%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO082-1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n001.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 07:12:17 AM UTC 2026
% Result : Unsatisfiable 97.95s 37.87s
% Output : Refutation 97.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 365 ( 57 ~; 58 |; 0 &; 250 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 ^; 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(part_of_decl,type,
part_of: $i > $i > $o ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(incident_c_decl,type,
incident_c: $i > $i > $o ).
thf(ax0_sk13_decl,type,
ax0_sk13: $i > $i > $i ).
thf(1,negated_conjecture,
sk15 @ ( sk14 @ part_of ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_antisymmetry_67) ).
thf(44,plain,
sk15 @ ( sk14 @ part_of ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) )
| ~ ( B @ ( A @ part_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_1) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) )
| ~ ( B @ ( A @ part_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) )
| ~ ( B @ ( A @ part_of ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(43897,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk14 @ part_of ) )
!= ( B @ ( A @ part_of ) ) )
| ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,135]) ).
thf(43898,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk14 @ part_of ) )
!= ( B @ ( A @ part_of ) ) )
| ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) ) ),
inference(simp,[status(thm)],[43897]) ).
thf(43899,plain,
! [A: $i] :
( ( sk15 @ ( A @ incident_c ) )
| ~ ( sk14 @ ( A @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[43898:[bind(A,$thf( sk14 )),bind(B,$thf( sk15 ))]]) ).
thf(44108,plain,
! [A: $i] :
( ( sk15 @ ( A @ incident_c ) )
| ~ ( sk14 @ ( A @ incident_c ) ) ),
inference(simp,[status(thm)],[43899]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ~ ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_48) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ~ ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ~ ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ~ ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(3,negated_conjecture,
sk14 != sk15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_antisymmetry_69) ).
thf(46,plain,
sk14 != sk15,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(47,plain,
sk14 != sk15,
inference(polarity_switch,[status(thm)],[46]) ).
thf(48,plain,
sk15 != sk14,
inference(lifteq,[status(thm)],[47]) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( A != sk15 )
| ( B != sk14 )
| ~ ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ~ ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[62,48]) ).
thf(337,plain,
! [A: $i] :
( ( A != sk14 )
| ~ ( A @ ( A @ ( sk15 @ ax0_sk13 ) @ incident_c ) )
| ~ ( sk15 @ ( A @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[336:[bind(A,$thf( sk15 ))]]) ).
thf(389,plain,
( ~ ( sk14 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) )
| ~ ( sk15 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9_45) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( A != sk15 )
| ( B != sk14 )
| ( A @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) )
| ( B @ ( B @ ( A @ ax0_sk13 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[116,48]) ).
thf(796,plain,
! [A: $i] :
( ( A != sk14 )
| ( sk15 @ ( A @ ( sk15 @ ax0_sk13 ) @ incident_c ) )
| ( A @ ( A @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[795:[bind(A,$thf( sk15 ))]]) ).
thf(831,plain,
( ( sk15 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) )
| ( sk14 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[796]) ).
thf(2,negated_conjecture,
sk14 @ ( sk15 @ part_of ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_antisymmetry_68) ).
thf(45,plain,
sk14 @ ( sk15 @ part_of ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43885,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk15 @ part_of ) )
!= ( B @ ( A @ part_of ) ) )
| ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,135]) ).
thf(43886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk15 @ part_of ) )
!= ( B @ ( A @ part_of ) ) )
| ( B @ ( C @ incident_c ) )
| ~ ( A @ ( C @ incident_c ) ) ),
inference(simp,[status(thm)],[43885]) ).
thf(43887,plain,
! [A: $i] :
( ( sk14 @ ( A @ incident_c ) )
| ~ ( sk15 @ ( A @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[43886:[bind(A,$thf( sk15 )),bind(B,$thf( sk14 ))]]) ).
thf(44104,plain,
! [A: $i] :
( ( sk14 @ ( A @ incident_c ) )
| ~ ( sk15 @ ( A @ incident_c ) ) ),
inference(simp,[status(thm)],[43887]) ).
thf(60402,plain,
! [A: $i] :
( ( ( sk15 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) )
!= ( sk15 @ ( A @ incident_c ) ) )
| ( sk14 @ ( A @ incident_c ) )
| ~ $true
| ( sk14 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[831,44104]) ).
thf(60403,plain,
! [A: $i] :
( ( ( sk15 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) )
!= ( sk15 @ ( A @ incident_c ) ) )
| ( sk14 @ ( A @ incident_c ) )
| ( sk14 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) ),
inference(simp,[status(thm)],[60402]) ).
thf(60404,plain,
( ( sk14 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) )
| ( sk14 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) ),
inference(pattern_uni,[status(thm)],[60403:[bind(A,$thf( sk14 @ ( sk15 @ ax0_sk13 ) ))]]) ).
thf(60643,plain,
sk14 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ),
inference(simp,[status(thm)],[60404]) ).
thf(61547,plain,
( ~ $true
| ~ ( sk15 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) ),
inference(rewrite,[status(thm)],[389,60643]) ).
thf(61548,plain,
~ ( sk15 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ),
inference(simp,[status(thm)],[61547]) ).
thf(100562,plain,
! [A: $i] :
( ( ( sk15 @ ( A @ incident_c ) )
!= ( sk15 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) )
| ~ $true
| ~ ( sk14 @ ( A @ incident_c ) ) ),
inference(paramod_ordered,[status(thm)],[44108,61548]) ).
thf(100563,plain,
! [A: $i] :
( ( ( sk15 @ ( A @ incident_c ) )
!= ( sk15 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ) )
| ~ ( sk14 @ ( A @ incident_c ) ) ),
inference(simp,[status(thm)],[100562]) ).
thf(100564,plain,
~ ( sk14 @ ( sk14 @ ( sk15 @ ax0_sk13 ) @ incident_c ) ),
inference(pattern_uni,[status(thm)],[100563:[bind(A,$thf( sk14 @ ( sk15 @ ax0_sk13 ) ))]]) ).
thf(105489,plain,
~ $true,
inference(rewrite,[status(thm)],[100564,60643]) ).
thf(105490,plain,
$false,
inference(simp,[status(thm)],[105489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO082-1 : TPTP v9.3.1. Released v2.4.0.
% 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
% 0.15/0.41 % Computer : n001.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 12:46:11 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.23 % [INFO] Parsing done (239ms).
% 1.42/1.25 % [INFO] Running in sequential loop mode.
% 2.14/1.65 % [INFO] eprover registered as external prover.
% 2.14/1.66 % [INFO] Scanning for conjecture ...
% 2.39/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 48 axioms. Running axiom selection ...
% 2.55/1.83 % [INFO] Axiom selection finished. Selected 40 axioms (removed 8 axioms).
% 2.81/1.90 % [INFO] Problem is propositional (TPTP CNF).
% 2.81/1.91 % [INFO] Type checking passed.
% 2.81/1.91 % [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 ...
% 97.95/37.86 % [INFO] Killing All external provers ...
% 97.95/37.86 % Time passed: 37302ms (effective reasoning time: 36610ms)
% 97.95/37.87 % Axioms used in derivation (3): part_of_defn_1, c9_48, c9_45
% 97.95/37.87 % No. of inferences in proof: 44
% 97.95/37.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 37302 ms resp. 36610 ms w/o parsing
% 97.95/37.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 97.95/37.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------