%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP687-1 : 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 : n005.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 07:21:46 AM UTC 2026
% Result : Unsatisfiable 3.57s 2.49s
% Output : Refutation 3.80s
% 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 : 90 ( 2 ~; 0 |; 0 &; 88 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% 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(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ ( A @ mult ) @ ( A @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( A @ ( A @ mult ) @ mult ) )
= ( C @ ( B @ ( A @ mult ) @ ( A @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
thf(20,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ mult ) @ ( b @ mult ) @ ( a @ mult ) )
!= ( c @ ( b @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(9,plain,
( ( c @ ( b @ mult ) @ ( b @ mult ) @ ( a @ mult ) )
!= ( c @ ( b @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(63,plain,
$false,
inference(e,[status(thm)],[24,14,20,9,22,12,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP687-1 : 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
% 0.20/0.43 % Computer : n005.cluster.edu
% 0.20/0.43 % Model : x86_64 x86_64
% 0.20/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.43 % Memory : 8046.5625MB
% 0.20/0.43 % OS : Linux 6.8.0-71-generic
% 0.20/0.43 % CPULimit : 300
% 0.20/0.43 % WCLimit : 300
% 0.20/0.43 % DateTime : Fri Sep 25 15:37:02 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.44 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
% 0.86/1.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.21 % [INFO] Parsing done (182ms).
% 1.31/1.22 % [INFO] Running in sequential loop mode.
% 1.87/1.62 % [INFO] eprover registered as external prover.
% 1.87/1.63 % [INFO] Scanning for conjecture ...
% 2.04/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.04/1.75 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.04/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.04/1.77 % [INFO] Type checking passed.
% 2.04/1.78 % [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 ...
% 3.57/2.49 % External prover 'e' found a proof!
% 3.57/2.49 % [INFO] Killing All external provers ...
% 3.57/2.49 % Time passed: 1911ms (effective reasoning time: 1263ms)
% 3.57/2.49 % Axioms used in derivation (7): c05, c04, c01, c03, c06, c02, c07
% 3.57/2.49 % No. of inferences in proof: 17
% 3.57/2.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1911 ms resp. 1263 ms w/o parsing
% 3.80/2.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.80/2.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------