%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL152-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 07:50:58 AM UTC 2026
% Result : Unsatisfiable 16.01s 4.93s
% Output : Refutation 16.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 95 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 206 ( 184 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 935 ( 155 ~; 111 |; 0 &; 669 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 110 ( 0 ^; 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(big_hat_decl,type,
big_hat: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(z_decl,type,
z: $i ).
thf(truth_decl,type,
truth: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(big_V_decl,type,
big_V: $i > $i > $i ).
thf(ordered_decl,type,
ordered: $i > $i > $o ).
thf(1,negated_conjecture,
( ( z @ ( y @ ( x @ big_hat ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( x @ implies ) @ implies ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
thf(10,plain,
( ( z @ ( y @ ( x @ big_hat ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( x @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
= truth )
| ~ ( B @ ( A @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition1) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
thf(13,plain,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
inference(lifteq,[status(thm)],[13]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
inference(lifteq,[status(thm)],[19]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
= truth ),
inference(lifteq,[status(thm)],[15]) ).
thf(116,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( E @ ( C @ implies ) @ ( E @ ( D @ implies ) @ implies ) ) )
| ( ( truth @ ( D @ ( C @ implies ) @ implies ) )
= truth ) ),
inference(paramod_ordered,[status(thm)],[20,16]) ).
thf(117,plain,
! [A: $i] :
( ( truth @ ( A @ not @ not @ ( A @ implies ) @ implies ) )
= truth ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( H @ not )),bind(B,$thf( H )),bind(C,$thf( H )),bind(D,$thf( H @ not @ not )),bind(E,$thf( H @ not ))]]) ).
thf(147,plain,
! [A: $i] :
( ( truth @ ( A @ not @ not @ ( A @ implies ) @ implies ) )
= truth ),
inference(simp,[status(thm)],[117]) ).
thf(11,plain,
( ( z @ ( y @ ( x @ big_hat ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( x @ implies ) @ implies ) ) ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( z @ ( y @ ( x @ big_hat ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( x @ implies ) @ implies ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(32,plain,
! [A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( z @ ( y @ ( x @ big_hat ) @ implies ) ) )
| ( A
!= ( z @ ( x @ implies ) @ ( y @ ( x @ implies ) @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,12]) ).
thf(34,plain,
( ( ( z @ ( x @ implies ) @ ( y @ ( x @ implies ) @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[32]) ).
thf(328,plain,
! [A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( x @ implies ) @ implies ) ) )
| ( A != z )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(paramod_ordered,[status(thm)],[14,34]) ).
thf(359,plain,
( ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( x @ implies ) )
!= truth )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[328]) ).
thf(834,plain,
! [A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( A != z )
| ( ( y @ ( x @ implies ) )
!= truth )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(paramod_ordered,[status(thm)],[14,359]) ).
thf(864,plain,
( ( z != z )
| ( truth != x )
| ( ( y @ ( x @ implies ) )
!= truth )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[834]) ).
thf(882,plain,
( ( truth != x )
| ( ( y @ ( x @ implies ) )
!= truth )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[864]) ).
thf(894,plain,
! [A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( truth != x )
| ( A != truth )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(paramod_ordered,[status(thm)],[14,882]) ).
thf(921,plain,
( ( truth != y )
| ( truth != x )
| ( truth != x )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[894]) ).
thf(925,plain,
( ( truth != y )
| ( truth != x )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[921]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
= truth ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( truth != x )
| ( truth != truth )
| ( ( y @ ( x @ big_hat ) )
!= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(paramod_ordered,[status(thm)],[27,882]) ).
thf(1177,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( truth != x )
| ( ( y @ ( x @ big_hat ) )
!= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(simp,[status(thm)],[1176]) ).
thf(1178,plain,
( ( truth != x )
| ( ( y @ ( x @ big_hat ) )
!= truth )
| ~ ( y @ ( x @ ordered ) ) ),
inference(pattern_uni,[status(thm)],[1177:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(330,plain,
! [A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( ( A @ ( y @ ( x @ implies ) @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(paramod_ordered,[status(thm)],[14,34]) ).
thf(362,plain,
! [A: $i] :
( ( A != z )
| ( truth != x )
| ( ( A @ ( y @ ( x @ implies ) @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[330]) ).
thf(367,plain,
( ( truth != x )
| ( ( z @ ( y @ ( x @ implies ) @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[362]) ).
thf(1044,plain,
! [A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( truth != x )
| ( ( z @ ( A @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(paramod_ordered,[status(thm)],[14,367]) ).
thf(1072,plain,
! [A: $i] :
( ( A != y )
| ( truth != x )
| ( truth != x )
| ( ( z @ ( A @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[1044]) ).
thf(1091,plain,
( ( truth != x )
| ( ( z @ ( y @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth ) ),
inference(simp,[status(thm)],[1072]) ).
thf(1156,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( truth != x )
| ( truth != z )
| ( ( y @ ( x @ big_hat ) )
!= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(paramod_ordered,[status(thm)],[27,1091]) ).
