%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CSR144^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n014.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 10.17s 3.71s
% Output : Refutation 10.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 4 unt; 0 typ; 1 def)
% Number of atoms : 129 ( 17 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 253 ( 37 ~; 17 |; 0 &; 194 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 3 ^; 58 !; 10 ?; 72 :)
% ( 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(lMax_THFTYPE_i_decl,type,
lMax_THFTYPE_i: $i ).
thf(wife_THFTYPE_IiioI_decl,type,
wife_THFTYPE_IiioI: $i > $i > $o ).
thf(inverse_THFTYPE_IIiioIIiioIoI_decl,type,
inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i] :
@+[B: $i] : ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ A @ $true ) ) ) ) ).
thf(3,axiom,
inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax) ).
thf(10,plain,
inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',ax_001) ).
thf(11,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)],[4]) ).
thf(12,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)],[11]) ).
thf(13,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)],[12]) ).
thf(85,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)],[10,13]) ).
thf(86,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)],[85]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( wife_THFTYPE_IiioI @ B @ A )
= ( husband_THFTYPE_IiioI @ A @ B ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( wife_THFTYPE_IiioI )),bind(B,$thf( husband_THFTYPE_IiioI )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( wife_THFTYPE_IiioI @ B @ A )
= ( husband_THFTYPE_IiioI @ A @ B ) ),
inference(simp,[status(thm)],[87]) ).
thf(5,axiom,
! [A: $o,B: $i] :
( ( believes_THFTYPE_IiooI @ B @ A )
=> ? [C: $i] : ( holdsDuring_THFTYPE_IiooI @ C @ ( considers_THFTYPE_IiooI @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_002) ).
thf(14,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)],[5]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',ax_003) ).
thf(19,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)],[6]) ).
thf(20,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)],[19]) ).
thf(21,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)],[20]) ).
thf(507,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)],[21,417]) ).
thf(1,conjecture,
? [A: $i] :
~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
file('/export/starexec/sandbox2/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(7,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(8,plain,
~ ~ ! [A: $i] : ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(miniscope,[status(thm)],[7]) ).
thf(9,plain,
! [A: $i] : ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(15,plain,
! [A: $i] :
( ( believes_THFTYPE_IiooI @ A @ $true )
=> ? [B: $i] : ( holdsDuring_THFTYPE_IiooI @ B @ ( considers_THFTYPE_IiooI @ A @ $true ) ) ),
inference(instance,[status(thm)],[14]) ).
thf(17,plain,
! [A: $i] :
( ~ ( believes_THFTYPE_IiooI @ A @ $true )
| ( holdsDuring_THFTYPE_IiooI @ ( sk1 @ A ) @ ( considers_THFTYPE_IiooI @ A @ $true ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( believes_THFTYPE_IiooI @ A @ $true )
| ~ $true
| ( ( holdsDuring_THFTYPE_IiooI @ ( sk1 @ A ) @ ( considers_THFTYPE_IiooI @ A @ $true ) )
!= ( holdsDuring_THFTYPE_IiooI @ C @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ B @ lMax_THFTYPE_i ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,21]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( believes_THFTYPE_IiooI @ A @ $true )
| ( ( holdsDuring_THFTYPE_IiooI @ ( sk1 @ A ) @ ( considers_THFTYPE_IiooI @ A @ $true ) )
!= ( holdsDuring_THFTYPE_IiooI @ C @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ B @ lMax_THFTYPE_i ) ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( believes_THFTYPE_IiooI @ A @ $true )
| ( ( sk1 @ A )
!= C )
| ( ( considers_THFTYPE_IiooI @ A @ $true )
!= ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ B @ lMax_THFTYPE_i ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( believes_THFTYPE_IiooI @ A @ $true )
| ( ( considers_THFTYPE_IiooI @ A @ $true )
!= ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ B @ lMax_THFTYPE_i ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( believes_THFTYPE_IiooI @ A @ $true )
| ( A != lMax_THFTYPE_i )
| ~ ( wife_THFTYPE_IiioI @ B @ lMax_THFTYPE_i ) ),
inference(simp,[status(thm)],[28]) ).
thf(35,plain,
! [A: $i] :
( ~ ( wife_THFTYPE_IiioI @ A @ lMax_THFTYPE_i )
| ~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( lMax_THFTYPE_i ))]]) ).
thf(39,plain,
! [A: $i] :
( ~ ( wife_THFTYPE_IiioI @ A @ lMax_THFTYPE_i )
| ~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true ) ),
inference(simp,[status(thm)],[35]) ).
thf(505,plain,
! [A: $i] :
( ~ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ A )
| ~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true ) ),
inference(rewrite,[status(thm)],[39,417]) ).
thf(503,plain,
( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI
@ ^ [A: $i,B: $i] : ( husband_THFTYPE_IiioI @ B @ A ) ),
inference(rewrite,[status(thm)],[10,417]) ).
thf(710,plain,
$false,
inference(e,[status(thm)],[10,417,14,507,9,17,7,505,11,19,13,503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR144^1 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.11/0.21 % Computer : n014.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 17:56:45 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (201ms).
% 1.25/1.02 % [INFO] Running in sequential loop mode.
% 2.16/1.41 % [INFO] eprover registered as external prover.
% 2.16/1.42 % [INFO] Scanning for conjecture ...
% 2.36/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.36/1.54 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.36/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.36/1.57 % [INFO] Type checking passed.
% 2.36/1.58 % [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 ...
% 10.17/3.71 % External prover 'e' found a proof!
% 10.17/3.71 % [INFO] Killing All external provers ...
% 10.17/3.71 % Time passed: 3352ms (effective reasoning time: 2682ms)
% 10.17/3.71 % 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)>
% 10.17/3.71 % Axioms used in derivation (4): ax, ax_001, ax_002, ax_003
% 10.17/3.71 % No. of inferences in proof: 34
% 10.17/3.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3352 ms resp. 2682 ms w/o parsing
% 10.17/3.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.17/3.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------