%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET907+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 : 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 : Sun Sep 27 08:31:18 AM UTC 2026
% Result : Theorem 2.86s 6.66s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 11 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 143 ( 14 ~; 0 |; 7 &; 108 @)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 49 ( 0 ^; 45 !; 4 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ in ) )
& ( B @ ( A @ in ) ) )
=> ( ( B @ ( C @ ( A @ unordered_pair ) @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ in ) )
& ( B @ ( A @ in ) ) )
=> ( ( B @ ( C @ ( A @ unordered_pair ) @ set_union2 ) )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ in ) )
& ( B @ ( A @ in ) ) )
=> ( ( B @ ( C @ ( A @ unordered_pair ) @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(28,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(39,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(31,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ unordered_pair ) @ subset ) )
<=> ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(47,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( C @ ( B @ ( A @ unordered_pair ) @ subset ) ) )
& ( ( C @ ( B @ ( A @ unordered_pair ) @ subset ) )
=> ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(42,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(37,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,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(25,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(57,plain,
$false,
inference(e,[status(thm)],[14,20,28,34,39,31,47,42,37,25,22,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET907+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
% 0.14/5.40 % Computer : n014.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.40 % DateTime : Sat Sep 26 08:24:37 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 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
% 0.17/5.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/5.79 % [INFO] Parsing done (95ms).
% 0.17/5.80 % [INFO] Running in sequential loop mode.
% 0.17/5.98 % [INFO] eprover registered as external prover.
% 0.17/5.99 % [INFO] Scanning for conjecture ...
% 1.46/6.03 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.46/6.05 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.46/6.06 % [INFO] Problem is first-order (TPTP FOF).
% 1.46/6.07 % [INFO] Type checking passed.
% 1.46/6.07 % [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 ...
% 2.86/6.65 % External prover 'e' found a proof!
% 2.86/6.65 % [INFO] Killing All external provers ...
% 2.86/6.66 % Time passed: 1162ms (effective reasoning time: 855ms)
% 2.86/6.66 % 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)>
% 2.86/6.66 % Axioms used in derivation (11): fc2_xboole_0, commutativity_k2_xboole_0, fc3_xboole_0, commutativity_k2_tarski, t38_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, t12_xboole_1, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 2.86/6.66 % No. of inferences in proof: 26
% 2.86/6.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1162 ms resp. 855 ms w/o parsing
% 3.18/6.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.18/6.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------