INFO] Found a conjecture (or negated_conjecture) and 37 axioms. Running axiom selection ...
% 3.78/2.79 % [INFO] Axiom selection finished. Selected 37 axioms (removed 0 axioms).
% 4.03/2.88 % [INFO] Problem is propositional (TPTP CNF).
% 4.32/2.90 % [INFO] Type checking passed.
% 4.32/2.91 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.43/4.48 % External prover 'e' found a proof!
% 8.43/4.48 % [INFO] Killing All external provers ...
% 8.43/4.48 % Time passed: 3587ms (effective reasoning time: 2615ms)
% 8.43/4.48 % Axioms used in derivation (37): invert_adjacent2, and_definition1, connect_definition1, or_definition1, invert_adjacent1, join_nearest_middle2, join_across_middle1, not_definition1, connect_definition2, or_definition4, not_definition3, or_table_definition, join_to_middle2, input_configuration, split_and_keep_middle2, or_definition5, not_table_definition, join_to_middle1, and_definition2, join_across_empty_middle1, or_definition2, and_definition4, and_definition5, split_and_keep_middle1, and_definition3, and_table_definition, full_table, join_across_empty_middle2, empty_table, split_and_omit_middle1, or_definition3, split_and_omit_middle2, subsume_symmetric, invert_middle, join_nearest_middle1, join_across_middle2, not_definition2
% 8.43/4.48 % No. of inferences in proof: 77
% 8.43/4.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3587 ms resp. 2615 ms w/o parsing
% 9.62/4.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.62/4.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------