%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU531_8 : TPTP v9.3.1. Released v8.0.0.
% 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 08:39:17 AM UTC 2026
% Result : Theorem 7.77s 3.50s
% Output : Refutation 7.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 20 unt; 0 typ; 3 def)
% Number of atoms : 115 ( 52 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 290 ( 32 ~; 43 |; 7 &; 172 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 68 !; 0 ?; 71 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setadjoinE_decl,type,
setadjoinE: $o ).
thf(uniqinunit_decl,type,
uniqinunit: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( emptyset @ ( B @ setadjoin ) @ ( A @ setadjoin ) @ ( C @ in ) )
=> ( ( C = B )
| ( C = A ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( emptyset @ ( A @ setadjoin ) @ ( sk1 @ setadjoin ) @ ( B @ in ) )
=> ( ( B = A )
| ( B = sk1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( emptyset @ ( sk2 @ setadjoin ) @ ( sk1 @ setadjoin ) @ ( A @ in ) )
=> ( ( A = sk2 )
| ( A = sk1 ) ) ) ) ) ).
thf(1,conjecture,
( setadjoinE
=> ( uniqinunit
=> ! [A: $i,B: $i,C: $i] :
( ( emptyset @ ( B @ setadjoin ) @ ( A @ setadjoin ) @ ( C @ in ) )
=> ( ( C = B )
| ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(2,negated_conjecture,
~ ( setadjoinE
=> ( uniqinunit
=> ! [A: $i,B: $i,C: $i] :
( ( emptyset @ ( B @ setadjoin ) @ ( A @ setadjoin ) @ ( C @ in ) )
=> ( ( C = B )
| ( C = A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( setadjoinE
=> ( uniqinunit
=> ! [A: $i,B: $i,C: $i] :
( ( emptyset @ ( B @ setadjoin ) @ ( A @ setadjoin ) @ ( C @ in ) )
=> ( ( C = B )
| ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( sk3 != sk2 )
& ( sk3 != sk1 )
& ( emptyset @ ( sk2 @ setadjoin ) @ ( sk1 @ setadjoin ) @ ( sk3 @ in ) )
& uniqinunit
& setadjoinE ),
inference(cnf,[status(esa)],[5]) ).
thf(11,plain,
emptyset @ ( sk2 @ setadjoin ) @ ( sk1 @ setadjoin ) @ ( sk3 @ in ),
inference(cnfConj,[status(thm)],[6]) ).
thf(4,axiom,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ setadjoin ) @ ( C @ in ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( B @ ( C @ in ) )
=> D )
=> D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(16,plain,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ setadjoin ) @ ( C @ in ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( B @ ( C @ in ) )
=> D )
=> D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ setadjoin ) @ ( C @ in ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( B @ ( C @ in ) )
=> D )
=> D ) ) ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(7,plain,
setadjoinE,
inference(cnfConj,[status(thm)],[6]) ).
thf(20,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ setadjoin ) @ ( C @ in ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( B @ ( C @ in ) )
=> D )
=> D ) ) ),
inference(rewrite,[status(thm)],[17,7]) ).
thf(21,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( D
| ~ D
| ~ D
| ~ ( B @ ( A @ setadjoin ) @ ( C @ in ) ) )
& ( D
| ( B @ ( C @ in ) )
| ~ D
| ~ ( B @ ( A @ setadjoin ) @ ( C @ in ) ) )
& ( D
| ~ D
| ( C = A )
| ~ ( B @ ( A @ setadjoin ) @ ( C @ in ) ) )
& ( D
| ( B @ ( C @ in ) )
| ( C = A )
| ~ ( B @ ( A @ setadjoin ) @ ( C @ in ) ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( D
| ( B @ ( C @ in ) )
| ( C = A )
| ~ ( B @ ( A @ setadjoin ) @ ( C @ in ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(109,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( D
| ( B @ ( C @ in ) )
| ~ ( B @ ( A @ setadjoin ) @ ( C @ in ) )
| ( C = A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(168,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ( emptyset @ ( sk2 @ setadjoin ) @ ( sk1 @ setadjoin ) @ ( sk3 @ in ) )
!= ( B @ ( A @ setadjoin ) @ ( C @ in ) ) )
| D
| ( B @ ( C @ in ) )
| ~ $true
| ( C = A ) ),
inference(paramod_ordered,[status(thm)],[11,109]) ).
