%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 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 : n004.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 07:52:07 AM UTC 2026
% Result : Theorem 28.40s 11.02s
% Output : Refutation 28.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 52
% Syntax : Number of formulae : 106 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 234 ( 21 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 712 ( 2 ~; 0 |; 29 &; 582 @)
% ( 23 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 33 con; 0-2 aty)
% Number of variables : 149 ( 0 ^; 149 !; 0 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(axiom_4_decl,type,
axiom_4: $o ).
thf(axiom_m4_decl,type,
axiom_m4: $o ).
thf(op_or_decl,type,
op_or: $o ).
thf(axiom_m1_decl,type,
axiom_m1: $o ).
thf(axiom_m3_decl,type,
axiom_m3: $o ).
thf(op_strict_equiv_decl,type,
op_strict_equiv: $o ).
thf(axiom_m9_decl,type,
axiom_m9: $o ).
thf(op_implies_and_decl,type,
op_implies_and: $o ).
thf(op_possibly_decl,type,
op_possibly: $o ).
thf(axiom_m5_decl,type,
axiom_m5: $o ).
thf(axiom_s3_decl,type,
axiom_s3: $o ).
thf(axiom_m2_decl,type,
axiom_m2: $o ).
thf(axiom_m6_decl,type,
axiom_m6: $o ).
thf(op_strict_implies_decl,type,
op_strict_implies: $o ).
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(strict_implies_decl,type,
strict_implies: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(possibly_decl,type,
possibly: $i > $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(substitution_strict_equiv_decl,type,
substitution_strict_equiv: $o ).
thf(axiom_s2_decl,type,
axiom_s2: $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(modus_ponens_strict_implies_decl,type,
modus_ponens_strict_implies: $o ).
thf(necessarily_decl,type,
necessarily: $i > $i ).
thf(adjunction_decl,type,
adjunction: $o ).
thf(strict_equiv_decl,type,
strict_equiv: $i > $i > $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(op_equiv_decl,type,
op_equiv: $o ).
thf(axiom_m7_decl,type,
axiom_m7: $o ).
thf(op_and_decl,type,
op_and: $o ).
thf(equiv_decl,type,
equiv: $i > $i > $i ).
thf(axiom_M_decl,type,
axiom_M: $o ).
thf(axiom_K_decl,type,
axiom_K: $o ).
thf(axiom_5_decl,type,
axiom_5: $o ).
thf(necessitation_decl,type,
necessitation: $o ).
thf(axiom_s4_decl,type,
axiom_s4: $o ).
thf(axiom_B_decl,type,
axiom_B: $o ).
thf(axiom_s1_decl,type,
axiom_s1: $o ).
thf(op_necessarily_decl,type,
op_necessarily: $o ).
thf(axiom_m8_decl,type,
axiom_m8: $o ).
thf(axiom_m10_decl,type,
axiom_m10: $o ).
thf(op_implies_or_decl,type,
op_implies_or: $o ).
thf(17,axiom,
( axiom_s3
<=> ! [A: $i,B: $i] : ( A @ possibly @ not @ ( B @ possibly @ not @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s3) ).
thf(69,plain,
( ( ! [A: $i,B: $i] : ( A @ possibly @ not @ ( B @ possibly @ not @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem )
=> axiom_s3 )
& ( axiom_s3
=> ! [A: $i,B: $i] : ( A @ possibly @ not @ ( B @ possibly @ not @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
( op_necessarily
=> ! [A: $i] :
( ( A @ necessarily )
= ( A @ not @ possibly @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_necessarily) ).
thf(170,plain,
( op_necessarily
=> ! [A: $i] :
( ( A @ necessarily )
= ( A @ not @ possibly @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(51,axiom,
( modus_ponens_strict_implies
<=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ strict_implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ( ( B @ ( A @ strict_implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) )
=> modus_ponens_strict_implies )
& ( modus_ponens_strict_implies
=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ strict_implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(27,axiom,
( axiom_m6
<=> ! [A: $i] : ( A @ possibly @ ( A @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m6) ).
thf(98,plain,
( ( ! [A: $i] : ( A @ possibly @ ( A @ strict_implies ) @ is_a_theorem )
=> axiom_m6 )
& ( axiom_m6
=> ! [A: $i] : ( A @ possibly @ ( A @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(46,axiom,
( op_strict_implies
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_implies ) )
= ( B @ ( A @ implies ) @ necessarily ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
thf(167,plain,
( op_strict_implies
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_implies ) )
= ( B @ ( A @ implies ) @ necessarily ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(52,axiom,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
thf(194,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(11,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m5) ).
thf(63,plain,
axiom_m5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(67,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(39,axiom,
( axiom_K
<=> ! [A: $i,B: $i] : ( B @ necessarily @ ( A @ necessarily @ implies ) @ ( B @ ( A @ implies ) @ necessarily @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_K) ).
