%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP049-1 : 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 : 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 09:52:36 AM UTC 2026
% Result : Unsatisfiable 3.66s 2.34s
% Output : Refutation 3.66s
% 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 : 110 ( 2 ~; 0 |; 0 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 11 con; 0-9 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(tuple_decl,type,
tuple: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a1_decl,type,
a1: $i ).
thf(a9_decl,type,
a9: $i ).
thf(a8_decl,type,
a8: $i ).
thf(a6_decl,type,
a6: $i ).
thf(a7_decl,type,
a7: $i ).
thf(a2_decl,type,
a2: $i ).
thf(a3_decl,type,
a3: $i ).
thf(a4_decl,type,
a4: $i ).
thf(a5_decl,type,
a5: $i ).
thf(a10_decl,type,
a10: $i ).
thf(product_decl,type,
product: $i > $i > $i ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ product ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ product ) @ product ) )
= ( C @ ( B @ product ) @ ( C @ ( A @ product ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_02) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ product ) @ product ) )
= ( C @ ( B @ product ) @ ( C @ ( A @ product ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).
thf(18,plain,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( a5 @ ( a4 @ ( a3 @ ( a2 @ ( a7 @ ( a6 @ ( a8 @ ( a9 @ ( a1 @ tuple ) ) ) ) ) ) ) ) )
!= ( a6 @ ( a5 @ ( a4 @ ( a3 @ ( a8 @ ( a7 @ ( a9 @ ( a10 @ ( a2 @ tuple ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(15,plain,
( ( a5 @ ( a4 @ ( a3 @ ( a2 @ ( a7 @ ( a6 @ ( a8 @ ( a9 @ ( a1 @ tuple ) ) ) ) ) ) ) ) )
!= ( a6 @ ( a5 @ ( a4 @ ( a3 @ ( a8 @ ( a7 @ ( a9 @ ( a10 @ ( a2 @ tuple ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
( a9
= ( a8 @ ( a4 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
thf(42,plain,
( a9
= ( a8 @ ( a4 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
( a1
= ( a7 @ ( a9 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
thf(24,plain,
( a1
= ( a7 @ ( a9 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
( a2
= ( a4 @ ( a3 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
thf(28,plain,
( a2
= ( a4 @ ( a3 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
( a10
= ( a9 @ ( a8 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
thf(38,plain,
( a10
= ( a9 @ ( a8 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
( a6
= ( a4 @ ( a5 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
thf(32,plain,
( a6
= ( a4 @ ( a5 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
( a7
= ( a1 @ ( a6 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
thf(34,plain,
( a7
= ( a1 @ ( a6 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
( a4
= ( a3 @ ( a10 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
thf(40,plain,
( a4
= ( a3 @ ( a10 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
( a3
= ( a2 @ ( a1 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
thf(26,plain,
( a3
= ( a2 @ ( a1 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
( a8
= ( a4 @ ( a7 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
thf(36,plain,
( a8
= ( a4 @ ( a7 @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
( a5
= ( a10 @ ( a2 @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).
thf(30,plain,
( a5
= ( a10 @ ( a2 @ product ) ) ),
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 : TOP049-1 : 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
% 0.14/0.41 % Computer : n005.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 20:50:01 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.93/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.19 % [INFO] Parsing done (182ms).
% 1.49/1.20 % [INFO] Running in sequential loop mode.
% 2.10/1.60 % [INFO] eprover registered as external prover.
% 2.10/1.61 % [INFO] Scanning for conjecture ...
% 2.30/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.30/1.73 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.30/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.30/1.76 % [INFO] Type checking passed.
% 2.30/1.76 % [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 ...
% 3.66/2.33 % External prover 'e' found a proof!
% 3.66/2.33 % [INFO] Killing All external provers ...
% 3.66/2.33 % Time passed: 1769ms (effective reasoning time: 1127ms)
% 3.66/2.34 % Axioms used in derivation (13): knot_07, knot_10, involutory_quandle, knot_03, knot_05, knot_08, involutory_quandle_02, involutory_quandle_01, knot_04, knot_11, knot_06, knot, knot_09
% 3.66/2.34 % No. of inferences in proof: 29
% 3.66/2.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1769 ms resp. 1127 ms w/o parsing
% 3.66/2.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.66/2.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------