thf(169,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ( emptyset @ ( sk2 @ setadjoin ) @ ( sk1 @ setadjoin ) @ ( sk3 @ in ) )
!= ( B @ ( A @ setadjoin ) @ ( C @ in ) ) )
| D
| ( B @ ( C @ in ) )
| ( C = A ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
! [A: $o] :
( A
| ( emptyset @ ( sk2 @ setadjoin ) @ ( sk3 @ in ) )
| ( sk3 = sk1 ) ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( sk1 )),bind(B,$thf( emptyset @ ( sk2 @ setadjoin ) )),bind(C,$thf( sk3 )),bind(D,$thf( D ))]]) ).
thf(224,plain,
! [A: $o] :
( A
| ( emptyset @ ( sk2 @ setadjoin ) @ ( sk3 @ in ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[170]) ).
thf(3,axiom,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( emptyset @ ( B @ setadjoin ) @ ( A @ in ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(14,plain,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( emptyset @ ( B @ setadjoin ) @ ( A @ in ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,plain,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( emptyset @ ( B @ setadjoin ) @ ( A @ in ) )
=> ( A = B ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(8,plain,
uniqinunit,
inference(cnfConj,[status(thm)],[6]) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( emptyset @ ( B @ setadjoin ) @ ( A @ in ) )
=> ( A = B ) ),
inference(rewrite,[status(thm)],[15,8]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( emptyset @ ( B @ setadjoin ) @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( emptyset @ ( B @ setadjoin ) @ ( A @ in ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(10,plain,
sk3 != sk2,
inference(cnfConj,[status(thm)],[6]) ).
thf(12,plain,
sk3 != sk2,
inference(lifteq,[status(thm)],[10]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A != sk3 )
| ( B != sk2 )
| ~ ( emptyset @ ( B @ setadjoin ) @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[26,12]) ).
thf(32,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( emptyset @ ( A @ setadjoin ) @ ( sk3 @ in ) ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( sk3 ))]]) ).
thf(70,plain,
~ ( emptyset @ ( sk2 @ setadjoin ) @ ( sk3 @ in ) ),
inference(simp,[status(thm)],[32]) ).
thf(554,plain,
! [A: $o] :
( A
| $false
| ( sk3 = sk1 ) ),
inference(rewrite,[status(thm)],[224,70]) ).
thf(555,plain,
! [A: $o] :
( A
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[554]) ).
thf(9,plain,
sk3 != sk1,
inference(cnfConj,[status(thm)],[6]) ).
thf(13,plain,
sk3 != sk1,
inference(lifteq,[status(thm)],[9]) ).
thf(556,plain,
! [A: $o] : A,
inference(simplifyReflect,[status(thm)],[555,13]) ).
thf(575,plain,
$false,
inference(prim_subst,[status(thm)],[556:[bind(A,$thf( $false ))]]) ).
thf(582,plain,
$false,
inference(simp,[status(thm)],[575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU531_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.12/0.40 % Computer : n008.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 10:09:41 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.18 % [INFO] Parsing done (185ms).
% 1.27/1.19 % [INFO] Running in sequential loop mode.
% 1.84/1.59 % [INFO] eprover registered as external prover.
% 1.84/1.60 % [INFO] Scanning for conjecture ...
% 2.04/1.68 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.68 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.22/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.22/1.76 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.22/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.22/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.22/1.77 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.22/1.77 % [INFO] Type checking passed.
% 2.22/1.78 % [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 ...
% 7.23/3.49 % [INFO] Killing All external provers ...
% 7.77/3.50 % Time passed: 2947ms (effective reasoning time: 2297ms)
% 7.77/3.50 % 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)>
% 7.77/3.50 % Axioms used in derivation (2): setadjoinE, uniqinunit
% 7.77/3.50 % No. of inferences in proof: 36
% 7.77/3.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2947 ms resp. 2297 ms w/o parsing
% 7.77/3.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.77/3.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------