%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU149+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 08:37:45 AM UTC 2026
% Result : Theorem 9.39s 4.10s
% Output : Refutation 9.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 20 unt; 0 typ; 7 def)
% Number of atoms : 171 ( 119 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 415 ( 46 ~; 55 |; 25 &; 251 @)
% ( 4 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 114 ( 10 ^; 94 !; 3 ?; 114 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(singleton_decl,type,
singleton: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $o ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ? [C: $i] :
( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ? [B: $i] :
( ( sk1 @ singleton )
= ( B @ ( A @ unordered_pair ) ) )
=> ( sk1 = A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ( sk1 @ singleton )
= ( A @ ( sk2 @ unordered_pair ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
~ ! [A: $i,B: $i] :
( ? [C: $i] :
( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[9]) ).
thf(11,plain,
( ( sk1 != sk2 )
& ( ( sk1 @ singleton )
= ( sk3 @ ( sk2 @ unordered_pair ) ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
( ( sk1 @ singleton )
= ( sk3 @ ( sk2 @ unordered_pair ) ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(14,plain,
( ( sk3 @ ( sk2 @ unordered_pair ) )
= ( sk1 @ singleton ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ unordered_pair ) )
!= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
= ( sk1 @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[14,20]) ).
thf(125,plain,
( ( sk2 @ ( sk3 @ unordered_pair ) )
= ( sk1 @ singleton ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(42,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[42]) ).
thf(44,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk8 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk6 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk8 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk8 ) ) )
= F )
| ( H @ ( G @ ( F @ sk6 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk6 ) ) )
| ( ( F @ ( G @ ( H @ sk7 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk6 ) ) )
| ( ( F @ ( G @ ( H @ sk7 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk6 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk7 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ( E != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C @ ( E @ in ) )
| ( E != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[44]) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(66,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ in ) ),
inference(simp,[status(thm)],[65]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ unordered_pair ) )
!= ( B @ ( A @ unordered_pair ) ) )
| ( sk1 @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[125,66]) ).
thf(142,plain,
sk1 @ singleton @ ( sk2 @ in ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ in ) )
| ( ( E @ ( F @ sk4 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk5 ) )
= E )
| ( ( E @ ( F @ sk4 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ in ) )
| ( F @ ( E @ ( F @ sk4 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk5 ) )
= E )
| ( F @ ( E @ ( F @ sk4 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ in ) )
| ( C = A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( A @ singleton @ ( B @ in ) )
| ( B = A ) ),
inference(simp,[status(thm)],[40]) ).
thf(799,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ singleton @ ( sk2 @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ~ $true
| ( B = A ) ),
inference(paramod_ordered,[status(thm)],[142,41]) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ singleton @ ( sk2 @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[799]) ).
thf(801,plain,
sk2 = sk1,
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(13,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[11]) ).
thf(15,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[13]) ).
thf(1284,plain,
$false,
inference(simplifyReflect,[status(thm)],[801,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU149+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 08:43:06 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.16 % [INFO] Parsing done (179ms).
% 1.19/1.18 % [INFO] Running in sequential loop mode.
% 1.71/1.57 % [INFO] eprover registered as external prover.
% 1.71/1.58 % [INFO] Scanning for conjecture ...
% 1.89/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.03/1.70 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.03/1.71 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.72 % [INFO] Type checking passed.
% 2.03/1.72 % [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 ...
% 9.39/4.09 % [INFO] Killing All external provers ...
% 9.39/4.09 % Time passed: 3547ms (effective reasoning time: 2907ms)
% 9.39/4.09 % 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)>
% 9.39/4.10 % Axioms used in derivation (3): commutativity_k2_tarski, d2_tarski, d1_tarski
% 9.39/4.10 % No. of inferences in proof: 35
% 9.39/4.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3547 ms resp. 2907 ms w/o parsing
% 9.83/4.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.83/4.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------