thf(1157,plain,
( ( truth != x )
| ( truth != z )
| ( ( y @ ( x @ big_hat ) )
!= truth )
| ~ ( z @ ( y @ ordered ) ) ),
inference(pattern_uni,[status(thm)],[1156:[bind(A,$thf( y )),bind(B,$thf( z ))]]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( B @ ( C @ implies ) ) )
| ( ( A @ ( C @ not @ ( B @ not @ implies ) @ implies ) )
= truth ) ),
inference(paramod_ordered,[status(thm)],[14,20]) ).
thf(59,plain,
! [A: $i] :
( ( A @ ( truth @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( truth ))]]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( truth @ not @ ( A @ not @ implies ) @ implies ) )
!= ( D @ ( B @ implies ) @ ( D @ ( C @ implies ) @ implies ) ) )
| ( ( truth @ ( C @ ( B @ implies ) @ implies ) )
= truth ) ),
inference(paramod_ordered,[status(thm)],[59,16]) ).
thf(176,plain,
! [A: $i] :
( ( truth @ ( truth @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ implies ) )
= truth ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( truth @ not @ ( G @ implies ) )),bind(B,$thf( G )),bind(C,$thf( truth @ not @ ( G @ implies ) @ not )),bind(D,$thf( truth @ not ))]]) ).
thf(198,plain,
! [A: $i] :
( ( truth @ ( truth @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ implies ) )
= truth ),
inference(simp,[status(thm)],[176]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( ( A @ ( truth @ not @ ( A @ not @ implies ) @ implies ) )
!= ( truth @ not @ ( B @ implies ) ) )
| ( ( truth @ ( truth @ not @ ( B @ implies ) @ implies ) )
= truth ) ),
inference(paramod_ordered,[status(thm)],[59,198]) ).
thf(395,plain,
( ( truth @ ( truth @ not @ ( truth @ not @ ( truth @ not @ not @ implies ) @ implies ) @ implies ) )
= truth ),
inference(pattern_uni,[status(thm)],[394:[bind(A,$thf( truth @ not )),bind(B,$thf( truth @ not @ ( truth @ not @ not @ implies ) ))]]) ).
thf(946,plain,
( ( truth @ ( truth @ implies ) )
= truth ),
inference(rewrite,[status(thm)],[395,59]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
!= truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition2) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
!= truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
!= truth ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
!= truth ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(1570,plain,
! [B: $i,A: $i] :
( ( ( truth @ ( truth @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( B @ ( A @ ordered ) )
| ( truth != truth ) ),
inference(paramod_ordered,[status(thm)],[946,30]) ).
thf(1571,plain,
! [B: $i,A: $i] :
( ( ( truth @ ( truth @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( B @ ( A @ ordered ) ) ),
inference(simp,[status(thm)],[1570]) ).
thf(1572,plain,
truth @ ( truth @ ordered ),
inference(pattern_uni,[status(thm)],[1571:[bind(A,$thf( truth )),bind(B,$thf( truth ))]]) ).
thf(31,plain,
( ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( truth != z )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) )
| ~ ( B @ ( A @ ordered ) ) ),
inference(paramod_ordered,[status(thm)],[27,31]) ).
thf(1223,plain,
( ( truth != z )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) )
| ~ ( z @ ( x @ ordered ) ) ),
inference(pattern_uni,[status(thm)],[1222:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ big_V ) )
= ( B @ ( B @ ( A @ implies ) @ implies ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_V_definition) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_V ) )
= ( B @ ( B @ ( A @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1217,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( x @ implies ) )
!= z )
| ( truth != truth )
| ( ( y @ ( x @ big_hat ) )
!= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(paramod_ordered,[status(thm)],[27,359]) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(simp,[status(thm)],[1217]) ).
thf(1219,plain,
( ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( x @ big_hat ) )
!= truth )
| ~ ( y @ ( x @ ordered ) ) ),
inference(pattern_uni,[status(thm)],[1218:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_V ) )
= ( B @ ( B @ ( A @ implies ) @ implies ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( B @ not @ not @ ( B @ implies ) ) )
| ( ( truth @ ( A @ implies ) )
= truth ) ),
inference(paramod_ordered,[status(thm)],[14,147]) ).
thf(214,plain,
( ( truth @ ( truth @ not @ not @ implies ) )
= truth ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( truth @ not @ not )),bind(B,$thf( truth ))]]) ).
thf(533,plain,
! [B: $i,A: $i] :
( ( ( truth @ ( truth @ not @ not @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( A @ ( A @ ( B @ implies ) @ implies ) )
= ( B @ ( truth @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[214,18]) ).
thf(534,plain,
( ( truth @ not @ not @ ( truth @ not @ not @ ( truth @ implies ) @ implies ) )
= ( truth @ ( truth @ implies ) ) ),
inference(pattern_uni,[status(thm)],[533:[bind(A,$thf( truth @ not @ not )),bind(B,$thf( truth ))]]) ).
thf(1258,plain,
( ( truth @ not @ not @ ( truth @ not @ not @ implies ) )
= truth ),
inference(rewrite,[status(thm)],[534,946,14]) ).
