%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 : Fri Sep 25 03:55:29 PM UTC 2026
% Result : Unsatisfiable 2.75s 1.18s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 86 ( 86 unt; 0 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-9 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).
fof(f2,axiom,
! [X0,X1] : product(product(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).
fof(f3,axiom,
! [X2,X0,X1] : product(product(X0,X1),X2) = product(product(X0,X2),product(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_02) ).
fof(f4,axiom,
a1 = product(a9,a7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
fof(f5,axiom,
a3 = product(a1,a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
fof(f6,axiom,
a2 = product(a3,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
fof(f8,axiom,
a6 = product(a5,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
fof(f9,axiom,
a7 = product(a6,a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
fof(f10,axiom,
a8 = product(a7,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
fof(f11,axiom,
a10 = product(a8,a9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
fof(f12,axiom,
a4 = product(a10,a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
fof(f13,axiom,
a9 = product(a4,a8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
fof(f14,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tcf(c_63,plain,
! [X0: $i] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),product(X2,X1)) = product(product(X0,X2),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
product(a9,a7) = a1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
product(a1,a2) = a3,
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
product(a3,a4) = a2,
inference(cnf_transformation,[],[f6]) ).
tcf(c_70,plain,
product(a5,a4) = a6,
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
product(a6,a1) = a7,
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
product(a7,a4) = a8,
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
product(a8,a9) = a10,
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,plain,
product(a10,a3) = a4,
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,plain,
product(a4,a8) = a9,
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(cnf_transformation,[],[f14]) ).
tcf(c_181,plain,
product(a1,a7) = a9,
inference(superposition,[status(thm)],[c_66,c_64]) ).
tcf(c_182,plain,
product(a3,a2) = a1,
inference(superposition,[status(thm)],[c_67,c_64]) ).
tcf(c_183,plain,
product(a2,a4) = a3,
inference(superposition,[status(thm)],[c_68,c_64]) ).
tcf(c_185,plain,
product(a6,a4) = a5,
inference(superposition,[status(thm)],[c_70,c_64]) ).
tcf(c_187,plain,
product(a8,a4) = a7,
inference(superposition,[status(thm)],[c_72,c_64]) ).
tcf(c_188,plain,
product(a10,a9) = a8,
inference(superposition,[status(thm)],[c_73,c_64]) ).
tcf(c_189,plain,
product(a4,a3) = a10,
inference(superposition,[status(thm)],[c_74,c_64]) ).
tcf(c_190,plain,
product(a9,a8) = a4,
inference(superposition,[status(thm)],[c_75,c_64]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c_63,c_65]) ).
tcf(c_205,plain,
! [X0: $i] : product(product(a9,X0),a7) = product(a1,product(X0,a7)),
inference(superposition,[status(thm)],[c_66,c_65]) ).
tcf(c_211,plain,
! [X0: $i] : product(product(a7,X0),a4) = product(a8,product(X0,a4)),
inference(superposition,[status(thm)],[c_72,c_65]) ).
tcf(c_213,plain,
! [X0: $i] : product(product(a10,X0),a3) = product(a4,product(X0,a3)),
inference(superposition,[status(thm)],[c_74,c_65]) ).
tcf(c_376,plain,
product(a8,product(a9,a8)) = product(a10,a8),
inference(superposition,[status(thm)],[c_73,c_202]) ).
tcf(c_378,plain,
product(a4,product(a8,a4)) = product(a9,a4),
inference(superposition,[status(thm)],[c_75,c_202]) ).
tcf(c_381,plain,
product(a2,product(a4,a2)) = product(a3,a2),
inference(superposition,[status(thm)],[c_183,c_202]) ).
tcf(c_385,plain,
product(a8,product(a4,a8)) = product(a7,a8),
inference(superposition,[status(thm)],[c_187,c_202]) ).
tcf(c_387,plain,
product(a4,product(a3,a4)) = product(a10,a4),
inference(superposition,[status(thm)],[c_189,c_202]) ).
tcf(c_398,plain,
product(a4,a2) = product(a10,a4),
inference(light_normalisation,[status(thm)],[c_387,c_68]) ).
tcf(c_399,plain,
product(a7,a8) = a10,
inference(light_normalisation,[status(thm)],[c_385,c_73,c_75]) ).