thf(136,plain,
( ( ! [A: $i,B: $i] : ( B @ necessarily @ ( A @ necessarily @ implies ) @ ( B @ ( A @ implies ) @ necessarily @ implies ) @ is_a_theorem )
=> axiom_K )
& ( axiom_K
=> ! [A: $i,B: $i] : ( B @ necessarily @ ( A @ necessarily @ implies ) @ ( B @ ( A @ implies ) @ necessarily @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(4,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
thf(56,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
( axiom_B
<=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_B) ).
thf(153,plain,
( ( ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ implies ) @ is_a_theorem )
=> axiom_B )
& ( axiom_B
=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(50,axiom,
( axiom_m10
<=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m10) ).
thf(184,plain,
( ( ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ strict_implies ) @ is_a_theorem )
=> axiom_m10 )
& ( axiom_m10
=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(32,axiom,
( axiom_m1
<=> ! [A: $i,B: $i] : ( A @ ( B @ and ) @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1) ).
thf(110,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ and ) @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem )
=> axiom_m1 )
& ( axiom_m1
=> ! [A: $i,B: $i] : ( A @ ( B @ and ) @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(36,axiom,
( axiom_m2
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m2) ).
thf(125,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem )
=> axiom_m2 )
& ( axiom_m2
=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(44,axiom,
( adjunction
<=> ! [A: $i,B: $i] :
( ( ( B @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ ( A @ and ) @ is_a_theorem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adjunction) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
( ( ( B @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ ( A @ and ) @ is_a_theorem ) )
=> adjunction )
& ( adjunction
=> ! [A: $i,B: $i] :
( ( ( B @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ ( A @ and ) @ is_a_theorem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(25,axiom,
( axiom_m9
<=> ! [A: $i] : ( A @ possibly @ ( A @ possibly @ possibly @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m9) ).
thf(93,plain,
( ( ! [A: $i] : ( A @ possibly @ ( A @ possibly @ possibly @ strict_implies ) @ is_a_theorem )
=> axiom_m9 )
& ( axiom_m9
=> ! [A: $i] : ( A @ possibly @ ( A @ possibly @ possibly @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(5,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
thf(57,plain,
axiom_m1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,axiom,
( axiom_s2
<=> ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ and ) @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s2) ).
thf(78,plain,
( ( ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ and ) @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem )
=> axiom_s2 )
& ( axiom_s2
=> ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ and ) @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(61,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,axiom,
( axiom_M
<=> ! [A: $i] : ( A @ ( A @ necessarily @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
thf(132,plain,
( ( ! [A: $i] : ( A @ ( A @ necessarily @ implies ) @ is_a_theorem )
=> axiom_M )
& ( axiom_M
=> ! [A: $i] : ( A @ ( A @ necessarily @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(8,axiom,
axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
thf(60,plain,
axiom_m9,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
thf(85,plain,
modus_ponens_strict_implies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
( op_strict_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) )
= ( A @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
thf(102,plain,
( op_strict_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) )
= ( A @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(53,axiom,
( axiom_4
<=> ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(197,plain,
( ( ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ implies ) @ is_a_theorem )
=> axiom_4 )
& ( axiom_4
=> ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(13,axiom,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
thf(65,plain,
axiom_m2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(26,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction) ).
thf(97,plain,
adjunction,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(31,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(109,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
thf(77,plain,
substitution_strict_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(48,axiom,
( substitution_strict_equiv
<=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) @ is_a_theorem )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv) ).
thf(173,plain,
( ( ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) @ is_a_theorem )
=> ( A = B ) )
=> substitution_strict_equiv )
& ( substitution_strict_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) @ is_a_theorem )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(37,axiom,
( op_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
thf(129,plain,
( op_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(18,axiom,
( axiom_m5
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ strict_implies ) @ ( C @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m5) ).
thf(73,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( A @ strict_implies ) @ ( C @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) @ strict_implies ) @ is_a_theorem )
=> axiom_m5 )
& ( axiom_m5
=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ strict_implies ) @ ( C @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
thf(105,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(12,axiom,
axiom_s3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_s3) ).
thf(64,plain,
axiom_s3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(49,axiom,
( axiom_m8
<=> ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m8) ).
thf(180,plain,
( ( ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem )
=> axiom_m8 )
& ( axiom_m8
=> ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(42,axiom,
( axiom_s4
<=> ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s4) ).
thf(149,plain,
( ( ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ strict_implies ) @ is_a_theorem )
=> axiom_s4 )
& ( axiom_s4
=> ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(7,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
thf(59,plain,
op_strict_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,axiom,
( axiom_m7
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m7) ).
thf(118,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem )
=> axiom_m7 )
& ( axiom_m7
=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
axiom_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_4) ).
thf(2,negated_conjecture,
~ axiom_4,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(54,plain,
~ axiom_4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(41,axiom,
( necessitation
<=> ! [A: $i] :
( ( A @ is_a_theorem )
=> ( A @ necessarily @ is_a_theorem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
thf(144,plain,
( ( ! [A: $i] :
( ( A @ is_a_theorem )
=> ( A @ necessarily @ is_a_theorem ) )
=> necessitation )
& ( necessitation
=> ! [A: $i] :
( ( A @ is_a_theorem )
=> ( A @ necessarily @ is_a_theorem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(23,axiom,
( axiom_m4
<=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4) ).
