%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n001.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 08:37:51 AM UTC 2026
% Result : Theorem 13.22s 4.24s
% Output : Refutation 13.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 13 unt; 0 typ; 8 def)
% Number of atoms : 180 ( 18 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 606 ( 73 ~; 55 |; 29 &; 430 @)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 104 ( 0 ^; 96 !; 0 ?; 104 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ cartesian_product2 ) @ ( A @ ( sk2 @ ordered_pair ) @ in ) )
=> ( ( C @ ( A @ in ) )
& ( B @ ( sk2 @ in ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ cartesian_product2 ) @ ( sk3 @ ( sk2 @ ordered_pair ) @ in ) )
=> ( ( B @ ( sk3 @ in ) )
& ( A @ ( sk2 @ in ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( A @ ( sk4 @ cartesian_product2 ) @ ( sk3 @ ( sk2 @ ordered_pair ) @ in ) )
=> ( ( A @ ( sk3 @ in ) )
& ( sk4 @ ( sk2 @ in ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( A @ in ) )
& ( B @ ( sk6 @ in ) ) )
=> ( C @ ( B @ cartesian_product2 ) @ ( A @ ( sk6 @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( sk7 @ in ) )
& ( A @ ( sk6 @ in ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ ( sk7 @ ( sk6 @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( ( A @ ( sk7 @ in ) )
& ( sk8 @ ( sk6 @ in ) ) )
=> ( A @ ( sk8 @ cartesian_product2 ) @ ( sk7 @ ( sk6 @ ordered_pair ) @ in ) ) ) ) ) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(42,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,plain,
( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[42]) ).
thf(44,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ cartesian_product2 ) @ ( F @ ( E @ ordered_pair ) @ in ) )
| ~ ( H @ ( F @ in ) )
| ~ ( G @ ( E @ in ) ) )
& ( ( D @ ( B @ in ) )
| ~ ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( C @ ( A @ in ) )
| ~ ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
| ~ ( D @ ( B @ in ) )
| ~ ( C @ ( A @ in ) ) ),
inference(cnfConj,[status(thm)],[44]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
| ~ ( D @ ( B @ in ) )
| ~ ( C @ ( A @ in ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
~ ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ( sk9 @ ( sk8 @ cartesian_product2 ) @ ( sk7 @ ( sk6 @ ordered_pair ) @ in ) )
| sk1 )
& ( ( sk9 @ ( sk7 @ in ) )
| sk1 )
& ( ( sk8 @ ( sk6 @ in ) )
| sk1 )
& ( ~ sk1
| ~ ( sk5 @ ( sk3 @ in ) )
| ~ ( sk4 @ ( sk2 @ in ) ) )
& ( ~ sk1
| ( sk5 @ ( sk4 @ cartesian_product2 ) @ ( sk3 @ ( sk2 @ ordered_pair ) @ in ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
( ~ ( sk9 @ ( sk8 @ cartesian_product2 ) @ ( sk7 @ ( sk6 @ ordered_pair ) @ in ) )
| sk1 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(21,plain,
( ~ sk1
| ( sk5 @ ( sk4 @ cartesian_product2 ) @ ( sk3 @ ( sk2 @ ordered_pair ) @ in ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ in ) )
| ~ ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) ),
inference(cnfConj,[status(thm)],[44]) ).
thf(326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ cartesian_product2 ) @ ( sk3 @ ( sk2 @ ordered_pair ) @ in ) )
!= ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
| ( D @ ( B @ in ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[21,46]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ cartesian_product2 ) @ ( sk3 @ ( sk2 @ ordered_pair ) @ in ) )
!= ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
| ( D @ ( B @ in ) )
| ~ sk1 ),
inference(simp,[status(thm)],[326]) ).
thf(328,plain,
( ( sk5 @ ( sk3 @ in ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 ))]]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ in ) )
| ~ ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) ),
inference(cnfConj,[status(thm)],[44]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ cartesian_product2 ) @ ( sk3 @ ( sk2 @ ordered_pair ) @ in ) )
!= ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
| ( C @ ( A @ in ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[21,45]) ).
thf(249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( sk4 @ cartesian_product2 ) @ ( sk3 @ ( sk2 @ ordered_pair ) @ in ) )
!= ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
| ( C @ ( A @ in ) )
| ~ sk1 ),
inference(simp,[status(thm)],[248]) ).
thf(250,plain,
( ( sk4 @ ( sk2 @ in ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[249:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 ))]]) ).
