%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP050-1 : 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 : n019.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 3.78s 7.23s
% Output : Refutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 35
% Syntax : Number of formulae : 71 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 70 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 282 ( 2 ~; 0 |; 0 &; 280 @)
% ( 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 : 36 ( 34 usr; 33 con; 0-31 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 > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a1_decl,type,
a1: $i ).
thf(a30_decl,type,
a30: $i ).
thf(a31_decl,type,
a31: $i ).
thf(a2_decl,type,
a2: $i ).
thf(a24_decl,type,
a24: $i ).
thf(a25_decl,type,
a25: $i ).
thf(a3_decl,type,
a3: $i ).
thf(a28_decl,type,
a28: $i ).
thf(a29_decl,type,
a29: $i ).
thf(a4_decl,type,
a4: $i ).
thf(a10_decl,type,
a10: $i ).
thf(a11_decl,type,
a11: $i ).
thf(a5_decl,type,
a5: $i ).
thf(a14_decl,type,
a14: $i ).
thf(a15_decl,type,
a15: $i ).
thf(a6_decl,type,
a6: $i ).
thf(a7_decl,type,
a7: $i ).
thf(a18_decl,type,
a18: $i ).
thf(a19_decl,type,
a19: $i ).
thf(a8_decl,type,
a8: $i ).
thf(a9_decl,type,
a9: $i ).
thf(a16_decl,type,
a16: $i ).
thf(a17_decl,type,
a17: $i ).
thf(a12_decl,type,
a12: $i ).
thf(a13_decl,type,
a13: $i ).
thf(a20_decl,type,
a20: $i ).
thf(a21_decl,type,
a21: $i ).
thf(a22_decl,type,
a22: $i ).
thf(a23_decl,type,
a23: $i ).
thf(a26_decl,type,
a26: $i ).
thf(a27_decl,type,
a27: $i ).
thf(a32_decl,type,
a32: $i ).
thf(product_decl,type,
product: $i > $i > $i ).
thf(25,axiom,
( ( a3 @ ( a24 @ product ) )
= a25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_24) ).
thf(85,plain,
( ( a3 @ ( a24 @ product ) )
= a25 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
( ( a25 @ ( a21 @ product ) )
= a22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_21) ).
thf(53,plain,
( ( a25 @ ( a21 @ product ) )
= a22 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
( ( a11 @ ( a4 @ product ) )
= a5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
thf(77,plain,
( ( a11 @ ( a4 @ product ) )
= a5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ product ) @ product ) )
= ( C @ ( B @ product ) @ ( C @ ( A @ product ) @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).
thf(41,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)],[3]) ).
thf(5,axiom,
( ( a7 @ ( a10 @ product ) )
= a11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
thf(45,plain,
( ( a7 @ ( a10 @ product ) )
= a11 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
( ( a21 @ ( a32 @ product ) )
= a1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_32) ).
thf(59,plain,
( ( a21 @ ( a32 @ product ) )
= a1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
( ( a19 @ ( a12 @ product ) )
= a13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_12) ).
thf(67,plain,
( ( a19 @ ( a12 @ product ) )
= a13 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
( ( a21 @ ( a27 @ product ) )
= a28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_27) ).
thf(55,plain,
( ( a21 @ ( a27 @ product ) )
= a28 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
( ( a1 @ ( a29 @ product ) )
= a30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_29) ).
thf(75,plain,
( ( a1 @ ( a29 @ product ) )
= a30 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,axiom,
( ( a5 @ ( a8 @ product ) )
= a9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
thf(79,plain,
( ( a5 @ ( a8 @ product ) )
= a9 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
( ( a21 @ ( a23 @ product ) )
= a24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_23) ).
thf(47,plain,
( ( a21 @ ( a23 @ product ) )
= a24 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
( ( a15 @ ( a5 @ product ) )
= a6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
thf(83,plain,
( ( a15 @ ( a5 @ product ) )
= a6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17,axiom,
( ( a3 @ ( a31 @ product ) )
= a32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_31) ).
