%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : TOP053-1 : 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 : n007.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 03:55:30 PM UTC 2026
% Result : Unsatisfiable 3.55s 1.08s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 19
% Syntax : Number of formulae : 176 ( 176 unt; 0 def)
% Number of atoms : 176 ( 175 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 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 : 17 ( 17 usr; 15 con; 0-14 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?; 30 :)
% 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,
product(a1,a2) = a3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
fof(f5,axiom,
product(a3,a4) = a5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
fof(f6,axiom,
product(a5,a6) = a7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
fof(f7,axiom,
product(a7,a3) = a8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).
fof(f8,axiom,
product(a8,a2) = a9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
fof(f9,axiom,
product(a9,a1) = a10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
fof(f10,axiom,
product(a10,a11) = a12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
fof(f11,axiom,
product(a12,a3) = a13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
fof(f12,axiom,
product(a13,a8) = a6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
fof(f13,plain,
a6 = product(a13,a8),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
product(a6,a7) = a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
fof(f15,plain,
a2 = product(a6,a7),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
product(a2,a12) = a14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_12) ).
fof(f17,axiom,
product(a14,a3) = a15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_13) ).
fof(f18,axiom,
product(a15,a8) = a4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_14) ).
fof(f19,plain,
a4 = product(a15,a8),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
product(a4,a7) = a11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_15) ).
fof(f21,plain,
a11 = product(a4,a7),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
product(a11,a10) = a1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_16) ).
fof(f23,plain,
a1 = product(a11,a10),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tcf(c_68,plain,
! [X0: $i] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_70,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_71,plain,
product(a1,a2) = a3,
inference(cnf_transformation,[],[f4]) ).
tcf(c_72,plain,
product(a3,a4) = a5,
inference(cnf_transformation,[],[f5]) ).
tcf(c_73,plain,
product(a5,a6) = a7,
inference(cnf_transformation,[],[f6]) ).
tcf(c_74,plain,
product(a7,a3) = a8,
inference(cnf_transformation,[],[f7]) ).
tcf(c_75,plain,
product(a8,a2) = a9,
inference(cnf_transformation,[],[f8]) ).
tcf(c_76,plain,
product(a9,a1) = a10,
inference(cnf_transformation,[],[f9]) ).
tcf(c_77,plain,
product(a10,a11) = a12,
inference(cnf_transformation,[],[f10]) ).
tcf(c_78,plain,
product(a12,a3) = a13,
inference(cnf_transformation,[],[f11]) ).
tcf(c_79,plain,
product(a13,a8) = a6,
inference(cnf_transformation,[],[f13]) ).
tcf(c_80,plain,
product(a6,a7) = a2,
inference(cnf_transformation,[],[f15]) ).
tcf(c_81,plain,
product(a2,a12) = a14,
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,plain,
product(a14,a3) = a15,
inference(cnf_transformation,[],[f17]) ).
tcf(c_83,plain,
product(a15,a8) = a4,
inference(cnf_transformation,[],[f19]) ).
tcf(c_84,plain,
product(a4,a7) = a11,
inference(cnf_transformation,[],[f21]) ).
tcf(c_85,plain,
product(a11,a10) = a1,
inference(cnf_transformation,[],[f23]) ).
tcf(c_86,negated_conjecture,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(cnf_transformation,[],[f24]) ).
tcf(c_221,plain,
product(a3,a2) = a1,
inference(superposition,[status(thm)],[c_71,c_69]) ).
tcf(c_222,plain,
product(a5,a4) = a3,
inference(superposition,[status(thm)],[c_72,c_69]) ).
tcf(c_223,plain,
product(a7,a6) = a5,
inference(superposition,[status(thm)],[c_73,c_69]) ).
tcf(c_224,plain,
product(a8,a3) = a7,
inference(superposition,[status(thm)],[c_74,c_69]) ).
tcf(c_225,plain,
product(a9,a2) = a8,
inference(superposition,[status(thm)],[c_75,c_69]) ).
