%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS262+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 : n002.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 07:44:57 AM UTC 2026
% Result : Theorem 11.90s 4.28s
% Output : Refutation 12.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 33
% Syntax : Number of formulae : 68 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 321 ( 0 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1063 ( 64 ~; 2 |; 130 &; 746 @)
% ( 28 <=>; 91 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 27 usr; 20 con; 0-3 aty)
% Number of variables : 297 ( 0 ^; 161 !; 136 ?; 297 :)
% Comments :
%------------------------------------------------------------------------------
thf(mighta_decl,type,
mighta: $i > $i > $o ).
thf(tau_decl,type,
tau: $i ).
thf(thm_decl,type,
thm: $i ).
thf(model_decl,type,
model: $i > $i > $o ).
thf(status_decl,type,
status: $i > $i > $i > $o ).
thf(wth_decl,type,
wth: $i ).
thf(wca_decl,type,
wca: $i ).
thf(sap_decl,type,
sap: $i ).
thf(sca_decl,type,
sca: $i ).
thf(tac_decl,type,
tac: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(csa_decl,type,
csa: $i ).
thf(xora_decl,type,
xora: $i > $i > $o ).
thf(wec_decl,type,
wec: $i ).
thf(nota_decl,type,
nota: $i > $i > $o ).
thf(eth_decl,type,
eth: $i ).
thf(uns_decl,type,
uns: $i ).
thf(isa_decl,type,
isa: $i > $i > $o ).
thf(noc_decl,type,
noc: $i ).
thf(nevera_decl,type,
nevera: $i > $i > $o ).
thf(unp_decl,type,
unp: $i ).
thf(tca_decl,type,
tca: $i ).
thf(cax_decl,type,
cax: $i ).
thf(eqv_decl,type,
eqv: $i ).
thf(esa_decl,type,
esa: $i ).
thf(sat_decl,type,
sat: $i ).
thf(wtc_decl,type,
wtc: $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( wca @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wca) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( ( wca @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wca @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
<~> ( B @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ xora ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xora) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ xora ) )
=> ! [C: $i,D: $i] :
~ ( ( ( B @ ( D @ ( C @ status ) ) )
=> ( A @ ( D @ ( C @ status ) ) ) )
& ( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( ( B @ ( D @ ( C @ status ) ) )
=> ( A @ ( D @ ( C @ status ) ) ) )
& ( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) ) )
=> ( B @ ( A @ xora ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
<=> ( tau @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tau) ).
thf(297,plain,
! [A: $i,B: $i] :
( ( ( tau @ ( B @ ( A @ status ) ) )
=> ! [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
=> ( tau @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(18,axiom,
? [A: $i,B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ model ) )
| ~ ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sat_non_taut_pair) ).
thf(169,plain,
? [A: $i,B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ model ) )
| ~ ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
<=> ( sat @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sat) ).
thf(256,plain,
! [A: $i,B: $i] :
( ( ( sat @ ( B @ ( A @ status ) ) )
=> ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
& ( ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
=> ( sat @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( wth @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wth) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( wth @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wth @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
thm @ ( tau @ mighta ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta_tau_thm) ).
thf(2,negated_conjecture,
~ ( thm @ ( tau @ mighta ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ( thm @ ( tau @ mighta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ? [C: $i,D: $i] :
( ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ mighta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta) ).
thf(282,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ mighta ) )
=> ? [C: $i,D: $i] :
( ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) ) )
& ( ? [C: $i,D: $i] :
( ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
=> ( B @ ( A @ mighta ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ isa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa) ).
thf(177,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ isa ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ( B @ ( D @ ( C @ status ) ) ) )
=> ( B @ ( A @ isa ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tautology) ).
thf(175,plain,
? [A: $i] :
! [B: $i] : ( A @ ( B @ model ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
? [A: $i] :
( ? [B: $i] :
~ ( A @ ( B @ model ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satisfiable) ).