tcf(c_401,plain,
product(a2,product(a4,a2)) = a1,
inference(light_normalisation,[status(thm)],[c_381,c_182]) ).
tcf(c_403,plain,
product(a9,a4) = product(a4,a7),
inference(light_normalisation,[status(thm)],[c_378,c_187]) ).
tcf(c_404,plain,
product(a10,a8) = a7,
inference(light_normalisation,[status(thm)],[c_376,c_187,c_190]) ).
tcf(c_465,plain,
product(a1,product(a8,a7)) = product(a4,a7),
inference(superposition,[status(thm)],[c_190,c_205]) ).
tcf(c_624,plain,
product(a1,product(a4,a2)) = a2,
inference(superposition,[status(thm)],[c_401,c_64]) ).
tcf(c_1179,plain,
product(a8,product(a8,a4)) = product(a10,a4),
inference(superposition,[status(thm)],[c_399,c_211]) ).
tcf(c_1186,plain,
product(a4,a2) = product(a8,a7),
inference(light_normalisation,[status(thm)],[c_1179,c_187,c_398]) ).
tcf(c_1191,plain,
product(a1,product(a4,a2)) = product(a4,a7),
inference(demodulation,[status(thm)],[c_465,c_1186]) ).
tcf(c_1193,plain,
product(a4,a7) = a2,
inference(light_normalisation,[status(thm)],[c_1191,c_624]) ).
tcf(c_1194,plain,
product(a9,a4) = a2,
inference(demodulation,[status(thm)],[c_403,c_1193]) ).
tcf(c_1246,plain,
product(a4,product(a3,a3)) = a10,
inference(superposition,[status(thm)],[c_213,c_64]) ).
tcf(c_1302,plain,
product(a4,product(a7,a4)) = product(a2,a4),
inference(superposition,[status(thm)],[c_1193,c_202]) ).
tcf(c_1306,plain,
a9 = a3,
inference(light_normalisation,[status(thm)],[c_1302,c_72,c_75,c_183]) ).
tcf(c_1320,plain,
product(a2,a4) = a9,
inference(demodulation,[status(thm)],[c_183,c_1306]) ).
tcf(c_1322,plain,
product(a10,a9) = a4,
inference(demodulation,[status(thm)],[c_74,c_1306]) ).
tcf(c_1325,plain,
tuple(a1,a9,a8,a6,a7,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[c_76,c_1306]) ).
tcf(c_1326,plain,
a4 = a8,
inference(demodulation,[status(thm)],[c_188,c_1322]) ).
tcf(c_1329,plain,
product(a7,a4) = a10,
inference(demodulation,[status(thm)],[c_399,c_1326]) ).
tcf(c_1330,plain,
product(a10,a4) = a7,
inference(demodulation,[status(thm)],[c_404,c_1326]) ).
tcf(c_1331,plain,
product(a9,a4) = a4,
inference(demodulation,[status(thm)],[c_190,c_1326]) ).
tcf(c_1332,plain,
product(a4,a4) = a7,
inference(demodulation,[status(thm)],[c_187,c_1326]) ).
tcf(c_1338,plain,
product(a4,a2) = a7,
inference(demodulation,[status(thm)],[c_398,c_1330]) ).
tcf(c_1339,plain,
product(a1,a7) = a2,
inference(demodulation,[status(thm)],[c_624,c_1338]) ).
tcf(c_1341,plain,
a9 = a2,
inference(light_normalisation,[status(thm)],[c_1339,c_181]) ).
tcf(c_1342,plain,
product(a4,a7) = a9,
inference(demodulation,[status(thm)],[c_1193,c_1341]) ).
tcf(c_1358,plain,
tuple(a1,a9,a4,a6,a7,a9,a9,a4,a5) != tuple(a9,a10,a9,a7,a4,a9,a4,a5,a6),
inference(light_normalisation,[status(thm)],[c_1325,c_1326,c_1341]) ).
tcf(c_1359,plain,
a9 = a4,
inference(light_normalisation,[status(thm)],[c_1194,c_1331,c_1341]) ).
tcf(c_1360,plain,
tuple(a1,a4,a4,a6,a7,a4,a4,a4,a5) != tuple(a4,a10,a4,a7,a4,a4,a4,a5,a6),
inference(demodulation,[status(thm)],[c_1358,c_1359]) ).
