%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CSR144^2 : TPTP v9.3.1. Released v4.1.0.
% 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 : n011.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 : Wed Sep 30 07:46:59 AM UTC 2026
% Result : Theorem 150.49s 40.61s
% Output : Refutation 150.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 15 unt; 0 typ; 1 def)
% Number of atoms : 175 ( 29 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 335 ( 43 ~; 20 |; 0 &; 267 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 1 ^; 78 !; 10 ?; 90 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(num_type,type,
num: $tType ).
thf(believes_THFTYPE_IiooI_decl,type,
believes_THFTYPE_IiooI: $i > $o > $o ).
thf(considers_THFTYPE_IiooI_decl,type,
considers_THFTYPE_IiooI: $i > $o > $o ).
thf(holdsDuring_THFTYPE_IiooI_decl,type,
holdsDuring_THFTYPE_IiooI: $i > $o > $o ).
thf(husband_THFTYPE_IiioI_decl,type,
husband_THFTYPE_IiioI: $i > $i > $o ).
thf(instance_THFTYPE_IIiioIioI_decl,type,
instance_THFTYPE_IIiioIioI: ( $i > $i > $o ) > $i > $o ).
thf(inverse_THFTYPE_IIiioIIiioIoI_decl,type,
inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(lIrreflexiveRelation_THFTYPE_i_decl,type,
lIrreflexiveRelation_THFTYPE_i: $i ).
thf(lMax_THFTYPE_i_decl,type,
lMax_THFTYPE_i: $i ).
thf(wife_THFTYPE_IiioI_decl,type,
wife_THFTYPE_IiioI: $i > $i > $o ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] : ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ A @ $false ) ) ) ) ).
thf(1,conjecture,
? [A: $i] :
~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(155,plain,
~ ? [A: $i] :
~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(156,plain,
~ ~ ! [A: $i] : ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(miniscope,[status(thm)],[155]) ).
thf(157,plain,
! [A: $i] : ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(cnf,[status(esa)],[156]) ).
thf(148,axiom,
! [A: $o,B: $i] :
( ( believes_THFTYPE_IiooI @ B @ A )
=> ? [C: $i] : ( holdsDuring_THFTYPE_IiooI @ C @ ( considers_THFTYPE_IiooI @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_058) ).
thf(356,plain,
! [A: $o,B: $i] :
( ( believes_THFTYPE_IiooI @ B @ A )
=> ? [C: $i] : ( holdsDuring_THFTYPE_IiooI @ C @ ( considers_THFTYPE_IiooI @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(358,plain,
! [A: $i] :
( ( believes_THFTYPE_IiooI @ A @ $false )
=> ? [B: $i] : ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ A @ $false ) ) ),
inference(instance,[status(thm)],[356]) ).
thf(360,plain,
! [A: $i] :
( ~ ( believes_THFTYPE_IiooI @ A @ $false )
| ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ A ) @ ( considers_THFTYPE_IiooI @ A @ $false ) ) ),
inference(cnf,[status(esa)],[358]) ).
thf(27805,plain,
! [B: $i,A: $i] :
( ~ $true
| ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ B ) @ ( considers_THFTYPE_IiooI @ B @ $false ) )
| ( ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) )
!= ( believes_THFTYPE_IiooI @ B @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[157,360]) ).
thf(27806,plain,
! [B: $i,A: $i] :
( ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ B ) @ ( considers_THFTYPE_IiooI @ B @ $false ) )
| ( ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) )
!= ( believes_THFTYPE_IiooI @ B @ $false ) ) ),
inference(simp,[status(thm)],[27805]) ).
thf(28013,plain,
! [B: $i,A: $i] :
( ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ B ) @ ( considers_THFTYPE_IiooI @ B @ $false ) )
| ( lMax_THFTYPE_i != B )
| ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(simp,[status(thm)],[27806]) ).
thf(28115,plain,
! [A: $i] :
( ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ lMax_THFTYPE_i ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) )
| ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(simp,[status(thm)],[28013]) ).
thf(64,axiom,
! [A: $i > $i > $o] :
( ( instance_THFTYPE_IIiioIioI @ A @ lIrreflexiveRelation_THFTYPE_i )
= ( ! [B: $i] :
~ ( A @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_029) ).
