%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP748+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 : n016.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 07:21:54 AM UTC 2026
% Result : Theorem 3.36s 16.84s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 261 ( 2 ~; 11 |; 0 &; 248 @)
% ( 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 : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% 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(i_decl,type,
i: $i > $i ).
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/sandbox/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(14,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/sandbox/benchmark/theBenchmark.p',f04) ).
thf(33,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] :
( ( A @ i @ ( A @ ( B @ mult ) @ mult ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( A @ i @ ( A @ ( B @ mult ) @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ mult ) @ ( B @ ld ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ mult ) @ ( B @ ld ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ mult ) @ ( B @ i @ mult ) )
= A )
| ( ( A @ ( B @ mult ) )
= ( B @ ( A @ mult ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ mult ) @ ( B @ i @ mult ) )
= A )
| ( ( A @ ( B @ mult ) )
= ( B @ ( A @ mult ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(39,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ i @ ( A @ mult ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
thf(48,plain,
! [A: $i] :
( ( A @ i @ ( A @ mult ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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/sandbox/benchmark/theBenchmark.p',f07) ).
thf(42,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(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(36,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ rd ) @ mult ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ rd ) @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( A @ i @ mult ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( A @ i @ mult ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,plain,
$false,
inference(e,[status(thm)],[14,33,45,27,54,39,48,42,24,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP748+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/15.48 % CPULimit : 300
% 0.13/15.48 % WCLimit : 300
% 0.13/15.48 % DateTime : Fri Sep 25 15:44:02 UTC 2026
% 0.13/15.49 % CPUTime :
% 0.13/15.49 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
% 0.38/15.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.38/15.87 % [INFO] Parsing done (95ms).
% 0.38/15.88 % [INFO] Running in sequential loop mode.
% 1.51/16.07 % [INFO] eprover registered as external prover.
% 1.51/16.07 % [INFO] Scanning for conjecture ...
% 1.51/16.13 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.51/16.15 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.79/16.16 % [INFO] Problem is first-order (TPTP FOF).
% 1.79/16.16 % [INFO] Type checking passed.
% 1.79/16.16 % [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 ...
% 3.36/16.83 % External prover 'e' found a proof!
% 3.36/16.83 % [INFO] Killing All external provers ...
% 3.36/16.84 % Time passed: 1260ms (effective reasoning time: 951ms)
% 3.36/16.84 % 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)>
% 3.36/16.84 % Axioms used in derivation (11): f08, f03, f02, f07, f10, f06, f11, f05, f01, f04, f09
% 3.36/16.84 % No. of inferences in proof: 26
% 3.36/16.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1260 ms resp. 951 ms w/o parsing
% 3.36/16.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.36/16.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------