thf(1265,plain,
! [B: $i,A: $i] :
( ( ( truth @ not @ not @ ( truth @ not @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) @ ( truth @ implies ) )
= truth ) ),
inference(paramod_ordered,[status(thm)],[1258,20]) ).
thf(1266,plain,
( ( truth @ not @ ( truth @ not @ implies ) @ ( truth @ implies ) )
= truth ),
inference(pattern_uni,[status(thm)],[1265:[bind(A,$thf( truth @ not )),bind(B,$thf( truth @ not ))]]) ).
thf(1371,plain,
( ( truth @ not @ ( truth @ not @ implies ) )
= truth ),
inference(rewrite,[status(thm)],[1266,14]) ).
thf(46,plain,
! [A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( A != z )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,31]) ).
thf(48,plain,
( ( z != z )
| ( truth != x )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(49,plain,
( ( truth != x )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ big_hat ) )
= ( B @ not @ ( A @ not @ big_V ) @ not ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_hat_definition) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_hat ) )
= ( B @ not @ ( A @ not @ big_V ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_hat ) )
= ( B @ not @ ( A @ not @ big_V ) @ not ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ big_hat ) )
!= ( y @ ( x @ big_hat ) ) )
| ( truth != x )
| ( ( B @ not @ ( A @ not @ big_V ) @ not )
!= ( y @ ( x @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,49]) ).
thf(51,plain,
( ( truth != x )
| ( ( y @ not @ ( x @ not @ big_V ) @ not )
!= ( y @ ( x @ implies ) ) ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(82,plain,
! [A: $i] :
( ( ( A @ ( truth @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( truth != x )
| ( A
!= ( y @ not @ ( x @ not @ big_V ) @ not ) ) ),
inference(paramod_ordered,[status(thm)],[14,51]) ).
thf(87,plain,
( ( ( y @ not @ ( x @ not @ big_V ) @ not )
!= y )
| ( truth != x )
| ( truth != x ) ),
inference(simp,[status(thm)],[82]) ).
thf(89,plain,
( ( ( y @ not @ ( x @ not @ big_V ) @ not )
!= y )
| ( truth != x ) ),
inference(simp,[status(thm)],[87]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ big_V ) @ not )
!= ( y @ not @ ( x @ not @ big_V ) @ not ) )
| ( ( B @ ( A @ big_hat ) )
!= y )
| ( truth != x ) ),
inference(paramod_ordered,[status(thm)],[24,89]) ).
thf(91,plain,
( ( ( y @ ( x @ big_hat ) )
!= y )
| ( truth != x ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(304,plain,
( ( ( truth @ ( truth @ not @ not @ implies ) )
!= ( z @ ( x @ implies ) ) )
| ( truth != z )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[214,31]) ).
thf(307,plain,
( ( truth != z )
| ( ( truth @ not @ not )
!= x )
| ( truth != z )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(319,plain,
( ( ( truth @ not @ not )
!= x )
| ( truth != z )
| ( ( y @ ( x @ big_hat ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[307]) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ implies ) @ implies ) )
!= ( C @ ( truth @ not @ ( C @ not @ implies ) @ implies ) ) )
| ( ( A @ ( A @ ( B @ implies ) @ implies ) )
= truth ) ),
inference(paramod_ordered,[status(thm)],[18,59]) ).
thf(510,plain,
( ( truth @ not @ not @ ( truth @ not @ not @ ( truth @ not @ implies ) @ implies ) )
= truth ),
inference(pattern_uni,[status(thm)],[509:[bind(A,$thf( truth @ not @ not )),bind(B,$thf( truth @ not )),bind(C,$thf( truth @ not ))]]) ).
thf(2787,plain,
$false,
inference(e,[status(thm)],[10,25,14,147,925,1178,13,18,1157,15,882,20,1572,1223,1091,28,21,1219,34,17,22,59,27,12,1371,49,1258,367,91,198,16,359,31,319,946,23,510,214,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL152-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n006.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 21:55:40 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.15 % [INFO] Parsing done (190ms).
% 1.26/1.17 % [INFO] Running in sequential loop mode.
% 1.86/1.55 % [INFO] eprover registered as external prover.
% 1.86/1.56 % [INFO] Scanning for conjecture ...
% 2.05/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.05/1.68 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.05/1.69 % [INFO] Problem is propositional (TPTP CNF).
% 2.20/1.70 % [INFO] Type checking passed.
% 2.20/1.70 % [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 ...
% 16.01/4.92 % External prover 'e' found a proof!
% 16.01/4.92 % [INFO] Killing All external provers ...
% 16.01/4.92 % Time passed: 4395ms (effective reasoning time: 3748ms)
% 16.01/4.93 % Axioms used in derivation (8): partial_order_definition1, wajsberg_3, big_V_definition, wajsberg_1, big_hat_definition, wajsberg_2, partial_order_definition2, wajsberg_4
% 16.01/4.93 % No. of inferences in proof: 95
% 16.01/4.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4395 ms resp. 3748 ms w/o parsing
% 16.01/4.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.01/4.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------