thf(36,plain,
? [A: $i] :
( ? [B: $i] :
~ ( A @ ( B @ model ) )
& ? [B: $i] : ( A @ ( B @ model ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( tca @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tca) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( ( tca @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( tca @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<=> ~ ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ not @ ( A @ model ) )
=> ( B @ ( A @ model ) ) )
& ( ( B @ ( A @ model ) )
=> ~ ( B @ not @ ( A @ model ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
<=> ( noc @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noc) ).
thf(184,plain,
! [A: $i,B: $i] :
( ( ( noc @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) ) )
& ( ( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
=> ( noc @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ~ ( B @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ nevera ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nevera) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ nevera ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ~ ( B @ ( D @ ( C @ status ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ status ) ) )
=> ~ ( B @ ( D @ ( C @ status ) ) ) )
=> ( B @ ( A @ nevera ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ? [C: $i,D: $i] :
( ~ ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
<=> ( B @ ( A @ nota ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nota) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ nota ) )
=> ? [C: $i,D: $i] :
( ~ ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) ) )
& ( ? [C: $i,D: $i] :
( ~ ( B @ ( D @ ( C @ status ) ) )
& ( A @ ( D @ ( C @ status ) ) ) )
=> ( B @ ( A @ nota ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
<=> ( csa @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',csa) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( csa @ ( B @ ( A @ status ) ) )
=> ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) ) )
& ( ? [C: $i] :
( ( B @ not @ ( C @ model ) )
& ( A @ ( C @ model ) ) )
=> ( csa @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
? [A: $i] :
! [B: $i] :
~ ( A @ ( B @ model ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contradiction) ).
thf(97,plain,
? [A: $i] :
! [B: $i] :
~ ( A @ ( B @ model ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ model ) )
<~> ( B @ not @ ( A @ model ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',completeness) ).
thf(224,plain,
! [A: $i,B: $i] :
~ ( ( ( B @ not @ ( A @ model ) )
=> ( B @ ( A @ model ) ) )
& ( ( B @ ( A @ model ) )
=> ( B @ not @ ( A @ model ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( sca @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sca) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( ( sca @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ? [C: $i] : ( B @ ( C @ model ) )
& ~ ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( sca @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( A @ ( C @ model ) )
<=> ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( esa @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',esa) ).
thf(244,plain,
! [A: $i,B: $i] :
( ( ( esa @ ( B @ ( A @ status ) ) )
=> ( ( ? [C: $i] : ( B @ ( C @ model ) )
=> ? [C: $i] : ( A @ ( C @ model ) ) )
& ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) ) ) )
& ( ( ( ? [C: $i] : ( B @ ( C @ model ) )
=> ? [C: $i] : ( A @ ( C @ model ) ) )
& ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) ) )
=> ( esa @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( wtc @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wtc) ).
thf(264,plain,
! [A: $i,B: $i] :
( ( ( wtc @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wtc @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ not @ ( C @ model ) )
& ! [C: $i] : ( A @ ( C @ model ) ) )
<=> ( uns @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uns) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( ( uns @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] : ( B @ not @ ( C @ model ) )
& ! [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] : ( B @ not @ ( C @ model ) )
& ! [C: $i] : ( A @ ( C @ model ) ) )
=> ( uns @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
? [A: $i,B: $i] :
( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ~ ( A @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mixed_pair) ).
thf(274,plain,
? [A: $i,B: $i] :
( ? [C: $i] :
~ ( B @ ( C @ model ) )
& ? [C: $i] :
( ( B @ ( C @ model ) )
& ~ ( A @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( tac @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tac) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( ( tac @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] : ( B @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( tac @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ model ) )
<=> ( B @ ( C @ model ) ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( eth @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eth) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ( eth @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] :
( ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) )
& ( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] :
( ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) )
& ( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [C: $i] :
~ ( A @ ( C @ model ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( eth @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( sap @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sap) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( sap @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) ) )
& ( ( ? [C: $i] : ( A @ ( C @ model ) )
=> ? [C: $i] : ( B @ ( C @ model ) ) )
=> ( sap @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
? [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( C @ ( D @ model ) )
& ~ ( C @ ( A @ model ) )
& ( B @ ( A @ model ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_thm_spt) ).
