%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 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 : n026.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 06:46:18 AM UTC 2026
% Result : Theorem 2.57s 11.40s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 11 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 64 ( 2 ~; 0 |; 10 &; 46 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 17 !; 3 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(element_decl,type,
element: $i > $o ).
thf(times_decl,type,
times: $i > $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( B @ ( A @ times ) ) )
& ( B @ element )
& ( A @ element ) )
=> ( C @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C
= ( B @ ( A @ times ) ) )
& ( B @ element )
& ( A @ element ) )
=> ( C @ element ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C
= ( B @ ( A @ times ) ) )
& ( B @ element )
& ( A @ element ) )
=> ( C @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ times ) @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(12,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ times ) @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ element )
<=> ? [B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(15,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) )
=> ( A @ element ) )
& ( ( A @ element )
=> ? [B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[5,12,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % 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
% 0.13/10.41 % Computer : n026.cluster.edu
% 0.13/10.41 % Model : x86_64 x86_64
% 0.13/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.41 % Memory : 8046.5625MB
% 0.13/10.41 % OS : Linux 6.8.0-71-generic
% 0.13/10.41 % CPULimit : 300
% 0.13/10.41 % WCLimit : 300
% 0.13/10.41 % DateTime : Sat Sep 26 21:28:52 UTC 2026
% 0.13/10.41 % CPUTime :
% 0.13/10.41 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
% 0.17/10.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/10.79 % [INFO] Parsing done (86ms).
% 0.17/10.80 % [INFO] Running in sequential loop mode.
% 0.17/10.98 % [INFO] eprover registered as external prover.
% 0.17/10.98 % [INFO] Scanning for conjecture ...
% 0.17/11.03 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.38/11.04 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.38/11.05 % [INFO] Problem is first-order (TPTP FOF).
% 1.38/11.05 % [INFO] Type checking passed.
% 1.38/11.05 % [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 ...
% 2.57/11.40 % External prover 'e' found a proof!
% 2.57/11.40 % [INFO] Killing All external provers ...
% 2.57/11.40 % Time passed: 898ms (effective reasoning time: 598ms)
% 2.57/11.40 % 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)>
% 2.57/11.40 % Axioms used in derivation (2): axiom_1, axiom_2
% 2.57/11.40 % No. of inferences in proof: 8
% 2.57/11.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 898 ms resp. 598 ms w/o parsing
% 2.57/11.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.57/11.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------