%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP685+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 : n020.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 07:21:45 AM UTC 2026
% Result : Theorem 5.53s 3.41s
% Output : Refutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 213 ( 2 ~; 0 |; 3 &; 208 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(ld_decl,type,
ld: $i > $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rd ) @ ( C @ ( B @ rd ) @ ( A @ mult ) @ rd ) )
= ( C @ ( C @ ( A @ mult ) @ rd ) ) )
& ( ( C @ ( B @ ld ) @ ( C @ ( B @ ld ) @ ( A @ mult ) @ rd ) )
= ( C @ ( C @ ( A @ mult ) @ rd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rd ) @ ( C @ ( B @ rd ) @ ( A @ mult ) @ rd ) )
= ( C @ ( C @ ( A @ mult ) @ rd ) ) )
& ( ( C @ ( B @ ld ) @ ( C @ ( B @ ld ) @ ( A @ mult ) @ rd ) )
= ( C @ ( C @ ( A @ mult ) @ rd ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rd ) @ ( C @ ( B @ rd ) @ ( A @ mult ) @ rd ) )
= ( C @ ( C @ ( A @ mult ) @ rd ) ) )
& ( ( C @ ( B @ ld ) @ ( C @ ( B @ ld ) @ ( A @ mult ) @ rd ) )
= ( C @ ( C @ ( A @ mult ) @ rd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ mult ) @ ( A @ ld ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( A @ mult ) @ ( A @ ld ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= ( A @ ( B @ mult ) @ ( B @ ld ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= ( A @ ( B @ mult ) @ ( B @ ld ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ rd ) @ ( A @ ( B @ rd ) @ ( C @ ( D @ mult ) @ mult ) @ rd ) )
= ( A @ ( A @ ( C @ mult ) @ rd ) @ ( D @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
thf(29,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ rd ) @ ( A @ ( B @ rd ) @ ( C @ ( D @ mult ) @ mult ) @ rd ) )
= ( A @ ( A @ ( C @ mult ) @ rd ) @ ( D @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ld ) @ ( B @ mult ) @ ( B @ ld ) )
= ( A @ ( A @ ( B @ ( B @ rd ) @ mult ) @ rd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ld ) @ ( B @ mult ) @ ( B @ ld ) )
= ( A @ ( A @ ( B @ ( B @ rd ) @ mult ) @ rd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ mult ) @ rd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ mult ) @ rd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ mult ) @ ( C @ ( D @ ld ) @ mult ) @ ( C @ ( D @ ld ) @ ld ) )
= ( A @ ( B @ ( D @ mult ) @ ( D @ ld ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(26,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ mult ) @ ( C @ ( D @ ld ) @ mult ) @ ( C @ ( D @ ld ) @ ld ) )
= ( A @ ( B @ ( D @ mult ) @ ( D @ ld ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ rd ) @ mult ) )
= ( A @ ( A @ ( B @ mult ) @ rd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ rd ) @ mult ) )
= ( A @ ( A @ ( B @ mult ) @ rd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[10,14,20,29,32,17,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP685+1 : 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
% 0.15/0.40 % Computer : n020.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 15:38:18 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 1.27/1.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.75/1.55 % [INFO] Parsing done (278ms).
% 1.75/1.57 % [INFO] Running in sequential loop mode.
% 2.71/2.19 % [INFO] eprover registered as external prover.
% 2.79/2.20 % [INFO] Scanning for conjecture ...
% 2.97/2.35 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 3.14/2.41 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 3.14/2.45 % [INFO] Problem is first-order (TPTP FOF).
% 3.14/2.45 % [INFO] Type checking passed.
% 3.14/2.46 % [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 ...
% 5.53/3.40 % External prover 'e' found a proof!
% 5.53/3.40 % [INFO] Killing All external provers ...
% 5.53/3.40 % Time passed: 2786ms (effective reasoning time: 1823ms)
% 5.53/3.40 % 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)>
% 5.53/3.41 % Axioms used in derivation (7): f03, f02, f07, f06, f05, f04, f01
% 5.53/3.41 % No. of inferences in proof: 18
% 5.53/3.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2786 ms resp. 1823 ms w/o parsing
% 5.53/3.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.53/3.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------