tcf(c_226,plain,
product(a10,a1) = a9,
inference(superposition,[status(thm)],[c_76,c_69]) ).
tcf(c_228,plain,
product(a13,a3) = a12,
inference(superposition,[status(thm)],[c_78,c_69]) ).
tcf(c_229,plain,
product(a6,a8) = a13,
inference(superposition,[status(thm)],[c_79,c_69]) ).
tcf(c_230,plain,
product(a2,a7) = a6,
inference(superposition,[status(thm)],[c_80,c_69]) ).
tcf(c_231,plain,
product(a14,a12) = a2,
inference(superposition,[status(thm)],[c_81,c_69]) ).
tcf(c_235,plain,
product(a1,a10) = a11,
inference(superposition,[status(thm)],[c_85,c_69]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c_68,c_70]) ).
tcf(c_248,plain,
! [X0: $i] : product(product(a1,X0),a2) = product(a3,product(X0,a2)),
inference(superposition,[status(thm)],[c_71,c_70]) ).
tcf(c_252,plain,
! [X0: $i] : product(product(a8,X0),a2) = product(a9,product(X0,a2)),
inference(superposition,[status(thm)],[c_75,c_70]) ).
tcf(c_253,plain,
! [X0: $i] : product(product(a9,X0),a1) = product(a10,product(X0,a1)),
inference(superposition,[status(thm)],[c_76,c_70]) ).
tcf(c_257,plain,
! [X0: $i] : product(product(a6,X0),a7) = product(a2,product(X0,a7)),
inference(superposition,[status(thm)],[c_80,c_70]) ).
tcf(c_259,plain,
! [X0: $i] : product(product(a14,X0),a3) = product(a15,product(X0,a3)),
inference(superposition,[status(thm)],[c_82,c_70]) ).
tcf(c_260,plain,
! [X0: $i] : product(product(a15,X0),a8) = product(a4,product(X0,a8)),
inference(superposition,[status(thm)],[c_83,c_70]) ).
tcf(c_261,plain,
! [X0: $i] : product(product(a4,X0),a7) = product(a11,product(X0,a7)),
inference(superposition,[status(thm)],[c_84,c_70]) ).
tcf(c_267,plain,
! [X0: $i] : product(product(a9,X0),a2) = product(a8,product(X0,a2)),
inference(superposition,[status(thm)],[c_225,c_70]) ).
tcf(c_270,plain,
! [X0: $i] : product(product(a13,X0),a3) = product(a12,product(X0,a3)),
inference(superposition,[status(thm)],[c_228,c_70]) ).
tcf(c_273,plain,
! [X0: $i] : product(product(X0,a1),a2) = product(product(X0,a2),a3),
inference(superposition,[status(thm)],[c_71,c_70]) ).
tcf(c_276,plain,
! [X0: $i] : product(product(X0,a3),a8) = product(product(X0,a7),a3),
inference(superposition,[status(thm)],[c_74,c_70]) ).
tcf(c_277,plain,
! [X0: $i] : product(product(X0,a2),a9) = product(product(X0,a8),a2),
inference(superposition,[status(thm)],[c_75,c_70]) ).
tcf(c_278,plain,
! [X0: $i] : product(product(X0,a1),a10) = product(product(X0,a9),a1),
inference(superposition,[status(thm)],[c_76,c_70]) ).
tcf(c_280,plain,
! [X0: $i] : product(product(X0,a3),a13) = product(product(X0,a12),a3),
inference(superposition,[status(thm)],[c_78,c_70]) ).
tcf(c_291,plain,
! [X0: $i] : product(product(X0,a3),a7) = product(product(X0,a8),a3),
inference(superposition,[status(thm)],[c_224,c_70]) ).
tcf(c_489,plain,
! [X0: $i] : product(product(X0,a1),a10) = product(product(X0,a10),a11),
inference(superposition,[status(thm)],[c_235,c_70]) ).
tcf(c_510,plain,
product(a2,product(a12,a2)) = product(a14,a2),
inference(superposition,[status(thm)],[c_81,c_245]) ).
