%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n017.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 08:31:26 AM UTC 2026
% Result : Theorem 3.43s 2.39s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 166 ( 12 ~; 0 |; 2 &; 148 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 39 !; 4 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(14,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(20,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(28,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(17,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ set_union2 ) @ set_union2 ) )
= ( C @ ( B @ set_union2 ) @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ set_union2 ) @ set_union2 ) )
= ( C @ ( B @ set_union2 ) @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( C @ cartesian_product2 ) )
= ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ set_union2 ) ) )
& ( ( C @ ( B @ ( A @ set_union2 ) @ cartesian_product2 ) )
= ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ set_union2 ) @ ( C @ cartesian_product2 ) )
= ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ set_union2 ) ) )
& ( ( C @ ( B @ ( A @ set_union2 ) @ cartesian_product2 ) )
= ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ set_union2 ) @ ( B @ ( A @ set_union2 ) @ cartesian_product2 ) )
= ( D @ ( B @ cartesian_product2 ) @ ( C @ ( B @ cartesian_product2 ) @ ( D @ ( A @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ set_union2 ) @ ( B @ ( A @ set_union2 ) @ cartesian_product2 ) )
= ( D @ ( B @ cartesian_product2 ) @ ( C @ ( B @ cartesian_product2 ) @ ( D @ ( A @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ set_union2 ) @ ( B @ ( A @ set_union2 ) @ cartesian_product2 ) )
= ( D @ ( B @ cartesian_product2 ) @ ( C @ ( B @ cartesian_product2 ) @ ( D @ ( A @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ set_union2 ) @ set_union2 ) @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(26,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(23,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,plain,
$false,
inference(e,[status(thm)],[14,20,28,17,39,31,11,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 08:23:18 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.83/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.09/1.15 % [INFO] Parsing done (186ms).
% 1.28/1.17 % [INFO] Running in sequential loop mode.
% 1.79/1.57 % [INFO] eprover registered as external prover.
% 1.79/1.58 % [INFO] Scanning for conjecture ...
% 1.98/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.13/1.71 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.13/1.73 % [INFO] Problem is first-order (TPTP FOF).
% 2.13/1.74 % [INFO] Type checking passed.
% 2.13/1.74 % [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 ...
% 3.43/2.39 % External prover 'e' found a proof!
% 3.43/2.39 % [INFO] Killing All external provers ...
% 3.43/2.39 % Time passed: 1857ms (effective reasoning time: 1216ms)
% 3.43/2.39 % 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)>
% 3.43/2.39 % Axioms used in derivation (8): fc2_xboole_0, commutativity_k2_xboole_0, fc3_xboole_0, t120_zfmisc_1, t4_xboole_1, rc1_xboole_0, idempotence_k2_xboole_0, rc2_xboole_0
% 3.43/2.39 % No. of inferences in proof: 20
% 3.43/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1857 ms resp. 1216 ms w/o parsing
% 3.75/2.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.75/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------