thf(259,plain,
! [A: $i > $i > $o] :
( ( instance_THFTYPE_IIiioIioI @ A @ lIrreflexiveRelation_THFTYPE_i )
= ( ! [B: $i] :
~ ( A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(260,plain,
! [A: $i > $i > $o] :
( ( instance_THFTYPE_IIiioIioI @ A @ lIrreflexiveRelation_THFTYPE_i )
= ( ! [B: $i] :
~ ( A @ B @ B ) ) ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [A: $i > $i > $o] :
( ( instance_THFTYPE_IIiioIioI @ A @ lIrreflexiveRelation_THFTYPE_i )
= ( ! [B: $i] :
~ ( A @ B @ B ) ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(154,axiom,
instance_THFTYPE_IIiioIioI @ husband_THFTYPE_IiioI @ lIrreflexiveRelation_THFTYPE_i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_267) ).
thf(370,plain,
instance_THFTYPE_IIiioIioI @ husband_THFTYPE_IiioI @ lIrreflexiveRelation_THFTYPE_i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(5394,plain,
! [A: $i > $i > $o] :
( ! [B: $i] :
~ ( A @ B @ B )
| ( ( instance_THFTYPE_IIiioIioI @ A @ lIrreflexiveRelation_THFTYPE_i )
!= ( instance_THFTYPE_IIiioIioI @ husband_THFTYPE_IiioI @ lIrreflexiveRelation_THFTYPE_i ) ) ),
inference(paramod_ordered,[status(thm)],[261,370]) ).
thf(5395,plain,
! [A: $i] :
~ ( husband_THFTYPE_IiioI @ A @ A ),
inference(pattern_uni,[status(thm)],[5394:[bind(A,$thf( husband_THFTYPE_IiioI ))]]) ).
thf(5490,plain,
! [A: $i] :
~ ( husband_THFTYPE_IiioI @ A @ A ),
inference(cnf,[status(esa)],[5395]) ).
thf(40575,plain,
! [B: $i,A: $i] :
( ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ lMax_THFTYPE_i ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) )
| ~ $true
| ( ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A )
!= ( husband_THFTYPE_IiioI @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[28115,5490]) ).
thf(40576,plain,
! [B: $i,A: $i] :
( ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ lMax_THFTYPE_i ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) )
| ( ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A )
!= ( husband_THFTYPE_IiioI @ B @ B ) ) ),
inference(simp,[status(thm)],[40575]) ).
thf(40577,plain,
holdsDuring_THFTYPE_IiooI @ ( sk8 @ lMax_THFTYPE_i ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ),
inference(pattern_uni,[status(thm)],[40576:[bind(A,$thf( lMax_THFTYPE_i )),bind(B,$thf( lMax_THFTYPE_i ))]]) ).
thf(141,axiom,
! [A: $i] :
~ ? [B: $i] : ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ A @ lMax_THFTYPE_i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_088) ).
thf(345,plain,
! [A: $i] :
~ ? [B: $i] : ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ A @ lMax_THFTYPE_i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(346,plain,
~ ? [A: $i,B: $i] : ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ A @ lMax_THFTYPE_i ) ) ),
inference(miniscope,[status(thm)],[345]) ).
thf(347,plain,
! [B: $i,A: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ A @ lMax_THFTYPE_i ) ) ),
inference(cnf,[status(esa)],[346]) ).
thf(153,axiom,
inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_096) ).
thf(369,plain,
inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(135,axiom,
! [A: $i > $i > $o,B: $i > $i > $o] :
( ( inverse_THFTYPE_IIiioIIiioIoI @ B @ A )
=> ! [C: $i,D: $i] :
( ( B @ C @ D )
= ( A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_005) ).
thf(337,plain,
! [A: $i > $i > $o,B: $i > $i > $o] :
( ( inverse_THFTYPE_IIiioIIiioIoI @ B @ A )
=> ! [C: $i,D: $i] :
( ( B @ C @ D )
= ( A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(338,plain,
! [D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( inverse_THFTYPE_IIiioIIiioIoI @ B @ A )
| ( ( B @ C @ D )
= ( A @ D @ C ) ) ),
inference(cnf,[status(esa)],[337]) ).
thf(339,plain,
! [D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( ( B @ C @ D )
= ( A @ D @ C ) )
| ~ ( inverse_THFTYPE_IIiioIIiioIoI @ B @ A ) ),
inference(lifteq,[status(thm)],[338]) ).
thf(19169,plain,
! [D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( ( B @ C @ D )
= ( A @ D @ C ) )
| ~ $true
| ( ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI )
!= ( inverse_THFTYPE_IIiioIIiioIoI @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[369,339]) ).
