%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU167+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n007.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 08:37:52 AM UTC 2026
% Result : Theorem 55.93s 14.95s
% Output : Refutation 55.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 108 ( 12 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 409 ( 31 ~; 23 |; 15 &; 328 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 88 ( 0 ^; 84 !; 0 ?; 88 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( A @ ( sk1 @ subset ) ) )
=> ( C @ ( A @ cartesian_product2 ) @ ( B @ ( sk1 @ cartesian_product2 ) @ subset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ subset ) )
& ( sk2 @ ( sk1 @ subset ) ) )
=> ( B @ ( sk2 @ cartesian_product2 ) @ ( A @ ( sk1 @ cartesian_product2 ) @ subset ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( A @ ( sk3 @ subset ) )
& ( sk2 @ ( sk1 @ subset ) ) )
=> ( A @ ( sk2 @ cartesian_product2 ) @ ( sk3 @ ( sk1 @ cartesian_product2 ) @ subset ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ~ ( sk4 @ ( sk2 @ cartesian_product2 ) @ ( sk3 @ ( sk1 @ cartesian_product2 ) @ subset ) )
& ( sk4 @ ( sk3 @ subset ) )
& ( sk2 @ ( sk1 @ subset ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
sk2 @ ( sk1 @ subset ),
inference(cnfConj,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
& ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(15,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
& ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ! [C: $i] : ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
& ! [C: $i] : ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ) ),
inference(miniscope,[status(thm)],[15]) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ cartesian_product2 ) @ ( A @ ( D @ cartesian_product2 ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) )
& ( ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[17]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9,18]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
! [A: $i] : ( A @ ( sk2 @ cartesian_product2 ) @ ( A @ ( sk1 @ cartesian_product2 ) @ subset ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(51,plain,
! [A: $i] : ( A @ ( sk2 @ cartesian_product2 ) @ ( A @ ( sk1 @ cartesian_product2 ) @ subset ) ),
inference(simp,[status(thm)],[42]) ).
thf(10,plain,
sk4 @ ( sk3 @ subset ),
inference(cnfConj,[status(thm)],[8]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[17]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,20]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(55,plain,
! [A: $i] : ( sk4 @ ( A @ cartesian_product2 ) @ ( sk3 @ ( A @ cartesian_product2 ) @ subset ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(77,plain,
! [A: $i] : ( sk4 @ ( A @ cartesian_product2 ) @ ( sk3 @ ( A @ cartesian_product2 ) @ subset ) ),
inference(simp,[status(thm)],[55]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(21,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ cartesian_product2 ) @ ( sk3 @ ( A @ cartesian_product2 ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( D @ ( B @ subset ) )
| ~ ( D @ ( C @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[77,22]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ cartesian_product2 ) @ ( sk3 @ ( A @ cartesian_product2 ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( D @ ( B @ subset ) )
| ~ ( D @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ ( B @ cartesian_product2 ) @ subset ) )
| ~ ( A @ ( sk4 @ ( B @ cartesian_product2 ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( G )),bind(B,$thf( sk3 @ ( G @ cartesian_product2 ) )),bind(C,$thf( sk4 @ ( G @ cartesian_product2 ) )),bind(D,$thf( D ))]]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ ( B @ cartesian_product2 ) @ subset ) )
| ~ ( A @ ( sk4 @ ( B @ cartesian_product2 ) @ subset ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(9427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ cartesian_product2 ) @ ( A @ ( sk1 @ cartesian_product2 ) @ subset ) )
!= ( B @ ( sk4 @ ( C @ cartesian_product2 ) @ subset ) ) )
| ( B @ ( sk3 @ ( C @ cartesian_product2 ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[51,233]) ).
thf(9428,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ cartesian_product2 ) @ ( A @ ( sk1 @ cartesian_product2 ) @ subset ) )
!= ( B @ ( sk4 @ ( C @ cartesian_product2 ) @ subset ) ) )
| ( B @ ( sk3 @ ( C @ cartesian_product2 ) @ subset ) ) ),
inference(simp,[status(thm)],[9427]) ).
thf(9429,plain,
sk4 @ ( sk2 @ cartesian_product2 ) @ ( sk3 @ ( sk1 @ cartesian_product2 ) @ subset ),
inference(pattern_uni,[status(thm)],[9428:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ ( sk2 @ cartesian_product2 ) )),bind(C,$thf( sk1 ))]]) ).
thf(11,plain,
~ ( sk4 @ ( sk2 @ cartesian_product2 ) @ ( sk3 @ ( sk1 @ cartesian_product2 ) @ subset ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(9684,plain,
$false,
inference(rewrite,[status(thm)],[9429,11]) ).
thf(9685,plain,
$false,
inference(simp,[status(thm)],[9684]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU167+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.24/0.50 % Computer : n007.cluster.edu
% 0.24/0.50 % Model : x86_64 x86_64
% 0.24/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50 % Memory : 8046.5625MB
% 0.24/0.50 % OS : Linux 6.8.0-71-generic
% 0.24/0.51 % CPULimit : 300
% 0.24/0.51 % WCLimit : 300
% 0.24/0.51 % DateTime : Sat Sep 26 08:41:53 UTC 2026
% 0.24/0.51 % CPUTime :
% 0.24/0.51 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
% 1.57/1.40 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.94/1.69 % [INFO] Parsing done (282ms).
% 2.14/1.71 % [INFO] Running in sequential loop mode.
% 3.03/2.36 % [INFO] eprover registered as external prover.
% 3.03/2.37 % [INFO] Scanning for conjecture ...
% 3.40/2.51 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.40/2.57 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.40/2.59 % [INFO] Problem is first-order (TPTP FOF).
% 3.40/2.59 % [INFO] Type checking passed.
% 3.58/2.60 % [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 ...
% 55.93/14.95 % [INFO] Killing All external provers ...
% 55.93/14.95 % Time passed: 14221ms (effective reasoning time: 13233ms)
% 55.93/14.95 % 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)>
% 55.93/14.95 % Axioms used in derivation (2): t118_zfmisc_1, t1_xboole_1
% 55.93/14.95 % No. of inferences in proof: 34
% 55.93/14.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14221 ms resp. 13233 ms w/o parsing
% 55.93/14.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 55.93/14.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------