tcf(c_520,plain,
product(a10,product(a1,a10)) = product(a9,a10),
inference(superposition,[status(thm)],[c_226,c_245]) ).
tcf(c_524,plain,
product(a2,product(a7,a2)) = product(a6,a2),
inference(superposition,[status(thm)],[c_230,c_245]) ).
tcf(c_529,plain,
product(a1,product(a10,a1)) = product(a11,a1),
inference(superposition,[status(thm)],[c_235,c_245]) ).
tcf(c_538,plain,
product(a1,a9) = product(a11,a1),
inference(light_normalisation,[status(thm)],[c_529,c_226]) ).
tcf(c_539,plain,
product(a9,a10) = a12,
inference(light_normalisation,[status(thm)],[c_520,c_77,c_235]) ).
tcf(c_609,plain,
! [X0: $i] : product(product(X0,a9),a10) = product(product(X0,a10),a12),
inference(superposition,[status(thm)],[c_539,c_70]) ).
tcf(c_726,plain,
product(product(a11,a1),a2) = product(a3,product(a9,a2)),
inference(superposition,[status(thm)],[c_538,c_248]) ).
tcf(c_735,plain,
product(product(a11,a1),a2) = product(a3,a8),
inference(light_normalisation,[status(thm)],[c_726,c_225]) ).
tcf(c_1304,plain,
product(product(a11,a2),a3) = product(a3,a8),
inference(demodulation,[status(thm)],[c_735,c_273]) ).
tcf(c_1307,plain,
product(product(a3,a8),a3) = product(a11,a2),
inference(superposition,[status(thm)],[c_1304,c_69]) ).
tcf(c_1344,plain,
product(a9,product(a3,a2)) = product(a7,a2),
inference(superposition,[status(thm)],[c_224,c_252]) ).
tcf(c_1352,plain,
product(a7,a2) = a10,
inference(light_normalisation,[status(thm)],[c_1344,c_76,c_221]) ).
tcf(c_1355,plain,
product(a2,a10) = product(a6,a2),
inference(demodulation,[status(thm)],[c_524,c_1352]) ).
tcf(c_1361,plain,
product(a3,a7) = product(a11,a2),
inference(demodulation,[status(thm)],[c_1307,c_68,c_291]) ).
tcf(c_1370,plain,
product(a7,product(a2,a7)) = product(a10,a7),
inference(superposition,[status(thm)],[c_1352,c_245]) ).
tcf(c_1372,plain,
product(a10,a2) = a7,
inference(superposition,[status(thm)],[c_1352,c_69]) ).
tcf(c_1373,plain,
! [X0: $i] : product(product(X0,a2),a10) = product(product(X0,a7),a2),
inference(superposition,[status(thm)],[c_1352,c_70]) ).
tcf(c_1375,plain,
product(a10,a7) = a5,
inference(light_normalisation,[status(thm)],[c_1370,c_223,c_230]) ).
tcf(c_1454,plain,
product(a10,product(a10,a1)) = product(a12,a1),
inference(superposition,[status(thm)],[c_539,c_253]) ).
tcf(c_1462,plain,
product(a10,a9) = product(a12,a1),
inference(light_normalisation,[status(thm)],[c_1454,c_226]) ).
tcf(c_1845,plain,
product(a2,product(a8,a7)) = product(a13,a7),
inference(superposition,[status(thm)],[c_229,c_257]) ).
tcf(c_1908,plain,
product(a15,product(a12,a3)) = product(a2,a3),
inference(superposition,[status(thm)],[c_231,c_259]) ).
tcf(c_1916,plain,
product(a2,a3) = product(a15,a13),
inference(light_normalisation,[status(thm)],[c_1908,c_78]) ).
tcf(c_1928,plain,
product(product(a2,a3),a13) = a15,
inference(superposition,[status(thm)],[c_1916,c_69]) ).
tcf(c_2027,plain,
product(product(a2,a3),a8) = product(a4,product(a13,a8)),
inference(superposition,[status(thm)],[c_1916,c_260]) ).
