%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM129+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/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 06:58:03 AM UTC 2026
% Result : Theorem 164.85s 91.09s
% Output : Refutation 164.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 106 ( 41 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 363 ( 59 ~; 37 |; 7 &; 245 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 85 ( 0 ^; 81 !; 0 ?; 85 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(vgensym_decl,type,
vgensym: $i > $i ).
thf(vapp_decl,type,
vapp: $i > $i > $i ).
thf(vvar_decl,type,
vvar: $i > $i ).
thf(visFreeVar_decl,type,
visFreeVar: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( C
= ( B @ vvar @ ( D @ ( A @ vapp ) @ vapp ) @ vgensym ) )
=> ~ ( D @ ( C @ visFreeVar ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( B
= ( A @ vvar @ ( C @ ( sk1 @ vapp ) @ vapp ) @ vgensym ) )
=> ~ ( C @ ( B @ visFreeVar ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( A
= ( sk2 @ vvar @ ( B @ ( sk1 @ vapp ) @ vapp ) @ vgensym ) )
=> ~ ( B @ ( A @ visFreeVar ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( sk3
= ( sk2 @ vvar @ ( A @ ( sk1 @ vapp ) @ vapp ) @ vgensym ) )
=> ~ ( A @ ( sk3 @ visFreeVar ) ) ) ) ) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B
= ( E @ ( C @ vapp ) ) )
& ( A = D ) )
=> ( ( ( B @ ( A @ visFreeVar ) )
=> ( ( E @ ( D @ visFreeVar ) )
| ( C @ ( D @ visFreeVar ) ) ) )
& ( ( ( E @ ( D @ visFreeVar ) )
| ( C @ ( D @ visFreeVar ) ) )
=> ( B @ ( A @ visFreeVar ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar2) ).
thf(456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B
= ( E @ ( C @ vapp ) ) )
& ( A = D ) )
=> ( ( ( B @ ( A @ visFreeVar ) )
=> ( ( E @ ( D @ visFreeVar ) )
| ( C @ ( D @ visFreeVar ) ) ) )
& ( ( ( E @ ( D @ visFreeVar ) )
| ( C @ ( D @ visFreeVar ) ) )
=> ( B @ ( A @ visFreeVar ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(457,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ visFreeVar ) )
| ( C @ ( D @ visFreeVar ) )
| ~ ( B @ ( A @ visFreeVar ) )
| ( B
!= ( E @ ( C @ vapp ) ) )
| ( A != D ) )
& ( ( B @ ( A @ visFreeVar ) )
| ~ ( E @ ( D @ visFreeVar ) )
| ( B
!= ( E @ ( C @ vapp ) ) )
| ( A != D ) )
& ( ( B @ ( A @ visFreeVar ) )
| ~ ( C @ ( D @ visFreeVar ) )
| ( B
!= ( E @ ( C @ vapp ) ) )
| ( A != D ) ) ),
inference(cnf,[status(esa)],[456]) ).
thf(459,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ visFreeVar ) )
| ~ ( E @ ( D @ visFreeVar ) )
| ( B
!= ( E @ ( C @ vapp ) ) )
| ( A != D ) ),
inference(cnfConj,[status(thm)],[457]) ).
thf(463,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ visFreeVar ) )
| ~ ( E @ ( D @ visFreeVar ) )
| ( B
!= ( E @ ( C @ vapp ) ) )
| ( A != D ) ),
inference(lifteq,[status(thm)],[459]) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ vapp ) @ ( B @ visFreeVar ) )
| ~ ( C @ ( B @ visFreeVar ) ) ),
inference(simp,[status(thm)],[463]) ).
thf(458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ visFreeVar ) )
| ~ ( C @ ( D @ visFreeVar ) )
| ( B
!= ( E @ ( C @ vapp ) ) )
| ( A != D ) ),
inference(cnfConj,[status(thm)],[457]) ).
thf(461,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ visFreeVar ) )
| ~ ( C @ ( D @ visFreeVar ) )
| ( B
!= ( E @ ( C @ vapp ) ) )
| ( A != D ) ),
inference(lifteq,[status(thm)],[458]) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ vapp ) @ ( B @ visFreeVar ) )
| ~ ( A @ ( B @ visFreeVar ) ) ),
inference(simp,[status(thm)],[461]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( B @ vvar @ ( D @ ( A @ vapp ) @ vapp ) @ vgensym ) )
=> ~ ( D @ ( C @ visFreeVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fresh-free-2') ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( B @ vvar @ ( D @ ( A @ vapp ) @ vapp ) @ vgensym ) )
=> ~ ( D @ ( C @ visFreeVar ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(68,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( C
= ( B @ vvar @ ( D @ ( A @ vapp ) @ vapp ) @ vgensym ) )
=> ~ ( D @ ( C @ visFreeVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(69,plain,
( ( sk4 @ ( sk3 @ visFreeVar ) )
& ( sk3
= ( sk2 @ vvar @ ( sk4 @ ( sk1 @ vapp ) @ vapp ) @ vgensym ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
( sk3
= ( sk2 @ vvar @ ( sk4 @ ( sk1 @ vapp ) @ vapp ) @ vgensym ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(72,plain,
( ( sk2 @ vvar @ ( sk4 @ ( sk1 @ vapp ) @ vapp ) @ vgensym )
= sk3 ),
inference(lifteq,[status(thm)],[70]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( B @ vgensym )
= A )
=> ~ ( B @ ( A @ visFreeVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gensym-is-fresh') ).
