%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP667+6 : 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 : n006.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 07:21:42 AM UTC 2026
% Result : Theorem 15.62s 4.80s
% Output : Refutation 15.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 22 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 251 ( 2 ~; 9 |; 0 &; 240 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(ld_decl,type,
ld: $i > $i > $i ).
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(unit_decl,type,
unit: $i ).
thf(f_decl,type,
f: $i > $i ).
thf(11,axiom,
! [A: $i] :
( ( A @ f @ ( A @ f @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
thf(46,plain,
! [A: $i] :
( ( A @ f @ ( A @ f @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ rd ) @ mult ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ rd ) @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(34,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
( ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( C @ mult ) @ mult ) )
= ( C @ ( B @ ( A @ mult ) @ mult ) @ ( C @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( C @ mult ) @ mult ) )
= ( C @ ( B @ ( A @ mult ) @ ( C @ mult ) @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( C @ mult ) @ ( A @ mult ) )
= ( C @ ( B @ ( C @ ( A @ mult ) @ mult ) @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ mult ) @ ( A @ mult ) @ ( C @ mult ) )
= ( B @ ( C @ ( A @ ( C @ mult ) @ mult ) @ mult ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( C @ mult ) @ mult ) )
= ( C @ ( B @ ( A @ mult ) @ mult ) @ ( C @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( C @ mult ) @ mult ) )
= ( C @ ( B @ ( A @ mult ) @ ( C @ mult ) @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( C @ mult ) @ ( A @ mult ) )
= ( C @ ( B @ ( C @ ( A @ mult ) @ mult ) @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ mult ) @ ( A @ mult ) @ ( C @ mult ) )
= ( B @ ( C @ ( A @ ( C @ mult ) @ mult ) @ mult ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( C @ mult ) @ mult ) )
= ( C @ ( B @ ( A @ mult ) @ mult ) @ ( C @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( C @ mult ) @ mult ) )
= ( C @ ( B @ ( A @ mult ) @ ( C @ mult ) @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mult ) @ ( C @ mult ) @ ( A @ mult ) )
= ( C @ ( B @ ( C @ ( A @ mult ) @ mult ) @ mult ) ) )
| ! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ mult ) @ ( A @ mult ) @ ( C @ mult ) )
= ( B @ ( C @ ( A @ ( C @ mult ) @ mult ) @ mult ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ mult ) @ rd ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ mult ) @ rd ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ mult ) @ mult ) )
= ( B @ ( A @ mult ) @ ( B @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ mult ) @ mult ) )
= ( B @ ( A @ mult ) @ ( B @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( A @ mult ) @ mult ) @ ( B @ ( C @ mult ) @ mult ) )
= ( A @ ( B @ ( A @ ( B @ mult ) @ mult ) @ ( C @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( A @ mult ) @ mult ) @ ( B @ ( C @ mult ) @ mult ) )
= ( A @ ( B @ ( A @ ( B @ mult ) @ mult ) @ ( C @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ mult ) @ ( B @ ld ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ mult ) @ ( B @ ld ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1687,plain,
$false,
inference(e,[status(thm)],[46,28,34,22,12,31,43,40,37,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP667+6 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.14/0.40 % Computer : n006.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 15:34:10 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.18 % [INFO] Parsing done (181ms).
% 1.24/1.19 % [INFO] Running in sequential loop mode.
% 1.86/1.59 % [INFO] eprover registered as external prover.
% 2.06/1.60 % [INFO] Scanning for conjecture ...
% 2.24/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 2.24/1.75 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.24/1.77 % [INFO] Problem is first-order (TPTP FOF).
% 2.24/1.77 % [INFO] Type checking passed.
% 2.24/1.78 % [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 ...
% 12.82/4.80 % External prover 'e' found a proof!
% 12.82/4.80 % [INFO] Killing All external provers ...
% 15.62/4.80 % Time passed: 4244ms (effective reasoning time: 3599ms)
% 15.62/4.80 % 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)>
% 15.62/4.80 % Axioms used in derivation (9): f08, f03, f02, f07, f06, f05, f01, f04, f09
% 15.62/4.80 % No. of inferences in proof: 22
% 15.62/4.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4244 ms resp. 3599 ms w/o parsing
% 15.62/4.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.62/4.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------