thf(20,plain,
( ~ sk1
| ~ ( sk5 @ ( sk3 @ in ) )
| ~ ( sk4 @ ( sk2 @ in ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(673,plain,
( ( ( sk4 @ ( sk2 @ in ) )
!= ( sk4 @ ( sk2 @ in ) ) )
| ~ sk1
| ~ ( sk5 @ ( sk3 @ in ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[250,20]) ).
thf(674,plain,
( ( ( sk4 @ ( sk2 @ in ) )
!= ( sk4 @ ( sk2 @ in ) ) )
| ~ ( sk5 @ ( sk3 @ in ) )
| ~ sk1 ),
inference(simp,[status(thm)],[673]) ).
thf(675,plain,
( ~ ( sk5 @ ( sk3 @ in ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[674:[]]) ).
thf(1110,plain,
( ( ( sk5 @ ( sk3 @ in ) )
!= ( sk5 @ ( sk3 @ in ) ) )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[328,675]) ).
thf(1111,plain,
( ( ( sk5 @ ( sk3 @ in ) )
!= ( sk5 @ ( sk3 @ in ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1110]) ).
thf(1112,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[1111:[]]) ).
thf(1149,plain,
( ~ ( sk9 @ ( sk8 @ cartesian_product2 ) @ ( sk7 @ ( sk6 @ ordered_pair ) @ in ) )
| $false ),
inference(rewrite,[status(thm)],[17,1112]) ).
thf(1150,plain,
~ ( sk9 @ ( sk8 @ cartesian_product2 ) @ ( sk7 @ ( sk6 @ ordered_pair ) @ in ) ),
inference(simp,[status(thm)],[1149]) ).
thf(1347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
!= ( sk9 @ ( sk8 @ cartesian_product2 ) @ ( sk7 @ ( sk6 @ ordered_pair ) @ in ) ) )
| ~ $true
| ~ ( D @ ( B @ in ) )
| ~ ( C @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[48,1150]) ).
thf(1348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
!= ( sk9 @ ( sk8 @ cartesian_product2 ) @ ( sk7 @ ( sk6 @ ordered_pair ) @ in ) ) )
| ~ ( D @ ( B @ in ) )
| ~ ( C @ ( A @ in ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1349,plain,
( ~ ( sk9 @ ( sk7 @ in ) )
| ~ ( sk8 @ ( sk6 @ in ) ) ),
inference(pattern_uni,[status(thm)],[1348:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 )),bind(C,$thf( sk8 )),bind(D,$thf( sk9 ))]]) ).
thf(18,plain,
( ( sk9 @ ( sk7 @ in ) )
| sk1 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(1151,plain,
( ( sk9 @ ( sk7 @ in ) )
| $false ),
inference(rewrite,[status(thm)],[18,1112]) ).
thf(1152,plain,
sk9 @ ( sk7 @ in ),
inference(simp,[status(thm)],[1151]) ).
thf(19,plain,
( ( sk8 @ ( sk6 @ in ) )
| sk1 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(1153,plain,
( ( sk8 @ ( sk6 @ in ) )
| $false ),
inference(rewrite,[status(thm)],[19,1112]) ).
thf(1154,plain,
sk8 @ ( sk6 @ in ),
inference(simp,[status(thm)],[1153]) ).
thf(1637,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1349,1152,1154]) ).
thf(1638,plain,
$false,
inference(simp,[status(thm)],[1637]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.14/0.39 % Computer : n001.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 08:48:42 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.71/0.75 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.93/0.85 % [INFO] Parsing done (95ms).
% 0.93/0.86 % [INFO] Running in sequential loop mode.
% 1.38/1.06 % [INFO] eprover registered as external prover.
% 1.38/1.07 % [INFO] Scanning for conjecture ...
% 1.60/1.15 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.60/1.17 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.60/1.18 % [INFO] Problem is first-order (TPTP FOF).
% 1.60/1.18 % [INFO] Type checking passed.
% 1.60/1.18 % [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 ...
% 13.22/4.23 % [INFO] Killing All external provers ...
% 13.22/4.24 % Time passed: 3705ms (effective reasoning time: 3373ms)
% 13.22/4.24 % 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)>
% 13.22/4.24 % Axioms used in derivation (1): l55_zfmisc_1
% 13.22/4.24 % No. of inferences in proof: 41
% 13.22/4.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3705 ms resp. 3373 ms w/o parsing
% 13.22/4.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.22/4.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------