%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG089+1 : 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 : 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 08:25:26 AM UTC 2026
% Result : Theorem 57.13s 25.04s
% Output : Refutation 57.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 165 ( 10 equ; 0 cnn)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 530 ( 64 ~; 54 |; 38 &; 349 @)
% ( 1 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 3 ^; 44 !; 0 ?; 50 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(sdtpldt1_decl,type,
sdtpldt1: $i > $i > $i ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(aIdeal0_decl,type,
aIdeal0: $i > $o ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(xz_decl,type,
xz: $i ).
thf(xk_decl,type,
xk: $i ).
thf(xI_decl,type,
xI: $i ).
thf(xl_decl,type,
xl: $i ).
thf(xJ_decl,type,
xJ: $i ).
thf(xx_decl,type,
xx: $i ).
thf(xy_decl,type,
xy: $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( A @ ( B @ aElementOf0 ) )
=> ( ! [C: $i] :
( ( C @ aElement0 )
=> ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [C: $i] :
( ( A @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ ( B @ sdtpldt0 ) @ aElementOf0 ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( A @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ ( A @ sk4 @ sdtpldt0 ) @ aElementOf0 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ aElement0 )
=> ( A @ ( A @ sk4 @ ( B @ sdtasdt0 ) @ aElementOf0 ) ) ) ) ) ).
thf(18,axiom,
! [A: $i] :
( ( A @ aIdeal0 )
<=> ( ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( ! [C: $i] :
( ( C @ aElement0 )
=> ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [C: $i] :
( ( A @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ ( B @ sdtpldt0 ) @ aElementOf0 ) ) ) ) )
& ( A @ aSet0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
thf(105,plain,
! [A: $i] :
( ( ( ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( ! [C: $i] :
( ( C @ aElement0 )
=> ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [C: $i] :
( ( A @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ ( B @ sdtpldt0 ) @ aElementOf0 ) ) ) ) )
& ( A @ aSet0 ) )
=> ( A @ aIdeal0 ) )
& ( ( A @ aIdeal0 )
=> ( ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( ! [C: $i] :
( ( C @ aElement0 )
=> ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [C: $i] :
( ( A @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ ( B @ sdtpldt0 ) @ aElementOf0 ) ) ) ) )
& ( A @ aSet0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(106,plain,
( ! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( ! [C: $i] :
( ( C @ aElement0 )
=> ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [C: $i] :
( ( A @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ ( B @ sdtpldt0 ) @ aElementOf0 ) ) ) ) )
& ( A @ aSet0 ) )
=> ( A @ aIdeal0 ) )
& ! [A: $i] :
( ( A @ aIdeal0 )
=> ( ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( ! [C: $i] :
( ( C @ aElement0 )
=> ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [C: $i] :
( ( A @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ ( B @ sdtpldt0 ) @ aElementOf0 ) ) ) ) )
& ( A @ aSet0 ) ) ) ),
inference(miniscope,[status(thm)],[105]) ).
thf(107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ aIdeal0 )
| ~ ( E @ ( E @ sk4 @ ( E @ sk6 @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( E @ ( E @ sk5 @ ( E @ sk4 @ sdtpldt0 ) @ aElementOf0 ) )
| ~ ( E @ aSet0 ) )
& ( ( E @ aIdeal0 )
| ( E @ sk6 @ aElement0 )
| ~ ( E @ ( E @ sk5 @ ( E @ sk4 @ sdtpldt0 ) @ aElementOf0 ) )
| ~ ( E @ aSet0 ) )
& ( ( E @ aIdeal0 )
| ~ ( E @ ( E @ sk4 @ ( E @ sk6 @ sdtasdt0 ) @ aElementOf0 ) )
| ( E @ ( E @ sk5 @ aElementOf0 ) )
| ~ ( E @ aSet0 ) )
& ( ( E @ aIdeal0 )
| ( E @ sk6 @ aElement0 )
| ( E @ ( E @ sk5 @ aElementOf0 ) )
| ~ ( E @ aSet0 ) )
& ( ( E @ aIdeal0 )
| ( E @ ( E @ sk4 @ aElementOf0 ) )
| ~ ( E @ aSet0 ) )
& ( ( A @ ( B @ ( D @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( D @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aIdeal0 ) )
& ( ( A @ ( C @ ( B @ sdtpldt0 ) @ aElementOf0 ) )
| ~ ( A @ ( C @ aElementOf0 ) )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aIdeal0 ) )
& ( ( A @ aSet0 )
| ~ ( A @ aIdeal0 ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( C @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aIdeal0 ) ),
inference(cnfConj,[status(thm)],[107]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( C @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aIdeal0 ) ),
inference(simp,[status(thm)],[113]) ).
thf(1,conjecture,
( ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) )
& ( xI @ ( xk @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) )
& ( xI @ ( xk @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(32,plain,
~ ( ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) )
& ( xI @ ( xk @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
( ~ ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( xI @ ( xk @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(17325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) )
!= ( xI @ ( xk @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ) )
| ~ ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) )
| ~ $true
| ~ ( C @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aIdeal0 ) ),
inference(paramod_ordered,[status(thm)],[118,33]) ).
thf(17326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) )
!= ( xI @ ( xk @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ) )
| ~ ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( C @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aIdeal0 ) ),
inference(simp,[status(thm)],[17325]) ).