thf(69,plain,
( ( a3 @ ( a31 @ product ) )
= a32 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(33,axiom,
( ( a15 @ ( a18 @ product ) )
= a19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_18) ).
thf(101,plain,
( ( a15 @ ( a18 @ product ) )
= a19 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(29,axiom,
( ( a7 @ ( a13 @ product ) )
= a14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_13) ).
thf(93,plain,
( ( a7 @ ( a13 @ product ) )
= a14 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(11,axiom,
( ( a31 @ ( a22 @ product ) )
= a23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_22) ).
thf(57,plain,
( ( a31 @ ( a22 @ product ) )
= a23 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
( ( a11 @ ( a19 @ product ) )
= a20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_19) ).
thf(61,plain,
( ( a11 @ ( a19 @ product ) )
= a20 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
( ( a29 @ ( a20 @ product ) )
= a21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_20) ).
thf(89,plain,
( ( a29 @ ( a20 @ product ) )
= a21 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(15,axiom,
( ( a5 @ ( a15 @ product ) )
= a16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_15) ).
thf(65,plain,
( ( a5 @ ( a15 @ product ) )
= a16 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
( ( a9 @ ( a17 @ product ) )
= a18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_17) ).
thf(97,plain,
( ( a9 @ ( a17 @ product ) )
= a18 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
( ( a1 @ ( a26 @ product ) )
= a27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_26) ).
thf(73,plain,
( ( a1 @ ( a26 @ product ) )
= a27 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
( ( a17 @ ( a9 @ product ) )
= a10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
thf(105,plain,
( ( a17 @ ( a9 @ product ) )
= a10 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(18,axiom,
( ( a29 @ ( a3 @ product ) )
= a4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
thf(71,plain,
( ( a29 @ ( a3 @ product ) )
= a4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
( ( a19 @ ( a16 @ product ) )
= a17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_16) ).
thf(49,plain,
( ( a19 @ ( a16 @ product ) )
= a17 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
( ( a5 @ ( a11 @ product ) )
= a12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
thf(81,plain,
( ( a5 @ ( a11 @ product ) )
= a12 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
thf(39,plain,
! [A: $i] :
( ( A @ ( A @ product ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,axiom,
( ( a23 @ ( a25 @ product ) )
= a26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_25) ).
thf(103,plain,
( ( a23 @ ( a25 @ product ) )
= a26 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(28,axiom,
( ( a23 @ ( a30 @ product ) )
= a31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_30) ).
thf(91,plain,
( ( a23 @ ( a30 @ product ) )
= a31 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
( ( a31 @ ( a1 @ product ) )
= a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
thf(63,plain,
( ( a31 @ ( a1 @ product ) )
= a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
( ( a25 @ ( a2 @ product ) )
= a3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
thf(95,plain,
( ( a25 @ ( a2 @ product ) )
= a3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
( ( a3 @ ( a28 @ product ) )
= a29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_28) ).
