%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM146+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 : n017.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 06:58:05 AM UTC 2026
% Result : Theorem 12.13s 4.21s
% Output : Refutation 12.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 77 ( 43 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 193 ( 26 ~; 10 |; 9 &; 131 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 52 ( 0 ^; 48 !; 0 ?; 52 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(vreduce_decl,type,
vreduce: $i > $i ).
thf(vvar_decl,type,
vvar: $i > $i ).
thf(vsomeExp_decl,type,
vsomeExp: $i > $i ).
thf(vtcheck_decl,type,
vtcheck: $i > $i > $i > $o ).
thf(vnoExp_decl,type,
vnoExp: $i ).
thf(visSomeExp_decl,type,
visSomeExp: $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] :
( ( ( D @ ( A @ vvar @ ( B @ vtcheck ) ) )
& ( ( A @ vvar @ vreduce )
= ( C @ vsomeExp ) ) )
=> ( D @ ( C @ ( B @ vtcheck ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( sk1 @ vvar @ ( A @ vtcheck ) ) )
& ( ( sk1 @ vvar @ vreduce )
= ( B @ vsomeExp ) ) )
=> ( C @ ( B @ ( A @ vtcheck ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( sk1 @ vvar @ ( sk2 @ vtcheck ) ) )
& ( ( sk1 @ vvar @ vreduce )
= ( A @ vsomeExp ) ) )
=> ( B @ ( A @ ( sk2 @ vtcheck ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( A @ ( sk1 @ vvar @ ( sk2 @ vtcheck ) ) )
& ( ( sk1 @ vvar @ vreduce )
= ( sk3 @ vsomeExp ) ) )
=> ( A @ ( sk3 @ ( sk2 @ vtcheck ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( A @ vvar @ ( B @ vtcheck ) ) )
& ( ( A @ vvar @ vreduce )
= ( C @ vsomeExp ) ) )
=> ( D @ ( C @ ( B @ vtcheck ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Preservation-T-var') ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( A @ vvar @ ( B @ vtcheck ) ) )
& ( ( A @ vvar @ vreduce )
= ( C @ vsomeExp ) ) )
=> ( D @ ( C @ ( B @ vtcheck ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(61,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( A @ vvar @ ( B @ vtcheck ) ) )
& ( ( A @ vvar @ vreduce )
= ( C @ vsomeExp ) ) )
=> ( D @ ( C @ ( B @ vtcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(62,plain,
( ~ ( sk4 @ ( sk3 @ ( sk2 @ vtcheck ) ) )
& ( sk4 @ ( sk1 @ vvar @ ( sk2 @ vtcheck ) ) )
& ( ( sk1 @ vvar @ vreduce )
= ( sk3 @ vsomeExp ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
( ( sk1 @ vvar @ vreduce )
= ( sk3 @ vsomeExp ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(66,plain,
( ( sk3 @ vsomeExp )
= ( sk1 @ vvar @ vreduce ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ vsomeExp ) )
=> ( B @ visSomeExp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp1) ).
thf(367,plain,
! [A: $i,B: $i] :
( ( B
= ( A @ vsomeExp ) )
=> ( B @ visSomeExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( B @ visSomeExp )
| ( B
!= ( A @ vsomeExp ) ) ),
inference(cnf,[status(esa)],[367]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( B @ visSomeExp )
| ( B
!= ( A @ vsomeExp ) ) ),
inference(lifteq,[status(thm)],[368]) ).
thf(370,plain,
! [A: $i] : ( A @ vsomeExp @ visSomeExp ),
inference(simp,[status(thm)],[369]) ).
thf(597,plain,
! [A: $i] :
( ( ( sk3 @ vsomeExp )
!= ( A @ vsomeExp ) )
| ( sk1 @ vvar @ vreduce @ visSomeExp ) ),
inference(paramod_ordered,[status(thm)],[66,370]) ).
thf(598,plain,
sk1 @ vvar @ vreduce @ visSomeExp,
inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( sk3 ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( A = vnoExp )
=> ~ ( A @ visSomeExp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp0) ).
thf(158,plain,
! [A: $i] :
( ( A = vnoExp )
=> ~ ( A @ visSomeExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(159,plain,
! [A: $i] :
( ~ ( A @ visSomeExp )
| ( A != vnoExp ) ),
inference(cnf,[status(esa)],[158]) ).
thf(160,plain,
! [A: $i] :
( ~ ( A @ visSomeExp )
| ( A != vnoExp ) ),
inference(lifteq,[status(thm)],[159]) ).
thf(161,plain,
~ ( vnoExp @ visSomeExp ),
inference(simp,[status(thm)],[160]) ).
thf(604,plain,
( ( ( sk1 @ vvar @ vreduce @ visSomeExp )
!= ( vnoExp @ visSomeExp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[598,161]) ).
thf(605,plain,
( ( sk1 @ vvar @ vreduce @ visSomeExp )
!= ( vnoExp @ visSomeExp ) ),
inference(simp,[status(thm)],[604]) ).
thf(606,plain,
( ( sk1 @ vvar @ vreduce )
!= vnoExp ),
inference(simp,[status(thm)],[605]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( B
= ( A @ vvar ) )
=> ( ( C
= ( B @ vreduce ) )
=> ( C = vnoExp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce0) ).
thf(358,plain,
! [A: $i,B: $i,C: $i] :
( ( B
= ( A @ vvar ) )
=> ( ( C
= ( B @ vreduce ) )
=> ( C = vnoExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(359,plain,
! [A: $i,B: $i] :
( ( B
= ( A @ vvar ) )
=> ! [C: $i] :
( ( C
= ( B @ vreduce ) )
=> ( C = vnoExp ) ) ),
inference(miniscope,[status(thm)],[358]) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ( C = vnoExp )
| ( C
!= ( B @ vreduce ) )
| ( B
!= ( A @ vvar ) ) ),
inference(cnf,[status(esa)],[359]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( C = vnoExp )
| ( C
!= ( B @ vreduce ) )
| ( B
!= ( A @ vvar ) ) ),
inference(lifteq,[status(thm)],[360]) ).
thf(362,plain,
! [A: $i] :
( ( A @ vvar @ vreduce )
= vnoExp ),
inference(simp,[status(thm)],[361]) ).
thf(610,plain,
vnoExp != vnoExp,
inference(rewrite,[status(thm)],[606,362]) ).
thf(611,plain,
$false,
inference(simp,[status(thm)],[610]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM146+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
% 0.14/0.41 % Computer : n017.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 23:30:20 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.87/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.52/1.25 % [INFO] Parsing done (272ms).
% 1.52/1.26 % [INFO] Running in sequential loop mode.
% 2.39/1.64 % [INFO] eprover registered as external prover.
% 2.39/1.65 % [INFO] Scanning for conjecture ...
% 2.64/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 58 axioms. Running axiom selection ...
% 2.81/1.87 % [INFO] Axiom selection finished. Selected 58 axioms (removed 0 axioms).
% 3.10/2.02 % [INFO] Problem is first-order (TPTP FOF).
% 3.42/2.05 % [INFO] Type checking passed.
% 3.42/2.06 % [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 ...
% 12.13/4.21 % [INFO] Killing All external provers ...
% 12.13/4.21 % Time passed: 3657ms (effective reasoning time: 2941ms)
% 12.13/4.21 % 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)>
% 12.13/4.21 % Axioms used in derivation (3): isSomeExp1, isSomeExp0, reduce0
% 12.13/4.21 % No. of inferences in proof: 29
% 12.13/4.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3657 ms resp. 2941 ms w/o parsing
% 12.13/4.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.13/4.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------