%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM144+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 : n012.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 11.84s 3.84s
% Output : Refutation 11.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 16 unt; 0 typ; 5 def)
% Number of atoms : 60 ( 41 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 225 ( 21 ~; 5 |; 10 &; 175 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 64 ( 0 ^; 58 !; 1 ?; 64 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(vreduce_decl,type,
vreduce: $i > $i ).
thf(vabs_decl,type,
vabs: $i > $i > $i > $i ).
thf(ve1_decl,type,
ve1: $i ).
thf(vsomeExp_decl,type,
vsomeExp: $i > $i ).
thf(vtcheck_decl,type,
vtcheck: $i > $i > $i > $o ).
thf(vnoExp_decl,type,
vnoExp: $i ).
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(sk5_decl,type,
sk5: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( ve1 @ ( B @ ( A @ vabs ) ) @ ( C @ vtcheck ) ) )
& ( ( ve1 @ ( B @ ( A @ vabs ) ) @ vreduce )
= ( D @ vsomeExp ) ) )
=> ( E @ ( D @ ( C @ vtcheck ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( ve1 @ ( A @ ( sk1 @ vabs ) ) @ ( B @ vtcheck ) ) )
& ( ( ve1 @ ( A @ ( sk1 @ vabs ) ) @ vreduce )
= ( C @ vsomeExp ) ) )
=> ( D @ ( C @ ( B @ vtcheck ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ ( A @ vtcheck ) ) )
& ( ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ vreduce )
= ( B @ vsomeExp ) ) )
=> ( C @ ( B @ ( A @ vtcheck ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ ( sk3 @ vtcheck ) ) )
& ( ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ vreduce )
= ( A @ vsomeExp ) ) )
=> ( B @ ( A @ ( sk3 @ vtcheck ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( A @ ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ ( sk3 @ vtcheck ) ) )
& ( ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ vreduce )
= ( sk4 @ vsomeExp ) ) )
=> ( A @ ( sk4 @ ( sk3 @ vtcheck ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( ve1 @ ( B @ ( A @ vabs ) ) @ ( C @ vtcheck ) ) )
& ( ( ve1 @ ( B @ ( A @ vabs ) ) @ vreduce )
= ( D @ vsomeExp ) ) )
=> ( E @ ( D @ ( C @ vtcheck ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Preservation-T-abs') ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( ve1 @ ( B @ ( A @ vabs ) ) @ ( C @ vtcheck ) ) )
& ( ( ve1 @ ( B @ ( A @ vabs ) ) @ vreduce )
= ( D @ vsomeExp ) ) )
=> ( E @ ( D @ ( C @ vtcheck ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(62,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( ve1 @ ( B @ ( A @ vabs ) ) @ ( C @ vtcheck ) ) )
& ( ( ve1 @ ( B @ ( A @ vabs ) ) @ vreduce )
= ( D @ vsomeExp ) ) )
=> ( E @ ( D @ ( C @ vtcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,plain,
( ~ ( sk5 @ ( sk4 @ ( sk3 @ vtcheck ) ) )
& ( sk5 @ ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ ( sk3 @ vtcheck ) ) )
& ( ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ vreduce )
= ( sk4 @ vsomeExp ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
( ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ vreduce )
= ( sk4 @ vsomeExp ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(67,plain,
( ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ vreduce )
= ( sk4 @ vsomeExp ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(41,axiom,
! [A: $i] :
( vnoExp
!= ( A @ vsomeExp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
thf(479,plain,
! [A: $i] :
( vnoExp
!= ( A @ vsomeExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(480,plain,
~ ? [A: $i] :
( vnoExp
= ( A @ vsomeExp ) ),
inference(miniscope,[status(thm)],[479]) ).
thf(481,plain,
! [A: $i] :
( vnoExp
!= ( A @ vsomeExp ) ),
inference(cnf,[status(esa)],[480]) ).
thf(482,plain,
! [A: $i] :
( ( A @ vsomeExp )
!= vnoExp ),
inference(lifteq,[status(thm)],[481]) ).
thf(598,plain,
! [A: $i] :
( ( ( sk4 @ vsomeExp )
!= ( A @ vsomeExp ) )
| ( ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ vreduce )
!= vnoExp ) ),
inference(paramod_ordered,[status(thm)],[67,482]) ).
thf(599,plain,
( ( ve1 @ ( sk2 @ ( sk1 @ vabs ) ) @ vreduce )
!= vnoExp ),
inference(pattern_uni,[status(thm)],[598:[bind(A,$thf( sk4 ))]]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D
= ( C @ ( B @ ( A @ vabs ) ) ) )
=> ( ( E
= ( D @ vreduce ) )
=> ( E = vnoExp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce1) ).
thf(541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D
= ( C @ ( B @ ( A @ vabs ) ) ) )
=> ( ( E
= ( D @ vreduce ) )
=> ( E = vnoExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( C @ ( B @ ( A @ vabs ) ) ) )
=> ! [E: $i] :
( ( E
= ( D @ vreduce ) )
=> ( E = vnoExp ) ) ),
inference(miniscope,[status(thm)],[541]) ).
thf(543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = vnoExp )
| ( E
!= ( D @ vreduce ) )
| ( D
!= ( C @ ( B @ ( A @ vabs ) ) ) ) ),
inference(cnf,[status(esa)],[542]) ).
thf(544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = vnoExp )
| ( E
!= ( D @ vreduce ) )
| ( D
!= ( C @ ( B @ ( A @ vabs ) ) ) ) ),
inference(lifteq,[status(thm)],[543]) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ vabs ) ) @ vreduce )
= vnoExp ),
inference(simp,[status(thm)],[544]) ).
thf(675,plain,
vnoExp != vnoExp,
inference(rewrite,[status(thm)],[599,545]) ).
thf(676,plain,
$false,
inference(simp,[status(thm)],[675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM144+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % 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
% 0.06/0.32 % Computer : n012.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Sat Sep 26 23:34:50 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.32 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
% 0.64/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.85/0.85 % [INFO] Parsing done (151ms).
% 0.85/0.86 % [INFO] Running in sequential loop mode.
% 1.50/1.09 % [INFO] eprover registered as external prover.
% 1.50/1.09 % [INFO] Scanning for conjecture ...
% 1.87/1.20 % [INFO] Found a conjecture (or negated_conjecture) and 59 axioms. Running axiom selection ...
% 1.87/1.28 % [INFO] Axiom selection finished. Selected 59 axioms (removed 0 axioms).
% 2.36/1.42 % [INFO] Problem is first-order (TPTP FOF).
% 2.36/1.44 % [INFO] Type checking passed.
% 2.36/1.44 % [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 ...
% 11.84/3.83 % [INFO] Killing All external provers ...
% 11.84/3.83 % Time passed: 3411ms (effective reasoning time: 2969ms)
% 11.84/3.84 % 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)>
% 11.84/3.84 % Axioms used in derivation (2): DIFF-noExp-someExp, reduce1
% 11.84/3.84 % No. of inferences in proof: 21
% 11.84/3.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3411 ms resp. 2969 ms w/o parsing
% 11.84/3.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.84/3.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------