thf(19170,plain,
! [D: $i,C: $i,B: $i > $i > $o,A: $i > $i > $o] :
( ( ( B @ C @ D )
= ( A @ D @ C ) )
| ( ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI )
!= ( inverse_THFTYPE_IIiioIIiioIoI @ B @ A ) ) ),
inference(simp,[status(thm)],[19169]) ).
thf(19171,plain,
! [B: $i,A: $i] :
( ( wife_THFTYPE_IiioI @ B @ A )
= ( husband_THFTYPE_IiioI @ A @ B ) ),
inference(pattern_uni,[status(thm)],[19170:[bind(A,$thf( wife_THFTYPE_IiioI )),bind(B,$thf( husband_THFTYPE_IiioI )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(22741,plain,
! [B: $i,A: $i] :
( ( wife_THFTYPE_IiioI @ B @ A )
= ( husband_THFTYPE_IiioI @ A @ B ) ),
inference(simp,[status(thm)],[19171]) ).
thf(27373,plain,
! [B: $i,A: $i] :
~ ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ) ),
inference(rewrite,[status(thm)],[347,22741]) ).
thf(40695,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ lMax_THFTYPE_i ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) )
!= ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[40577,27373]) ).
thf(40696,plain,
! [B: $i,A: $i] :
( ( holdsDuring_THFTYPE_IiooI @ ( sk8 @ lMax_THFTYPE_i ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) )
!= ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ) ) ),
inference(simp,[status(thm)],[40695]) ).
thf(40830,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ lMax_THFTYPE_i )
!= B )
| ( ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) )
!= ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) ) ),
inference(simp,[status(thm)],[40696]) ).
thf(40953,plain,
! [A: $i] :
( ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) )
!= ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) ),
inference(simp,[status(thm)],[40830]) ).
thf(41127,plain,
! [A: $i] :
( ( lMax_THFTYPE_i != lMax_THFTYPE_i )
| ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(simp,[status(thm)],[40953]) ).
thf(41152,plain,
! [A: $i] : ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ),
inference(pattern_uni,[status(thm)],[41127:[]]) ).
thf(41262,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A )
!= ( husband_THFTYPE_IiioI @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[41152,5490]) ).
thf(41263,plain,
! [B: $i,A: $i] :
( ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A )
!= ( husband_THFTYPE_IiioI @ B @ B ) ),
inference(simp,[status(thm)],[41262]) ).
thf(41264,plain,
$false,
inference(pattern_uni,[status(thm)],[41263:[bind(A,$thf( lMax_THFTYPE_i )),bind(B,$thf( lMax_THFTYPE_i ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CSR144^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.10 % 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
% 0.23/0.30 % Computer : n011.cluster.edu
% 0.23/0.30 % Model : x86_64 x86_64
% 0.23/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.30 % Memory : 8046.5625MB
% 0.23/0.30 % OS : Linux 6.8.0-71-generic
% 0.23/0.30 % CPULimit : 300
% 0.23/0.30 % WCLimit : 300
% 0.23/0.30 % DateTime : Tue Sep 29 17:57:01 UTC 2026
% 0.23/0.30 % CPUTime :
% 0.23/0.30 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
% 1.07/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.68/1.30 % [INFO] Parsing done (417ms).
% 2.68/1.32 % [INFO] Running in sequential loop mode.
% 3.98/1.72 % [INFO] eprover registered as external prover.
% 3.98/1.73 % [INFO] Scanning for conjecture ...
% 4.57/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 323 axioms. Running axiom selection ...
% 4.89/2.07 % [INFO] Axiom selection finished. Selected 152 axioms (removed 171 axioms).
% 5.42/2.17 % [INFO] Problem is higher-order (TPTP THF).
% 5.42/2.18 % [INFO] Type checking passed.
% 5.42/2.18 % [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 ...
% 150.49/40.60 % [INFO] Killing All external provers ...
% 150.49/40.61 % Time passed: 40120ms (effective reasoning time: 39281ms)
% 150.49/40.61 % 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)>
% 150.49/40.61 % Axioms used in derivation (6): ax_096, ax_058, ax_088, ax_005, ax_267, ax_029
% 150.49/40.61 % No. of inferences in proof: 49
% 150.49/40.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 40120 ms resp. 39281 ms w/o parsing
% 150.49/40.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 150.49/40.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------