%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM016+4 : TPTP v9.3.1. Released v4.0.0.
% 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 : n005.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 06:57:53 AM UTC 2026
% Result : Theorem 8.98s 3.92s
% Output : Refutation 8.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 141 ( 10 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 436 ( 45 ~; 55 |; 47 &; 289 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 19 ( 0 ^; 7 !; 10 ?; 19 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtmndtplgtdt0_decl,type,
sdtmndtplgtdt0: $i > $i > $i > $o ).
thf(aReductOfIn0_decl,type,
aReductOfIn0: $i > $i > $i > $o ).
thf(sdtmndtasgtdt0_decl,type,
sdtmndtasgtdt0: $i > $i > $i > $o ).
thf(xa_decl,type,
xa: $i ).
thf(xR_decl,type,
xR: $i ).
thf(xb_decl,type,
xb: $i ).
thf(xc_decl,type,
xc: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
( ( xc @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(12,axiom,
( ( xc @ ( xR @ ( xa @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xc @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xa @ ( xc @ aReductOfIn0 ) ) ) )
& ( xb @ ( xR @ ( xa @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731_02) ).
thf(103,plain,
( ( xc @ ( xR @ ( xa @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xc @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xa @ ( xc @ aReductOfIn0 ) ) ) )
& ( xb @ ( xR @ ( xa @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(104,plain,
( ( xc @ ( xR @ ( xa @ sdtmndtplgtdt0 ) ) )
& ( ( xc @ ( xR @ ( sk15 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xa @ ( xc @ aReductOfIn0 ) ) ) )
& ( ( xR @ ( xa @ ( sk15 @ aReductOfIn0 ) ) )
| ( xR @ ( xa @ ( xc @ aReductOfIn0 ) ) ) )
& ( ( sk15 @ aElement0 )
| ( xR @ ( xa @ ( xc @ aReductOfIn0 ) ) ) )
& ( xb @ ( xR @ ( xa @ sdtmndtplgtdt0 ) ) )
& ( ( xb @ ( xR @ ( sk14 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ) )
& ( ( xR @ ( xa @ ( sk14 @ aReductOfIn0 ) ) )
| ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ) )
& ( ( sk14 @ aElement0 )
| ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(110,plain,
( ( xb @ ( xR @ ( sk14 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ) ),
inference(cnfConj,[status(thm)],[104]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( xb @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [B: $i] :
( ( xb @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( B @ aElement0 ) )
| ( xR @ ( A @ ( xb @ aReductOfIn0 ) ) )
| ( A = xb ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( xb @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [B: $i] :
( ( xb @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( B @ aElement0 ) )
| ( xR @ ( A @ ( xb @ aReductOfIn0 ) ) )
| ( A = xb ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ? [A: $i] :
( ( ( xb @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ? [B: $i] :
( ( xb @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
& ( B @ aElement0 ) )
| ( xR @ ( A @ ( xb @ aReductOfIn0 ) ) )
| ( A = xb ) )
& ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ~ ( xb @ ( xR @ ( A @ sdtmndtasgtdt0 ) ) )
| ~ ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ~ ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ~ ( xb @ ( xR @ ( B @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( A @ ( B @ aReductOfIn0 ) ) )
| ~ ( B @ aElement0 )
| ~ ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ~ ( xR @ ( A @ ( xb @ aReductOfIn0 ) ) )
| ~ ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ( A != xb )
| ~ ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(26,plain,
! [A: $i] :
( ( A != xb )
| ~ ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(29,plain,
! [A: $i] :
( ~ ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 )
| ( A != xb ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(30,plain,
( ~ ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) )
| ~ ( xb @ aElement0 ) ),
inference(simp,[status(thm)],[29]) ).
thf(10,axiom,
( ( xc @ aElement0 )
& ( xb @ aElement0 )
& ( xa @ aElement0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
thf(96,plain,
( ( xc @ aElement0 )
& ( xb @ aElement0 )
& ( xa @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(97,plain,
( ( xc @ aElement0 )
& ( xb @ aElement0 )
& ( xa @ aElement0 ) ),
inference(cnf,[status(esa)],[96]) ).
thf(99,plain,
xb @ aElement0,
inference(cnfConj,[status(thm)],[97]) ).
thf(178,plain,
( ~ ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[30,99]) ).
thf(179,plain,
~ ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(108,plain,
( ( xR @ ( xa @ ( sk14 @ aReductOfIn0 ) ) )
| ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ) ),
inference(cnfConj,[status(thm)],[104]) ).
thf(325,plain,
( ( xR @ ( xa @ ( sk14 @ aReductOfIn0 ) ) )
| $false ),
inference(rewrite,[status(thm)],[108,179]) ).
thf(326,plain,
xR @ ( xa @ ( sk14 @ aReductOfIn0 ) ),
inference(simp,[status(thm)],[325]) ).
thf(25,plain,
! [A: $i] :
( ~ ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(346,plain,
! [A: $i] :
( ( ( xR @ ( xa @ ( sk14 @ aReductOfIn0 ) ) )
!= ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) ) )
| ~ ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ $true
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[326,25]) ).
thf(347,plain,
! [A: $i] :
( ( ( xR @ ( xa @ ( sk14 @ aReductOfIn0 ) ) )
!= ( xR @ ( xa @ ( A @ aReductOfIn0 ) ) ) )
| ~ ( xb @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[346]) ).
thf(348,plain,
( ~ ( xb @ ( xR @ ( sk14 @ sdtmndtplgtdt0 ) ) )
| ~ ( sk14 @ aElement0 ) ),
inference(pattern_uni,[status(thm)],[347:[bind(A,$thf( sk14 ))]]) ).
thf(107,plain,
( ( sk14 @ aElement0 )
| ( xR @ ( xa @ ( xb @ aReductOfIn0 ) ) ) ),
inference(cnfConj,[status(thm)],[104]) ).
thf(242,plain,
( ( sk14 @ aElement0 )
| $false ),
inference(rewrite,[status(thm)],[107,179]) ).
thf(243,plain,
sk14 @ aElement0,
inference(simp,[status(thm)],[242]) ).
thf(414,plain,
( ~ ( xb @ ( xR @ ( sk14 @ sdtmndtplgtdt0 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[348,243]) ).
thf(415,plain,
~ ( xb @ ( xR @ ( sk14 @ sdtmndtplgtdt0 ) ) ),
inference(simp,[status(thm)],[414]) ).
thf(489,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[110,179,415]) ).
thf(490,plain,
$false,
inference(simp,[status(thm)],[489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM016+4 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 23:22:03 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 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
% 0.89/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.24 % [INFO] Parsing done (225ms).
% 1.43/1.25 % [INFO] Running in sequential loop mode.
% 2.16/1.66 % [INFO] eprover registered as external prover.
% 2.16/1.67 % [INFO] Scanning for conjecture ...
% 2.41/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.62/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.83/1.91 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.83/1.92 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.83/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.83/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.83/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.83/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.83/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.83/1.97 % [INFO] Problem is first-order (TPTP FOF).
% 2.83/1.98 % [INFO] Type checking passed.
% 2.83/1.98 % [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 ...
% 8.98/3.91 % [INFO] Killing All external provers ...
% 8.98/3.91 % Time passed: 3342ms (effective reasoning time: 2651ms)
% 8.98/3.91 % 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)>
% 8.98/3.91 % Axioms used in derivation (2): m__731_02, m__731
% 8.98/3.91 % No. of inferences in proof: 31
% 8.98/3.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3342 ms resp. 2651 ms w/o parsing
% 8.98/3.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.98/3.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------