%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM021+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 06:57:54 AM UTC 2026
% Result : Theorem 49.34s 12.97s
% Output : Refutation 49.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 155 ( 35 equ; 0 cnn)
% Maximal formula atoms : 25 ( 6 avg)
% Number of connectives : 448 ( 21 ~; 56 |; 67 &; 304 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-3 aty)
% Number of variables : 17 ( 0 ^; 3 !; 11 ?; 17 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% 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(aNormalFormOfIn0_decl,type,
aNormalFormOfIn0: $i > $i > $i > $o ).
thf(xb_decl,type,
xb: $i ).
thf(xd_decl,type,
xd: $i ).
thf(xR_decl,type,
xR: $i ).
thf(xw_decl,type,
xw: $i ).
thf(xx_decl,type,
xx: $i ).
thf(sk24_decl,type,
sk24: $i ).
thf(sk25_decl,type,
sk25: $i ).
thf(sk26_decl,type,
sk26: $i ).
thf(sk24_def,definition,
( sk24
= ( @+[A: $i] :
( ( xd @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xw @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( @+[A: $i] :
( ( xx @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xb @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( @+[A: $i] :
( ( xx @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xd @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) ) ) ) ).
thf(22,axiom,
( ( xx @ ( xR @ ( xd @ sdtmndtasgtdt0 ) ) )
& ( ( ( xx @ ( xR @ ( xd @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xx @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xd @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xd @ ( xx @ aReductOfIn0 ) ) ) ) )
| ( xd = xx ) )
& ( xx @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
& ( ( ( xx @ ( xR @ ( xb @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xx @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xb @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xb @ ( xx @ aReductOfIn0 ) ) ) ) )
| ( xb = xx ) )
& ( xx @ aElement0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__850) ).
thf(204,plain,
( ( xx @ ( xR @ ( xd @ sdtmndtasgtdt0 ) ) )
& ( ( ( xx @ ( xR @ ( xd @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xx @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xd @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xd @ ( xx @ aReductOfIn0 ) ) ) ) )
| ( xd = xx ) )
& ( xx @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
& ( ( ( xx @ ( xR @ ( xb @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xx @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xb @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xb @ ( xx @ aReductOfIn0 ) ) ) ) )
| ( xb = xx ) )
& ( xx @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(205,plain,
( ( xx @ ( xR @ ( xd @ sdtmndtasgtdt0 ) ) )
& ( ( xx @ ( xR @ ( xd @ sdtmndtplgtdt0 ) ) )
| ( xd = xx ) )
& ( ( xx @ ( xR @ ( sk26 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xd @ ( xx @ aReductOfIn0 ) ) )
| ( xd = xx ) )
& ( ( xR @ ( xd @ ( sk26 @ aReductOfIn0 ) ) )
| ( xR @ ( xd @ ( xx @ aReductOfIn0 ) ) )
| ( xd = xx ) )
& ( ( sk26 @ aElement0 )
| ( xR @ ( xd @ ( xx @ aReductOfIn0 ) ) )
| ( xd = xx ) )
& ( xx @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
& ( ( xx @ ( xR @ ( xb @ sdtmndtplgtdt0 ) ) )
| ( xb = xx ) )
& ( ( xx @ ( xR @ ( sk25 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xb @ ( xx @ aReductOfIn0 ) ) )
| ( xb = xx ) )
& ( ( xR @ ( xb @ ( sk25 @ aReductOfIn0 ) ) )
| ( xR @ ( xb @ ( xx @ aReductOfIn0 ) ) )
| ( xb = xx ) )
& ( ( sk25 @ aElement0 )
| ( xR @ ( xb @ ( xx @ aReductOfIn0 ) ) )
| ( xb = xx ) )
& ( xx @ aElement0 ) ),
inference(cnf,[status(esa)],[204]) ).
thf(214,plain,
( ( xR @ ( xd @ ( sk26 @ aReductOfIn0 ) ) )
| ( xR @ ( xd @ ( xx @ aReductOfIn0 ) ) )
| ( xd = xx ) ),
inference(cnfConj,[status(thm)],[205]) ).
thf(224,plain,
( ( xR @ ( xd @ ( sk26 @ aReductOfIn0 ) ) )
| ( xR @ ( xd @ ( xx @ aReductOfIn0 ) ) )
| ( xx = xd ) ),
inference(lifteq,[status(thm)],[214]) ).
