%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n008.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 08:28:53 AM UTC 2026
% Result : Unsatisfiable 2.96s 7.29s
% Output : Refutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 6 ~; 6 |; 0 &; 58 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i ).
thf(r2_decl,type,
r2: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(singleton_set_decl,type,
singleton_set: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(m1_decl,type,
m1: $i ).
thf(m2_decl,type,
m2: $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( B @ ( A @ unordered_pair ) @ ( A @ singleton_set @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( B @ ( A @ unordered_pair ) @ ( A @ singleton_set @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
r1 != r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
thf(9,plain,
r1 != r2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ singleton_set @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_2) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ singleton_set @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( A @ ( B @ unordered_pair ) @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_2) ).
thf(17,plain,
! [B: $i,A: $i] : ( A @ ( B @ unordered_pair ) @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [A: $i] : ( A @ singleton_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_1) ).
thf(12,plain,
! [A: $i] : ( A @ singleton_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_3) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_1) ).
thf(16,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
( ( r1 @ ( m1 @ ordered_pair ) )
= ( r2 @ ( m2 @ ordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pairs) ).
thf(23,plain,
( ( r1 @ ( m1 @ ordered_pair ) )
= ( r2 @ ( m2 @ ordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[21,9,13,17,12,18,16,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.15/5.43 % Computer : n008.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Sat Sep 26 06:52:48 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.43 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
% 0.19/6.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/6.21 % [INFO] Parsing done (180ms).
% 1.30/6.22 % [INFO] Running in sequential loop mode.
% 1.87/6.62 % [INFO] eprover registered as external prover.
% 1.87/6.63 % [INFO] Scanning for conjecture ...
% 2.03/6.71 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.03/6.74 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.03/6.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.03/6.76 % [INFO] Type checking passed.
% 2.03/6.77 % [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 ...
% 2.96/7.29 % External prover 'e' found a proof!
% 2.96/7.29 % [INFO] Killing All external provers ...
% 2.96/7.29 % Time passed: 1712ms (effective reasoning time: 1061ms)
% 2.96/7.29 % Axioms used in derivation (7): unordered_pair_3, singleton_1, ordered_pair, unordered_pair_2, equal_ordered_pairs, unordered_pair_1, singleton_2
% 2.96/7.29 % No. of inferences in proof: 17
% 2.96/7.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1712 ms resp. 1061 ms w/o parsing
% 3.23/7.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.23/7.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------