%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM147+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 : n007.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 12.68s 4.58s
% Output : Refutation 13.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 36 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 164 ( 17 ~; 2 |; 8 &; 129 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 41 ( 0 ^; 32 !; 6 ?; 41 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(vtcheck_decl,type,
vtcheck: $i > $i > $i > $o ).
thf(vempty_decl,type,
vempty: $i ).
thf(vabs_decl,type,
vabs: $i > $i > $i > $i ).
thf(ve1_decl,type,
ve1: $i ).
thf(visValue_decl,type,
visValue: $i > $o ).
thf(vreduce_decl,type,
vreduce: $i > $i ).
thf(vsomeExp_decl,type,
vsomeExp: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ~ ( ve1 @ ( C @ ( B @ vabs ) ) @ visValue )
& ( A @ ( ve1 @ ( C @ ( B @ vabs ) ) @ ( vempty @ vtcheck ) ) ) )
=> ? [D: $i] :
( ( ve1 @ ( C @ ( B @ vabs ) ) @ vreduce )
= ( D @ vsomeExp ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ~ ( ve1 @ ( B @ ( A @ vabs ) ) @ visValue )
& ( sk1 @ ( ve1 @ ( B @ ( A @ vabs ) ) @ ( vempty @ vtcheck ) ) ) )
=> ? [C: $i] :
( ( ve1 @ ( B @ ( A @ vabs ) ) @ vreduce )
= ( C @ vsomeExp ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ~ ( ve1 @ ( A @ ( sk2 @ vabs ) ) @ visValue )
& ( sk1 @ ( ve1 @ ( A @ ( sk2 @ vabs ) ) @ ( vempty @ vtcheck ) ) ) )
=> ? [B: $i] :
( ( ve1 @ ( A @ ( sk2 @ vabs ) ) @ vreduce )
= ( B @ vsomeExp ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ve1 @ ( C @ ( B @ vabs ) ) @ visValue )
& ( A @ ( ve1 @ ( C @ ( B @ vabs ) ) @ ( vempty @ vtcheck ) ) ) )
=> ? [D: $i] :
( ( ve1 @ ( C @ ( B @ vabs ) ) @ vreduce )
= ( D @ vsomeExp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Progress-T-abs') ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( ve1 @ ( C @ ( B @ vabs ) ) @ visValue )
& ( A @ ( ve1 @ ( C @ ( B @ vabs ) ) @ ( vempty @ vtcheck ) ) ) )
=> ? [D: $i] :
( ( ve1 @ ( C @ ( B @ vabs ) ) @ vreduce )
= ( D @ vsomeExp ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(60,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( ve1 @ ( C @ ( B @ vabs ) ) @ visValue )
& ( A @ ( ve1 @ ( C @ ( B @ vabs ) ) @ ( vempty @ vtcheck ) ) ) )
=> ? [D: $i] :
( ( ve1 @ ( C @ ( B @ vabs ) ) @ vreduce )
= ( D @ vsomeExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(61,plain,
! [A: $i] :
( ( ( ve1 @ ( sk3 @ ( sk2 @ vabs ) ) @ vreduce )
!= ( A @ vsomeExp ) )
& ~ ( ve1 @ ( sk3 @ ( sk2 @ vabs ) ) @ visValue )
& ( sk1 @ ( ve1 @ ( sk3 @ ( sk2 @ vabs ) ) @ ( vempty @ vtcheck ) ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(63,plain,
~ ( ve1 @ ( sk3 @ ( sk2 @ vabs ) ) @ visValue ),
inference(cnfConj,[status(thm)],[61]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( C @ ( B @ ( A @ vabs ) ) ) )
=> ( D @ visValue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue0) ).
thf(311,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( C @ ( B @ ( A @ vabs ) ) ) )
=> ( D @ visValue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ visValue )
| ( D
!= ( C @ ( B @ ( A @ vabs ) ) ) ) ),
inference(cnf,[status(esa)],[311]) ).
thf(313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ visValue )
| ( D
!= ( C @ ( B @ ( A @ vabs ) ) ) ) ),
inference(lifteq,[status(thm)],[312]) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ vabs ) ) @ visValue ),
inference(simp,[status(thm)],[313]) ).
thf(607,plain,
~ $true,
inference(rewrite,[status(thm)],[63,314]) ).
thf(608,plain,
$false,
inference(simp,[status(thm)],[607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM147+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
% 0.14/0.39 % Computer : n007.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 23:34:39 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.26 % [INFO] Parsing done (283ms).
% 1.47/1.28 % [INFO] Running in sequential loop mode.
% 2.43/1.68 % [INFO] eprover registered as external prover.
% 2.43/1.69 % [INFO] Scanning for conjecture ...
% 2.86/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 57 axioms. Running axiom selection ...
% 3.07/1.92 % [INFO] Axiom selection finished. Selected 57 axioms (removed 0 axioms).
% 3.46/2.09 % [INFO] Problem is first-order (TPTP FOF).
% 3.46/2.11 % [INFO] Type checking passed.
% 3.46/2.12 % [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 ...
% 12.68/4.57 % [INFO] Killing All external provers ...
% 12.68/4.57 % Time passed: 4028ms (effective reasoning time: 3288ms)
% 12.68/4.57 % 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)>
% 12.68/4.58 % Axioms used in derivation (1): isValue0
% 12.68/4.58 % No. of inferences in proof: 12
% 12.68/4.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4028 ms resp. 3288 ms w/o parsing
% 13.18/4.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.18/4.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------