thf(99,plain,
( ( a3 @ ( a28 @ product ) )
= a29 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(26,axiom,
( ( a19 @ ( a7 @ product ) )
= a8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
thf(87,plain,
( ( a19 @ ( a7 @ product ) )
= a8 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1,negated_conjecture,
( ( a27 @ ( a26 @ ( a23 @ ( a22 @ ( a21 @ ( a20 @ ( a13 @ ( a12 @ ( a17 @ ( a16 @ ( a9 @ ( a8 @ ( a19 @ ( a18 @ ( a7 @ ( a6 @ ( a15 @ ( a14 @ ( a5 @ ( a11 @ ( a10 @ ( a4 @ ( a29 @ ( a28 @ ( a3 @ ( a25 @ ( a24 @ ( a2 @ ( a31 @ ( a30 @ ( a1 @ tuple ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( a28 @ ( a27 @ ( a24 @ ( a23 @ ( a22 @ ( a21 @ ( a14 @ ( a13 @ ( a18 @ ( a17 @ ( a10 @ ( a9 @ ( a20 @ ( a19 @ ( a8 @ ( a7 @ ( a16 @ ( a15 @ ( a6 @ ( a12 @ ( a11 @ ( a5 @ ( a30 @ ( a29 @ ( a4 @ ( a26 @ ( a25 @ ( a3 @ ( a32 @ ( a31 @ ( a2 @ tuple ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(36,plain,
( ( a27 @ ( a26 @ ( a23 @ ( a22 @ ( a21 @ ( a20 @ ( a13 @ ( a12 @ ( a17 @ ( a16 @ ( a9 @ ( a8 @ ( a19 @ ( a18 @ ( a7 @ ( a6 @ ( a15 @ ( a14 @ ( a5 @ ( a11 @ ( a10 @ ( a4 @ ( a29 @ ( a28 @ ( a3 @ ( a25 @ ( a24 @ ( a2 @ ( a31 @ ( a30 @ ( a1 @ tuple ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( a28 @ ( a27 @ ( a24 @ ( a23 @ ( a22 @ ( a21 @ ( a14 @ ( a13 @ ( a18 @ ( a17 @ ( a10 @ ( a9 @ ( a20 @ ( a19 @ ( a8 @ ( a7 @ ( a16 @ ( a15 @ ( a6 @ ( a12 @ ( a11 @ ( a5 @ ( a30 @ ( a29 @ ( a4 @ ( a26 @ ( a25 @ ( a3 @ ( a32 @ ( a31 @ ( a2 @ tuple ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
( ( a17 @ ( a14 @ product ) )
= a15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_14) ).
thf(51,plain,
( ( a17 @ ( a14 @ product ) )
= a15 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(132,plain,
$false,
inference(e,[status(thm)],[85,53,77,41,45,59,67,43,55,75,79,47,83,69,101,93,57,61,89,65,97,73,105,71,49,81,39,103,91,63,95,99,87,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP050-1 : 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
% 0.13/5.63 % Computer : n019.cluster.edu
% 0.13/5.63 % Model : x86_64 x86_64
% 0.13/5.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.63 % Memory : 8046.5625MB
% 0.13/5.63 % OS : Linux 6.8.0-71-generic
% 0.13/5.63 % CPULimit : 300
% 0.13/5.63 % WCLimit : 300
% 0.13/5.63 % DateTime : Sat Sep 26 20:50:43 UTC 2026
% 0.13/5.63 % CPUTime :
% 0.13/5.63 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
% 0.18/5.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/6.03 % [INFO] Parsing done (104ms).
% 0.97/6.03 % [INFO] Running in sequential loop mode.
% 1.34/6.22 % [INFO] eprover registered as external prover.
% 1.34/6.23 % [INFO] Scanning for conjecture ...
% 1.34/6.28 % [INFO] Found a conjecture (or negated_conjecture) and 34 axioms. Running axiom selection ...
% 1.60/6.34 % [INFO] Axiom selection finished. Selected 34 axioms (removed 0 axioms).
% 1.60/6.37 % [INFO] Problem is propositional (TPTP CNF).
% 1.60/6.38 % [INFO] Type checking passed.
% 1.60/6.38 % [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 ...
% 3.78/7.23 % External prover 'e' found a proof!
% 3.78/7.23 % [INFO] Killing All external provers ...
% 3.78/7.23 % Time passed: 1513ms (effective reasoning time: 1192ms)
% 3.78/7.23 % Axioms used in derivation (34): knot_19, knot_21, knot_29, knot_03, knot_12, knot_27, knot_23, knot_31, involutory_quandle_02, involutory_quandle_01, knot_04, knot_26, knot_18, knot_32, knot_07, knot_15, knot_10, knot_11, knot_06, knot_17, knot_14, knot_22, involutory_quandle, knot_25, knot_28, knot_30, knot_05, knot_16, knot, knot_09, knot_24, knot_13, knot_20, knot_08
% 3.78/7.23 % No. of inferences in proof: 71
% 3.78/7.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1513 ms resp. 1192 ms w/o parsing
% 4.24/7.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.24/7.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------