%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n013.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 08:30:21 AM UTC 2026
% Result : Theorem 3.88s 3.38s
% Output : Refutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 5 ~; 0 |; 10 &; 120 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(8,axiom,
! [A: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(37,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subset) ).
thf(14,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(29,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ difference ) @ ( D @ ( A @ difference ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th48) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ difference ) @ ( D @ ( A @ difference ) @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ difference ) @ ( D @ ( A @ difference ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ difference ) @ ( C @ member ) )
<=> ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(22,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ difference ) @ ( C @ member ) ) )
& ( ( B @ ( A @ difference ) @ ( C @ member ) )
=> ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ difference ) @ ( C @ ( A @ difference ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_subset1) ).
thf(16,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ difference ) @ ( C @ ( A @ difference ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( A @ ( C @ difference ) @ ( B @ ( C @ difference ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_subset2) ).
thf(19,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( A @ ( C @ difference ) @ ( B @ ( C @ difference ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(49,plain,
$false,
inference(e,[status(thm)],[37,14,29,9,22,16,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.13 % 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
% 0.07/0.49 % Computer : n013.cluster.edu
% 0.07/0.49 % Model : x86_64 x86_64
% 0.07/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.49 % Memory : 8046.5625MB
% 0.07/0.49 % OS : Linux 6.8.0-71-generic
% 0.07/0.49 % CPULimit : 300
% 0.07/0.49 % WCLimit : 300
% 0.07/0.49 % DateTime : Sat Sep 26 07:57:07 UTC 2026
% 0.07/0.50 % CPUTime :
% 0.07/0.50 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
% 0.92/1.38 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.62 % [INFO] Parsing done (236ms).
% 1.34/1.64 % [INFO] Running in sequential loop mode.
% 2.04/2.17 % [INFO] eprover registered as external prover.
% 2.04/2.18 % [INFO] Scanning for conjecture ...
% 2.25/2.32 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.25/2.37 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.37/2.40 % [INFO] Problem is first-order (TPTP FOF).
% 2.37/2.40 % [INFO] Type checking passed.
% 2.37/2.41 % [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 ...
% 3.88/3.37 % External prover 'e' found a proof!
% 3.88/3.37 % [INFO] Killing All external provers ...
% 3.88/3.37 % Time passed: 2657ms (effective reasoning time: 1732ms)
% 3.88/3.37 % 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)>
% 3.88/3.38 % Axioms used in derivation (6): reflexivity_of_subset, transitivity_of_subset, difference_subset2, subset_defn, difference_subset1, difference_defn
% 3.88/3.38 % No. of inferences in proof: 16
% 3.88/3.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2657 ms resp. 1732 ms w/o parsing
% 4.04/3.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.04/3.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------