thf(21,axiom,
( ( xR @ ( xw @ ( xd @ aNormalFormOfIn0 ) ) )
& ~ ? [A: $i] : ( xR @ ( xd @ ( A @ aReductOfIn0 ) ) )
& ( xd @ ( xR @ ( xw @ sdtmndtasgtdt0 ) ) )
& ( ( ( xd @ ( xR @ ( xw @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xd @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xw @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xw @ ( xd @ aReductOfIn0 ) ) ) ) )
| ( xw = xd ) )
& ( xd @ aElement0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
thf(190,plain,
( ( xR @ ( xw @ ( xd @ aNormalFormOfIn0 ) ) )
& ~ ? [A: $i] : ( xR @ ( xd @ ( A @ aReductOfIn0 ) ) )
& ( xd @ ( xR @ ( xw @ sdtmndtasgtdt0 ) ) )
& ( ( ( xd @ ( xR @ ( xw @ sdtmndtplgtdt0 ) ) )
& ( ? [A: $i] :
( ( xd @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xw @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xw @ ( xd @ aReductOfIn0 ) ) ) ) )
| ( xw = xd ) )
& ( xd @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(191,plain,
! [A: $i] :
( ( xR @ ( xw @ ( xd @ aNormalFormOfIn0 ) ) )
& ~ ( xR @ ( xd @ ( A @ aReductOfIn0 ) ) )
& ( xd @ ( xR @ ( xw @ sdtmndtasgtdt0 ) ) )
& ( ( xd @ ( xR @ ( xw @ sdtmndtplgtdt0 ) ) )
| ( xw = xd ) )
& ( ( xd @ ( xR @ ( sk24 @ sdtmndtplgtdt0 ) ) )
| ( xR @ ( xw @ ( xd @ aReductOfIn0 ) ) )
| ( xw = xd ) )
& ( ( xR @ ( xw @ ( sk24 @ aReductOfIn0 ) ) )
| ( xR @ ( xw @ ( xd @ aReductOfIn0 ) ) )
| ( xw = xd ) )
& ( ( sk24 @ aElement0 )
| ( xR @ ( xw @ ( xd @ aReductOfIn0 ) ) )
| ( xw = xd ) )
& ( xd @ aElement0 ) ),
inference(cnf,[status(esa)],[190]) ).
thf(197,plain,
! [A: $i] :
~ ( xR @ ( xd @ ( A @ aReductOfIn0 ) ) ),
inference(cnfConj,[status(thm)],[191]) ).
thf(23865,plain,
( $false
| $false
| ( xx = xd ) ),
inference(rewrite,[status(thm)],[224,197]) ).
thf(23866,plain,
xx = xd,
inference(simp,[status(thm)],[23865]) ).
thf(215,plain,
xx @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ),
inference(cnfConj,[status(thm)],[205]) ).
thf(1,conjecture,
( ( xd @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
| ( xd @ ( xR @ ( xb @ sdtmndtplgtdt0 ) ) )
| ? [A: $i] :
( ( xd @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xb @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xb @ ( xd @ aReductOfIn0 ) ) )
| ( xb = xd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xd @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
| ( xd @ ( xR @ ( xb @ sdtmndtplgtdt0 ) ) )
| ? [A: $i] :
( ( xd @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xb @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xb @ ( xd @ aReductOfIn0 ) ) )
| ( xb = xd ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ( ( xd @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
| ( xd @ ( xR @ ( xb @ sdtmndtplgtdt0 ) ) )
| ? [A: $i] :
( ( xd @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
& ( xR @ ( xb @ ( A @ aReductOfIn0 ) ) )
& ( A @ aElement0 ) )
| ( xR @ ( xb @ ( xd @ aReductOfIn0 ) ) )
| ( xb = xd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
! [A: $i] :
( ~ ( xd @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
& ~ ( xd @ ( xR @ ( xb @ sdtmndtplgtdt0 ) ) )
& ( ~ ( xd @ ( xR @ ( A @ sdtmndtplgtdt0 ) ) )
| ~ ( xR @ ( xb @ ( A @ aReductOfIn0 ) ) )
| ~ ( A @ aElement0 ) )
& ~ ( xR @ ( xb @ ( xd @ aReductOfIn0 ) ) )
& ( xb != xd ) ),
inference(cnf,[status(esa)],[27]) ).
thf(31,plain,
~ ( xd @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(456,plain,
( ( ( xx @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
!= ( xd @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[215,31]) ).
thf(457,plain,
( ( xx @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) )
!= ( xd @ ( xR @ ( xb @ sdtmndtasgtdt0 ) ) ) ),
inference(simp,[status(thm)],[456]) ).
thf(458,plain,
( ( xx != xd )
| ( xR != xR )
| ( xb != xb ) ),
inference(simp,[status(thm)],[457]) ).
thf(459,plain,
xx != xd,
inference(simp,[status(thm)],[458]) ).
thf(23867,plain,
$false,
inference(simplifyReflect,[status(thm)],[23866,459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM021+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
% 0.13/0.40 % Computer : n005.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 23:22:17 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.82/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.05 % [INFO] Parsing done (232ms).
% 1.35/1.06 % [INFO] Running in sequential loop mode.
% 2.10/1.46 % [INFO] eprover registered as external prover.
% 2.10/1.47 % [INFO] Scanning for conjecture ...
% 2.33/1.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/1.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 24 axioms. Running axiom selection ...
% 2.77/1.73 % [INFO] Axiom selection finished. Selected 24 axioms (removed 0 axioms).
% 2.77/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.05/1.80 % [INFO] Problem is first-order (TPTP FOF).
% 3.05/1.82 % [INFO] Type checking passed.
% 3.05/1.82 % [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 ...
% 49.34/12.96 % [INFO] Killing All external provers ...
% 49.34/12.96 % Time passed: 12470ms (effective reasoning time: 11891ms)
% 49.34/12.96 % 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)>
% 49.34/12.97 % Axioms used in derivation (2): m__850, m__818
% 49.34/12.97 % No. of inferences in proof: 22
% 49.34/12.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12470 ms resp. 11891 ms w/o parsing
% 49.34/13.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 49.34/13.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------