thf(86,plain,
( ( ! [A: $i] : ( A @ ( A @ and ) @ ( A @ strict_implies ) @ is_a_theorem )
=> axiom_m4 )
& ( axiom_m4
=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(40,axiom,
( axiom_5
<=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(140,plain,
( ( ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ implies ) @ is_a_theorem )
=> axiom_5 )
& ( axiom_5
=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14,axiom,
axiom_m6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
thf(66,plain,
axiom_m6,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
thf(108,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
thf(55,plain,
axiom_m4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
( axiom_m3
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( B @ and ) @ ( A @ and ) @ ( C @ ( B @ ( A @ and ) @ and ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m3) ).
thf(114,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( B @ and ) @ ( A @ and ) @ ( C @ ( B @ ( A @ and ) @ and ) @ strict_implies ) @ is_a_theorem )
=> axiom_m3 )
& ( axiom_m3
=> ! [A: $i,B: $i,C: $i] : ( C @ ( B @ and ) @ ( A @ and ) @ ( C @ ( B @ ( A @ and ) @ and ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(6,axiom,
axiom_m3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m3) ).
thf(58,plain,
axiom_m3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,axiom,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
thf(82,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(45,axiom,
( axiom_s1
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ necessarily @ ( C @ ( B @ implies ) @ necessarily @ ( B @ ( A @ implies ) @ necessarily @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s1) ).
thf(163,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ necessarily @ ( C @ ( B @ implies ) @ necessarily @ ( B @ ( A @ implies ) @ necessarily @ and ) @ implies ) @ is_a_theorem )
=> axiom_s1 )
& ( axiom_s1
=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ necessarily @ ( C @ ( B @ implies ) @ necessarily @ ( B @ ( A @ implies ) @ necessarily @ and ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(16,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
thf(68,plain,
op_strict_implies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
thf(62,plain,
op_possibly,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(24,axiom,
( op_possibly
=> ! [A: $i] :
( ( A @ possibly )
= ( A @ not @ necessarily @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_possibly) ).
thf(90,plain,
( op_possibly
=> ! [A: $i] :
( ( A @ possibly )
= ( A @ not @ necessarily @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(35,axiom,
( op_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
thf(122,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(505,plain,
$false,
inference(e,[status(thm)],[69,170,188,98,167,194,63,67,136,56,153,184,110,125,157,93,57,78,61,132,60,85,102,197,65,97,109,77,173,129,73,105,64,180,149,59,118,54,144,86,140,66,108,55,114,58,82,163,68,62,90,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 22:45:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 1.25/1.14 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.36 % [INFO] Parsing done (215ms).
% 1.63/1.37 % [INFO] Running in sequential loop mode.
% 2.78/1.71 % [INFO] eprover registered as external prover.
% 2.78/1.72 % [INFO] Scanning for conjecture ...
% 2.78/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 54 axioms. Running axiom selection ...
% 3.03/1.86 % [INFO] Axiom selection finished. Selected 51 axioms (removed 3 axioms).
% 3.30/1.94 % [INFO] Problem is first-order (TPTP FOF).
% 3.30/1.95 % [INFO] Type checking passed.
% 3.30/1.95 % [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 ...
% 28.40/11.01 % External prover 'e' found a proof!
% 28.40/11.01 % [INFO] Killing All external provers ...
% 28.40/11.01 % Time passed: 10477ms (effective reasoning time: 9634ms)
% 28.40/11.01 % Solved by 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)>
% 28.40/11.01 % Axioms used in derivation (51): axiom_m6, op_equiv, s1_0_axiom_m5, hilbert_op_implies_and, s1_0_axiom_m2, axiom_m2, axiom_B, op_necessarily, op_possibly, modus_ponens_strict_implies, s1_0_axiom_m4, s1_0_modus_ponens_strict_implies, s1_0_op_strict_equiv, axiom_m9, axiom_s3, s1_0_axiom_m1, axiom_m3, axiom_K, adjunction, s1_0_substitution_strict_equiv, s1_0_op_or, axiom_s2, s1_0_adjunction, s1_0_op_strict_implies, op_and, s1_0_op_equiv, axiom_m5, hilbert_op_or, axiom_M, s1_0_m6s3m9b_axiom_s3, axiom_m7, axiom_s1, s1_0_axiom_m3, axiom_m1, s1_0_m6s3m9b_axiom_m6, op_implies_and, op_strict_equiv, axiom_5, s1_0_m6s3m9b_axiom_m9, s1_0_op_possibly, axiom_m4, axiom_s4, axiom_m8, axiom_m10, op_or, op_implies_or, hilbert_op_equiv, necessitation, axiom_4, op_strict_implies, substitution_strict_equiv
% 28.40/11.02 % No. of inferences in proof: 106
% 28.40/11.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10477 ms resp. 9634 ms w/o parsing
% 28.96/11.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.96/11.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------