thf(17327,plain,
( ~ ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( xz @ aElement0 )
| ~ ( xI @ ( xk @ aElementOf0 ) )
| ~ ( xI @ aIdeal0 ) ),
inference(pattern_uni,[status(thm)],[17326:[bind(A,$thf( xI )),bind(B,$thf( xk )),bind(C,$thf( xz ))]]) ).
thf(23,axiom,
( ( xz @ aElement0 )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xy @ aElementOf0 ) )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xx @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
thf(141,plain,
( ( xz @ aElement0 )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xy @ aElementOf0 ) )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xx @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(142,plain,
( ( xz @ aElement0 )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xy @ aElementOf0 ) )
& ( xJ @ ( xI @ sdtpldt1 ) @ ( xx @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(145,plain,
xz @ aElement0,
inference(cnfConj,[status(thm)],[142]) ).
thf(15,axiom,
( ( xJ @ aIdeal0 )
& ( xI @ aIdeal0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
thf(65,plain,
( ( xJ @ aIdeal0 )
& ( xI @ aIdeal0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(66,plain,
( ( xJ @ aIdeal0 )
& ( xI @ aIdeal0 ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
xI @ aIdeal0,
inference(cnfConj,[status(thm)],[66]) ).
thf(16,axiom,
( ( xx
= ( xl @ ( xk @ sdtpldt0 ) ) )
& ( xJ @ ( xl @ aElementOf0 ) )
& ( xI @ ( xk @ aElementOf0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
thf(69,plain,
( ( xx
= ( xl @ ( xk @ sdtpldt0 ) ) )
& ( xJ @ ( xl @ aElementOf0 ) )
& ( xI @ ( xk @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(70,plain,
( ( xx
= ( xl @ ( xk @ sdtpldt0 ) ) )
& ( xJ @ ( xl @ aElementOf0 ) )
& ( xI @ ( xk @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
xI @ ( xk @ aElementOf0 ),
inference(cnfConj,[status(thm)],[70]) ).
thf(20296,plain,
( ~ ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) )
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[17327,145,67,71]) ).
thf(20297,plain,
~ ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ),
inference(simp,[status(thm)],[20296]) ).
thf(20319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) )
!= ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ) )
| ~ $true
| ~ ( C @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aIdeal0 ) ),
inference(paramod_ordered,[status(thm)],[118,20297]) ).
thf(20320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sdtasdt0 ) @ aElementOf0 ) )
!= ( xJ @ ( xl @ ( xz @ sdtasdt0 ) @ aElementOf0 ) ) )
| ~ ( C @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aIdeal0 ) ),
inference(simp,[status(thm)],[20319]) ).
thf(20321,plain,
( ~ ( xz @ aElement0 )
| ~ ( xJ @ ( xl @ aElementOf0 ) )
| ~ ( xJ @ aIdeal0 ) ),
inference(pattern_uni,[status(thm)],[20320:[bind(A,$thf( xJ )),bind(B,$thf( xl )),bind(C,$thf( xz ))]]) ).
thf(68,plain,
xJ @ aIdeal0,
inference(cnfConj,[status(thm)],[66]) ).
thf(72,plain,
xJ @ ( xl @ aElementOf0 ),
inference(cnfConj,[status(thm)],[70]) ).
thf(20856,plain,
( ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[20321,145,68,72]) ).
thf(20857,plain,
$false,
inference(simp,[status(thm)],[20856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.22 % Problem : RNG089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.03/0.28 % 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
% 0.13/10.62 % Computer : n008.cluster.edu
% 0.13/10.62 % Model : x86_64 x86_64
% 0.13/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.62 % Memory : 8046.5625MB
% 0.13/10.62 % OS : Linux 6.8.0-71-generic
% 0.13/10.62 % CPULimit : 300
% 0.13/10.62 % WCLimit : 300
% 0.13/10.62 % DateTime : Sat Sep 26 06:02:35 UTC 2026
% 0.13/10.62 % CPUTime :
% 0.13/10.62 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
% 0.17/10.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/11.03 % [INFO] Parsing done (111ms).
% 0.99/11.04 % [INFO] Running in sequential loop mode.
% 1.43/11.23 % [INFO] eprover registered as external prover.
% 1.43/11.24 % [INFO] Scanning for conjecture ...
% 1.43/11.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.43/11.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.43/11.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.75/11.32 % [INFO] Found a conjecture (or negated_conjecture) and 29 axioms. Running axiom selection ...
% 1.94/11.40 % [INFO] Axiom selection finished. Selected 29 axioms (removed 0 axioms).
% 1.94/11.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.94/11.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.94/11.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.94/11.45 % [INFO] Problem is first-order (TPTP FOF).
% 1.94/11.46 % [INFO] Type checking passed.
% 1.94/11.47 % [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 ...
% 57.13/25.03 % [INFO] Killing All external provers ...
% 57.13/25.04 % Time passed: 14317ms (effective reasoning time: 13993ms)
% 57.13/25.04 % 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)>
% 57.13/25.04 % Axioms used in derivation (4): mDefIdeal, m__901, m__870, m__934
% 57.13/25.04 % No. of inferences in proof: 34
% 57.13/25.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14317 ms resp. 13993 ms w/o parsing
% 57.13/25.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.13/25.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------