tcf(c_2035,plain,
product(product(a2,a3),a8) = product(a4,a6),
inference(light_normalisation,[status(thm)],[c_2027,c_79]) ).
tcf(c_2407,plain,
product(a8,product(a10,a2)) = product(a12,a2),
inference(superposition,[status(thm)],[c_539,c_267]) ).
tcf(c_2416,plain,
product(a8,a7) = product(a12,a2),
inference(light_normalisation,[status(thm)],[c_2407,c_1372]) ).
tcf(c_2421,plain,
product(a2,product(a8,a7)) = product(a14,a2),
inference(demodulation,[status(thm)],[c_510,c_2416]) ).
tcf(c_2422,plain,
product(a13,a7) = product(a14,a2),
inference(light_normalisation,[status(thm)],[c_2421,c_1845]) ).
tcf(c_2491,plain,
product(product(a13,a7),a2) = a14,
inference(superposition,[status(thm)],[c_2422,c_69]) ).
tcf(c_2547,plain,
product(product(a13,a2),a10) = a14,
inference(demodulation,[status(thm)],[c_2491,c_1373]) ).
tcf(c_2550,plain,
product(a13,a2) = product(a14,a10),
inference(superposition,[status(thm)],[c_2547,c_69]) ).
tcf(c_2731,plain,
product(a12,product(a8,a3)) = product(a6,a3),
inference(superposition,[status(thm)],[c_79,c_270]) ).
tcf(c_2743,plain,
product(a6,a3) = product(a12,a7),
inference(light_normalisation,[status(thm)],[c_2731,c_224]) ).
tcf(c_2759,plain,
product(product(a6,a3),a7) = a12,
inference(superposition,[status(thm)],[c_2743,c_69]) ).
tcf(c_2875,plain,
product(a2,product(a3,a7)) = a12,
inference(demodulation,[status(thm)],[c_2759,c_257]) ).
tcf(c_3154,plain,
product(product(a2,a3),a8) = product(a6,a3),
inference(superposition,[status(thm)],[c_230,c_276]) ).
tcf(c_3172,plain,
product(a4,a6) = product(a6,a3),
inference(light_normalisation,[status(thm)],[c_3154,c_2035]) ).
tcf(c_3183,plain,
product(a4,a6) = product(a12,a7),
inference(demodulation,[status(thm)],[c_2743,c_3172]) ).
tcf(c_3297,plain,
product(product(a15,a2),a9) = product(a4,a2),
inference(superposition,[status(thm)],[c_83,c_277]) ).
tcf(c_3366,plain,
product(product(a4,a6),a7) = product(a2,product(a3,a7)),
inference(superposition,[status(thm)],[c_3172,c_257]) ).
tcf(c_3367,plain,
product(product(a4,a6),a7) = a12,
inference(light_normalisation,[status(thm)],[c_3366,c_2875]) ).
tcf(c_3406,plain,
product(a3,a7) = a12,
inference(demodulation,[status(thm)],[c_3367,c_80,c_261,c_1361]) ).
tcf(c_3410,plain,
product(a2,a12) = a12,
inference(demodulation,[status(thm)],[c_2875,c_3406]) ).
tcf(c_3413,plain,
a12 = a14,
inference(demodulation,[status(thm)],[c_81,c_3410]) ).
tcf(c_3415,plain,
product(a12,a10) = product(a13,a2),
inference(demodulation,[status(thm)],[c_2550,c_3413]) ).
tcf(c_3427,plain,
product(a12,a3) = a15,
inference(demodulation,[status(thm)],[c_82,c_3413]) ).
tcf(c_3428,plain,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a12) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a12,a15),
inference(demodulation,[status(thm)],[c_86,c_3413]) ).
tcf(c_3429,plain,
a13 = a15,
inference(light_normalisation,[status(thm)],[c_3427,c_78]) ).
tcf(c_3434,plain,
product(product(a2,a3),a13) = a13,
inference(demodulation,[status(thm)],[c_1928,c_3429]) ).
