%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP703-12 : TPTP v9.3.1. Released v8.1.0.
% 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 : n015.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 07:21:48 AM UTC 2026
% Result : Unsatisfiable 2.25s 1.40s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 170 ( 2 ~; 0 |; 0 &; 168 @)
% ( 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 : 12 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(x2_decl,type,
x2: $i ).
thf(op_e_decl,type,
op_e: $i ).
thf(x3_decl,type,
x3: $i ).
thf(ld_decl,type,
ld: $i > $i > $i ).
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(unit_decl,type,
unit: $i ).
thf(op_c_decl,type,
op_c: $i ).
thf(op_d_decl,type,
op_d: $i ).
thf(op_f_decl,type,
op_f: $i ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( x3 @ ( op_e @ mult ) @ ( x2 @ mult ) )
!= ( x3 @ ( op_e @ ( x2 @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(15,plain,
( ( x3 @ ( op_e @ mult ) @ ( x2 @ mult ) )
!= ( x3 @ ( op_e @ ( x2 @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( op_f
= ( op_c @ ( B @ ( A @ mult ) @ ld ) @ ( B @ mult ) @ ( A @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f13) ).
thf(42,plain,
! [B: $i,A: $i] :
( op_f
= ( op_c @ ( B @ ( A @ mult ) @ ld ) @ ( B @ mult ) @ ( A @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i] :
( op_d
= ( A @ ( op_c @ mult ) @ ( A @ ld ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
thf(38,plain,
! [A: $i] :
( op_d
= ( A @ ( op_c @ mult ) @ ( A @ ld ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( op_c @ mult ) )
= ( B @ ( A @ ( op_c @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( op_c @ mult ) )
= ( B @ ( A @ ( op_c @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( op_c @ ( B @ mult ) @ ( A @ mult ) )
= ( op_c @ ( B @ ( A @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( op_c @ ( B @ mult ) @ ( A @ mult ) )
= ( op_c @ ( B @ ( A @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( op_e
= ( A @ ( B @ ( B @ ( A @ mult ) @ ( op_c @ rd ) @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f12) ).
thf(40,plain,
! [B: $i,A: $i] :
( op_e
= ( A @ ( B @ ( B @ ( A @ mult ) @ ( op_c @ rd ) @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(26,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( op_c @ mult ) @ ( A @ mult ) )
= ( B @ ( op_c @ ( A @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( op_c @ mult ) @ ( A @ mult ) )
= ( B @ ( op_c @ ( A @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( B @ mult ) @ ( A @ mult ) )
= ( C @ ( B @ ( B @ ( A @ mult ) @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( B @ mult ) @ ( A @ mult ) )
= ( C @ ( B @ ( B @ ( A @ mult ) @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(48,plain,
$false,
inference(e,[status(thm)],[20,22,18,15,42,24,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP703-12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n015.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 15:41:58 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.80 % [INFO] Parsing done (88ms).
% 0.94/0.81 % [INFO] Running in sequential loop mode.
% 1.14/0.99 % [INFO] eprover registered as external prover.
% 1.14/0.99 % [INFO] Scanning for conjecture ...
% 1.42/1.04 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 1.42/1.05 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.42/1.07 % [INFO] Problem is propositional (TPTP CNF).
% 1.42/1.07 % [INFO] Type checking passed.
% 1.42/1.07 % [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 ...
% 2.25/1.40 % External prover 'e' found a proof!
% 2.25/1.40 % [INFO] Killing All external provers ...
% 2.25/1.40 % Time passed: 892ms (effective reasoning time: 588ms)
% 2.25/1.40 % Axioms used in derivation (13): f08, f03, f07, f10, f06, f11, f05, f01, f12, f02, f13, f04, f09
% 2.25/1.40 % No. of inferences in proof: 29
% 2.25/1.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 892 ms resp. 588 ms w/o parsing
% 2.66/1.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.66/1.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------