thf(447,plain,
! [A: $i,B: $i] :
( ( ( B @ vgensym )
= A )
=> ~ ( B @ ( A @ visFreeVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(448,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ visFreeVar ) )
| ( ( B @ vgensym )
!= A ) ),
inference(cnf,[status(esa)],[447]) ).
thf(449,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ visFreeVar ) )
| ( ( B @ vgensym )
!= A ) ),
inference(lifteq,[status(thm)],[448]) ).
thf(450,plain,
! [A: $i] :
~ ( A @ ( A @ vgensym @ visFreeVar ) ),
inference(simp,[status(thm)],[449]) ).
thf(623,plain,
! [A: $i] :
( ( ( sk2 @ vvar @ ( sk4 @ ( sk1 @ vapp ) @ vapp ) @ vgensym )
!= ( A @ vgensym ) )
| ~ ( A @ ( sk3 @ visFreeVar ) ) ),
inference(paramod_ordered,[status(thm)],[72,450]) ).
thf(624,plain,
~ ( sk2 @ vvar @ ( sk4 @ ( sk1 @ vapp ) @ vapp ) @ ( sk3 @ visFreeVar ) ),
inference(pattern_uni,[status(thm)],[623:[bind(A,$thf( sk2 @ vvar @ ( sk4 @ ( sk1 @ vapp ) @ vapp ) ))]]) ).
thf(116005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ vapp ) @ ( B @ visFreeVar ) )
!= ( sk2 @ vvar @ ( sk4 @ ( sk1 @ vapp ) @ vapp ) @ ( sk3 @ visFreeVar ) ) )
| ~ $true
| ~ ( A @ ( B @ visFreeVar ) ) ),
inference(paramod_ordered,[status(thm)],[462,624]) ).
thf(116006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ vapp ) @ ( B @ visFreeVar ) )
!= ( sk2 @ vvar @ ( sk4 @ ( sk1 @ vapp ) @ vapp ) @ ( sk3 @ visFreeVar ) ) )
| ~ ( A @ ( B @ visFreeVar ) ) ),
inference(simp,[status(thm)],[116005]) ).
thf(116007,plain,
~ ( sk4 @ ( sk1 @ vapp ) @ ( sk3 @ visFreeVar ) ),
inference(pattern_uni,[status(thm)],[116006:[bind(A,$thf( sk4 @ ( sk1 @ vapp ) )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 @ vvar ))]]) ).
thf(118119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ vapp ) @ ( B @ visFreeVar ) )
!= ( sk4 @ ( sk1 @ vapp ) @ ( sk3 @ visFreeVar ) ) )
| ~ $true
| ~ ( C @ ( B @ visFreeVar ) ) ),
inference(paramod_ordered,[status(thm)],[464,116007]) ).
thf(118120,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ vapp ) @ ( B @ visFreeVar ) )
!= ( sk4 @ ( sk1 @ vapp ) @ ( sk3 @ visFreeVar ) ) )
| ~ ( C @ ( B @ visFreeVar ) ) ),
inference(simp,[status(thm)],[118119]) ).
thf(118121,plain,
~ ( sk4 @ ( sk3 @ visFreeVar ) ),
inference(pattern_uni,[status(thm)],[118120:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(71,plain,
sk4 @ ( sk3 @ visFreeVar ),
inference(cnfConj,[status(thm)],[69]) ).
thf(118671,plain,
~ $true,
inference(rewrite,[status(thm)],[118121,71]) ).
thf(118672,plain,
$false,
inference(simp,[status(thm)],[118671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM129+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n001.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 23:37:44 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.27 % [INFO] Parsing done (295ms).
% 1.47/1.29 % [INFO] Running in sequential loop mode.
% 2.48/1.66 % [INFO] eprover registered as external prover.
% 2.48/1.67 % [INFO] Scanning for conjecture ...
% 2.69/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 65 axioms. Running axiom selection ...
% 2.87/1.89 % [INFO] Axiom selection finished. Selected 65 axioms (removed 0 axioms).
% 3.44/2.06 % [INFO] Problem is first-order (TPTP FOF).
% 3.44/2.09 % [INFO] Type checking passed.
% 3.44/2.09 % [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 ...
% 164.85/91.09 % [INFO] Killing All external provers ...
% 164.85/91.09 % Time passed: 90553ms (effective reasoning time: 89793ms)
% 164.85/91.09 % 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)>
% 164.85/91.09 % Axioms used in derivation (2): isFreeVar2, gensym-is-fresh
% 164.85/91.09 % No. of inferences in proof: 31
% 164.85/91.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 90553 ms resp. 89793 ms w/o parsing
% 164.85/91.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 164.85/91.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------