thf(155,plain,
? [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( C @ ( D @ model ) )
& ~ ( C @ ( A @ model ) )
& ( B @ ( A @ model ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ model ) )
<=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( eqv @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqv) ).
thf(231,plain,
! [A: $i,B: $i] :
( ( ( eqv @ ( B @ ( A @ status ) ) )
=> ( ! [C: $i] :
( ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) )
& ( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ! [C: $i] :
( ( ( B @ ( C @ model ) )
=> ( A @ ( C @ model ) ) )
& ( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( eqv @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ~ ? [C: $i] : ( B @ ( C @ model ) ) )
<=> ( unp @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unp) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( ( unp @ ( B @ ( A @ status ) ) )
=> ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ~ ? [C: $i] : ( B @ ( C @ model ) ) ) )
& ( ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ~ ? [C: $i] : ( B @ ( C @ model ) ) )
=> ( unp @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] : ( A @ ( C @ model ) )
<=> ( cax @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cax) ).
thf(218,plain,
! [A: $i,B: $i] :
( ( ( cax @ ( B @ ( A @ status ) ) )
=> ~ ? [C: $i] : ( A @ ( C @ model ) ) )
& ( ~ ? [C: $i] : ( A @ ( C @ model ) )
=> ( cax @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
<=> ( thm @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(290,plain,
! [A: $i,B: $i] :
( ( ( thm @ ( B @ ( A @ status ) ) )
=> ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) ) )
& ( ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
=> ( thm @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
<=> ( wec @ ( B @ ( A @ status ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wec) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( wec @ ( B @ ( A @ status ) ) )
=> ( ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) ) )
& ( ( ? [C: $i] :
( ~ ( A @ ( C @ model ) )
& ( B @ ( C @ model ) ) )
& ! [C: $i] :
( ( A @ ( C @ model ) )
=> ( B @ ( C @ model ) ) )
& ? [C: $i] : ( A @ ( C @ model ) ) )
=> ( wec @ ( B @ ( A @ status ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1035,plain,
$false,
inference(e,[status(thm)],[56,106,297,169,256,41,35,282,177,175,36,210,100,184,196,132,89,97,224,73,244,264,161,274,81,140,66,155,231,203,218,290,119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS262+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % 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
% 0.11/0.37 % Computer : n002.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 : Fri Sep 25 19:53:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.89/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.24 % [INFO] Parsing done (232ms).
% 1.41/1.25 % [INFO] Running in sequential loop mode.
% 2.17/1.66 % [INFO] eprover registered as external prover.
% 2.17/1.66 % [INFO] Scanning for conjecture ...
% 2.41/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 2.60/1.82 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 2.86/1.90 % [INFO] Problem is first-order (TPTP FOF).
% 2.86/1.92 % [INFO] Type checking passed.
% 2.86/1.92 % [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 ...
% 11.90/4.28 % External prover 'e' found a proof!
% 11.90/4.28 % [INFO] Killing All external provers ...
% 11.90/4.28 % Time passed: 3776ms (effective reasoning time: 3024ms)
% 11.90/4.28 % 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)>
% 11.90/4.28 % Axioms used in derivation (32): wec, completeness, contradiction, tau, wtc, sat_non_taut_pair, satisfiable, wth, sat, sap, nevera, noc, tca, eth, thm, uns, nota, sca, csa, mighta, wca, eqv, isa, cax, tautology, tac, non_thm_spt, xora, not, unp, esa, mixed_pair
% 11.90/4.28 % No. of inferences in proof: 68
% 11.90/4.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3776 ms resp. 3024 ms w/o parsing
% 12.48/4.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.48/4.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------