tcf(c_1361,plain,
a2 = a4,
inference(demodulation,[status(thm)],[c_1341,c_1359]) ).
tcf(c_1362,plain,
a3 = a4,
inference(demodulation,[status(thm)],[c_1306,c_1359]) ).
tcf(c_1369,plain,
product(a4,a7) = a1,
inference(demodulation,[status(thm)],[c_66,c_1359]) ).
tcf(c_1370,plain,
a1 = a4,
inference(light_normalisation,[status(thm)],[c_1369,c_1342,c_1359]) ).
tcf(c_1376,plain,
product(a6,a4) = a7,
inference(demodulation,[status(thm)],[c_71,c_1370]) ).
tcf(c_1377,plain,
a7 = a5,
inference(demodulation,[status(thm)],[c_185,c_1376]) ).
tcf(c_1381,plain,
product(a7,a4) = a6,
inference(demodulation,[status(thm)],[c_70,c_1377]) ).
tcf(c_1382,plain,
a10 = a6,
inference(light_normalisation,[status(thm)],[c_1381,c_1329]) ).
tcf(c_1388,plain,
tuple(a4,a4,a4,a10,a7,a4,a4,a4,a7) != tuple(a4,a10,a4,a7,a4,a4,a4,a7,a10),
inference(light_normalisation,[status(thm)],[c_1360,c_1370,c_1377,c_1382]) ).
tcf(c_1391,plain,
a4 = a10,
inference(light_normalisation,[status(thm)],[c_1246,c_1332,c_1342,c_1359,c_1362]) ).
tcf(c_1393,plain,
tuple(a4,a4,a4,a7,a4,a4,a4,a7,a4) != tuple(a4,a4,a4,a4,a7,a4,a4,a4,a7),
inference(demodulation,[status(thm)],[c_1388,c_1391]) ).
tcf(c_1396,plain,
a7 = a4,
inference(light_normalisation,[status(thm)],[c_1320,c_1332,c_1359,c_1361]) ).
tcf(c_1399,plain,
$false,
inference(ground_joinability,[status(thm)],[c_1393,c_1396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Fri Sep 25 04:19:47 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.40 Running UEQ theorem proving
% 0.03/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.43 % Proving...
% 2.75/1.18 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.75/1.18 % SZS status Started for theBenchmark.p
% 2.75/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.75/1.18
% 2.75/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.75/1.18
% 2.75/1.18 % ------ iProver source info
% 2.75/1.18
% 2.75/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.75/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.75/1.18 % git: non_committed_changes: false
% 2.75/1.18
% 2.75/1.18 % ------ Parsing...% successful
% 2.75/1.18
% 2.75/1.18
% 2.75/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.75/1.18
% 2.75/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.75/1.18
% 2.75/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.75/1.18
% 2.75/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.75/1.18 % ------ Proving...
% 2.75/1.18 % ------ Problem Properties
% 2.75/1.18
% 2.75/1.18 %
% 2.75/1.18 % clauses 14
% 2.75/1.18 % conjectures 1
% 2.75/1.18 % EPR 0
% 2.75/1.18 % Horn 14
% 2.75/1.18 % unary 14
% 2.75/1.18 % binary 0
% 2.75/1.18 % lits 14
% 2.75/1.18 % lits eq 14
% 2.75/1.18 % fd_pure 0
% 2.75/1.18 % fd_pseudo 0
% 2.75/1.18 % fd_cond 0
% 2.75/1.18 % fd_pseudo_cond 0
% 2.75/1.18 % AC symbols 0
% 2.75/1.18
% 2.75/1.18 % ------ Input Options Time Limit: Unbounded
% 2.75/1.18
% 2.75/1.18
% 2.75/1.18 % ------
% 2.75/1.18 % Current options:
% 2.75/1.18 % ------
% 2.75/1.18
% 2.75/1.18
% 2.75/1.18 %
% 2.75/1.18
% 2.75/1.18 % ------ Proving...
% 2.75/1.18 %
% 2.75/1.18
% 2.75/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.75/1.18
% 2.75/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.75/1.18
% 2.75/1.18
%------------------------------------------------------------------------------