%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% 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 : n007.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 07:21:44 AM UTC 2026
% Result : Unsatisfiable 3.79s 2.49s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 162 ( 2 ~; 0 |; 0 &; 160 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(ld_decl,type,
ld: $i > $i > $i ).
thf(x0_decl,type,
x0: $i ).
thf(x1_decl,type,
x1: $i ).
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(x2_decl,type,
x2: $i ).
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ld ) @ ( A @ mult ) @ ( A @ ld ) )
= ( B @ ( B @ ( A @ ( A @ rd ) @ mult ) @ rd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ld ) @ ( A @ mult ) @ ( A @ ld ) )
= ( B @ ( B @ ( A @ ( A @ rd ) @ mult ) @ rd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ mult ) @ rd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ mult ) @ rd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ mult ) @ ( B @ ( A @ ld ) @ mult ) @ ( B @ ( A @ ld ) @ ld ) )
= ( D @ ( C @ ( A @ mult ) @ ( A @ ld ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(20,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ mult ) @ ( B @ ( A @ ld ) @ mult ) @ ( B @ ( A @ ld ) @ ld ) )
= ( D @ ( C @ ( A @ mult ) @ ( A @ ld ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( x2 @ ( x1 @ ( x0 @ ld ) @ mult ) @ ( x1 @ ( x0 @ ld ) @ ld ) )
!= ( x2 @ ( x0 @ mult ) @ ( x0 @ ld ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(9,plain,
( ( x2 @ ( x1 @ ( x0 @ ld ) @ mult ) @ ( x1 @ ( x0 @ ld ) @ ld ) )
!= ( x2 @ ( x0 @ mult ) @ ( x0 @ ld ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ rd ) @ ( D @ ( C @ rd ) @ ( B @ ( A @ mult ) @ mult ) @ rd ) )
= ( D @ ( D @ ( B @ mult ) @ rd ) @ ( A @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
thf(22,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ rd ) @ ( D @ ( C @ rd ) @ ( B @ ( A @ mult ) @ mult ) @ rd ) )
= ( D @ ( D @ ( B @ mult ) @ rd ) @ ( A @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ mult ) @ ( A @ ld ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(12,plain,
! [A: $i] :
( ( A @ ( A @ mult ) @ ( A @ ld ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= ( B @ ( B @ ( A @ mult ) @ rd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= ( B @ ( B @ ( A @ mult ) @ rd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= ( B @ ( A @ mult ) @ ( A @ ld ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= ( B @ ( A @ mult ) @ ( A @ ld ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,plain,
$false,
inference(e,[status(thm)],[24,14,20,9,22,12,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.16/0.41 % Computer : n007.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 15:33:53 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 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
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.18 % [INFO] Parsing done (177ms).
% 1.28/1.19 % [INFO] Running in sequential loop mode.
% 1.95/1.62 % [INFO] eprover registered as external prover.
% 1.95/1.63 % [INFO] Scanning for conjecture ...
% 2.19/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.19/1.75 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.19/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.19/1.78 % [INFO] Type checking passed.
% 2.19/1.78 % [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 ...
% 3.79/2.48 % External prover 'e' found a proof!
% 3.79/2.48 % [INFO] Killing All external provers ...
% 3.79/2.49 % Time passed: 1926ms (effective reasoning time: 1290ms)
% 3.79/2.49 % Axioms used in derivation (7): f03, f02, f07, f06, f05, f04, f01
% 3.79/2.49 % No. of inferences in proof: 17
% 3.79/2.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1926 ms resp. 1290 ms w/o parsing
% 4.07/2.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.07/2.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------