%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP747+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n014.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 07:21:53 AM UTC 2026
% Result : Theorem 19.25s 15.84s
% Output : Refutation 19.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 160 ( 2 ~; 2 |; 4 &; 152 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(ld_decl,type,
ld: $i > $i > $i ).
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(unit_decl,type,
unit: $i ).
thf(7,axiom,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(25,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(13,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ mult ) @ ( A @ mult ) )
= ( B @ ( C @ mult ) @ ( A @ mult ) ) )
& ( ( C @ ( B @ ( A @ mult ) @ mult ) )
= ( B @ ( C @ ( A @ mult ) @ mult ) ) ) )
| ( ( ( B @ ( C @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ mult ) @ ( A @ mult ) ) )
& ( ( C @ ( B @ ( A @ mult ) @ mult ) )
= ( B @ ( C @ mult ) @ ( A @ mult ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ mult ) @ ( A @ mult ) )
= ( B @ ( C @ mult ) @ ( A @ mult ) ) )
& ( ( C @ ( B @ ( A @ mult ) @ mult ) )
= ( B @ ( C @ ( A @ mult ) @ mult ) ) ) )
| ( ( ( B @ ( C @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ mult ) @ ( A @ mult ) ) )
& ( ( C @ ( B @ ( A @ mult ) @ mult ) )
= ( B @ ( C @ mult ) @ ( A @ mult ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ mult ) @ rd ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ mult ) @ rd ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
( ( c @ ( b @ ( a @ mult ) @ mult ) )
= ( c @ ( b @ mult ) @ ( a @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
( ( c @ ( b @ ( a @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
( ( c @ ( b @ ( a @ mult ) @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ rd ) @ mult ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ rd ) @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ mult ) @ ( B @ ld ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ mult ) @ ( B @ ld ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ mult ) @ mult ) @ mult ) )
= ( B @ ( A @ ( B @ mult ) @ mult ) @ ( C @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
thf(31,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)],[9]) ).
thf(1752,plain,
$false,
inference(e,[status(thm)],[25,28,13,34,22,11,19,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP747+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.15/10.42 % Computer : n014.cluster.edu
% 0.15/10.42 % Model : x86_64 x86_64
% 0.15/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.42 % Memory : 8046.5625MB
% 0.15/10.42 % OS : Linux 6.8.0-71-generic
% 0.15/10.43 % CPULimit : 300
% 0.15/10.43 % WCLimit : 300
% 0.15/10.43 % DateTime : Fri Sep 25 15:43:27 UTC 2026
% 0.15/10.43 % CPUTime :
% 0.15/10.43 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
% 1.31/11.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/11.51 % [INFO] Parsing done (262ms).
% 1.85/11.53 % [INFO] Running in sequential loop mode.
% 2.65/12.13 % [INFO] eprover registered as external prover.
% 2.65/12.14 % [INFO] Scanning for conjecture ...
% 2.97/12.24 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.97/12.27 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.15/12.30 % [INFO] Problem is first-order (TPTP FOF).
% 3.15/12.30 % [INFO] Type checking passed.
% 3.15/12.31 % [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 ...
% 19.25/15.83 % External prover 'e' found a proof!
% 19.25/15.83 % [INFO] Killing All external provers ...
% 19.25/15.83 % Time passed: 5213ms (effective reasoning time: 4295ms)
% 19.25/15.83 % 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)>
% 19.25/15.83 % Axioms used in derivation (8): f08, f03, f02, f07, f06, f05, f04, f01
% 19.25/15.83 % No. of inferences in proof: 20
% 19.25/15.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5213 ms resp. 4295 ms w/o parsing
% 19.25/15.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.25/15.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------