%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 07:21:51 AM UTC 2026
% Result : Theorem 12.80s 10.49s
% Output : Refutation 15.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 139 ( 2 ~; 0 |; 3 &; 134 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(op_a_decl,type,
op_a: $i ).
thf(op_b_decl,type,
op_b: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(op_0_decl,type,
op_0: $i ).
thf(minus_decl,type,
minus: $i > $i ).
thf(unit_decl,type,
unit: $i ).
thf(1,conjecture,
! [A: $i] :
( ( ( op_a @ ( op_b @ ( A @ mult ) @ mult ) )
= A )
& ( ( op_b @ ( op_a @ ( A @ mult ) @ mult ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( op_a @ ( op_b @ ( A @ mult ) @ mult ) )
= A )
& ( ( op_b @ ( op_a @ ( A @ mult ) @ mult ) )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i] :
( ( ( op_a @ ( op_b @ ( A @ mult ) @ mult ) )
= A )
& ( ( op_b @ ( op_a @ ( A @ mult ) @ mult ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
( ( op_b @ ( op_a @ mult ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
thf(45,plain,
( ( op_b @ ( op_a @ mult ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ minus @ ( A @ plus ) )
= op_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(27,plain,
! [A: $i] :
( ( A @ minus @ ( A @ plus ) )
= op_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
thf(39,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ plus ) @ plus ) )
= ( A @ ( B @ plus ) @ ( C @ plus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(18,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ plus ) @ plus ) )
= ( A @ ( B @ plus ) @ ( C @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
( ( op_a @ ( op_b @ mult ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
thf(47,plain,
( ( op_a @ ( op_b @ mult ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i] :
( ( op_0 @ ( A @ plus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(24,plain,
! [A: $i] :
( ( op_0 @ ( A @ plus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ plus ) )
= ( B @ ( A @ plus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ plus ) )
= ( B @ ( A @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ mult ) @ mult ) @ mult ) )
= ( B @ ( A @ ( B @ mult ) @ mult ) @ ( C @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ mult ) @ mult ) @ mult ) )
= ( B @ ( A @ ( B @ mult ) @ mult ) @ ( C @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ mult ) @ ( B @ mult ) )
= ( A @ ( A @ ( B @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ mult ) @ ( B @ mult ) )
= ( A @ ( A @ ( B @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ plus ) @ ( C @ mult ) )
= ( A @ ( C @ mult ) @ ( B @ ( C @ mult ) @ plus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ plus ) @ ( C @ mult ) )
= ( A @ ( C @ mult ) @ ( B @ ( C @ mult ) @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1320,plain,
$false,
inference(e,[status(thm)],[14,45,27,39,18,47,42,24,21,33,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.15/5.42 % Computer : n017.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Fri Sep 25 15:35:08 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.43 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
% 1.24/6.26 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.72/6.54 % [INFO] Parsing done (269ms).
% 1.72/6.56 % [INFO] Running in sequential loop mode.
% 2.30/7.04 % [INFO] eprover registered as external prover.
% 2.53/7.04 % [INFO] Scanning for conjecture ...
% 2.53/7.11 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.53/7.14 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.74/7.17 % [INFO] Problem is first-order (TPTP FOF).
% 2.74/7.17 % [INFO] Type checking passed.
% 2.74/7.17 % [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 ...
% 12.80/10.48 % External prover 'e' found a proof!
% 12.80/10.48 % [INFO] Killing All external provers ...
% 12.80/10.48 % Time passed: 4852ms (effective reasoning time: 3917ms)
% 12.80/10.48 % 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)>
% 12.80/10.48 % Axioms used in derivation (11): f08, f03, f02, f07, f10, f06, f11, f05, f01, f04, f09
% 12.80/10.48 % No. of inferences in proof: 26
% 12.80/10.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4852 ms resp. 3917 ms w/o parsing
% 15.78/10.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.78/10.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------