tcf(c_3439,plain,
product(a13,a8) = a4,
inference(demodulation,[status(thm)],[c_83,c_3429]) ).
tcf(c_3440,plain,
a4 = a6,
inference(demodulation,[status(thm)],[c_79,c_3439]) ).
tcf(c_3442,plain,
product(a4,a4) = product(a12,a7),
inference(demodulation,[status(thm)],[c_3183,c_3440]) ).
tcf(c_3453,plain,
product(a2,a10) = product(a4,a2),
inference(demodulation,[status(thm)],[c_1355,c_3440]) ).
tcf(c_3460,plain,
product(a2,a7) = a4,
inference(demodulation,[status(thm)],[c_230,c_3440]) ).
tcf(c_3462,plain,
product(a7,a4) = a5,
inference(demodulation,[status(thm)],[c_223,c_3440]) ).
tcf(c_3464,plain,
product(a5,a4) = a7,
inference(demodulation,[status(thm)],[c_73,c_3440]) ).
tcf(c_3465,plain,
a3 = a7,
inference(light_normalisation,[status(thm)],[c_3464,c_222]) ).
tcf(c_3466,plain,
product(a3,a3) = a12,
inference(demodulation,[status(thm)],[c_3406,c_3465]) ).
tcf(c_3484,plain,
product(a10,a3) = a5,
inference(demodulation,[status(thm)],[c_1375,c_3465]) ).
tcf(c_3487,plain,
product(a3,a2) = a10,
inference(demodulation,[status(thm)],[c_1352,c_3465]) ).
tcf(c_3493,plain,
product(a8,a3) = a3,
inference(demodulation,[status(thm)],[c_224,c_3465]) ).
tcf(c_3495,plain,
product(a3,a3) = a8,
inference(demodulation,[status(thm)],[c_74,c_3465]) ).
tcf(c_3499,plain,
a1 = a10,
inference(demodulation,[status(thm)],[c_221,c_3487]) ).
tcf(c_3505,plain,
product(a10,a9) = product(a12,a10),
inference(demodulation,[status(thm)],[c_1462,c_3499]) ).
tcf(c_3513,plain,
product(a10,a9) = product(a11,a10),
inference(demodulation,[status(thm)],[c_538,c_3499]) ).
tcf(c_3516,plain,
product(a11,a10) = a10,
inference(demodulation,[status(thm)],[c_85,c_3499]) ).
tcf(c_3517,plain,
product(a9,a10) = a10,
inference(demodulation,[status(thm)],[c_76,c_3499]) ).
tcf(c_3518,plain,
product(a10,a2) = a3,
inference(demodulation,[status(thm)],[c_71,c_3499]) ).
tcf(c_3519,plain,
a10 = a12,
inference(demodulation,[status(thm)],[c_539,c_3517]) ).
tcf(c_3534,plain,
product(a10,a11) = a10,
inference(demodulation,[status(thm)],[c_77,c_3519]) ).
tcf(c_3564,plain,
product(a12,a7) = a3,
inference(superposition,[status(thm)],[c_3406,c_69]) ).
tcf(c_3567,plain,
a3 = a5,
inference(light_normalisation,[status(thm)],[c_3564,c_3442,c_3465,c_3484,c_3519]) ).
tcf(c_3593,plain,
tuple(a2,a3,a4,a3,a4,a3,a8,a9,a10,a11,a10,a13,a10,a13) != tuple(a10,a2,a3,a4,a3,a4,a3,a8,a9,a10,a11,a10,a13,a10),
inference(light_normalisation,[status(thm)],[c_3428,c_3429,c_3440,c_3465,c_3499,c_3519,c_3567]) ).
tcf(c_3596,plain,
! [X0: $i] : product(product(X0,a10),a10) = product(product(X0,a10),a11),
inference(light_normalisation,[status(thm)],[c_278,c_489,c_609,c_3499,c_3519]) ).
tcf(c_3597,plain,
! [X0: $i] : product(product(X0,a10),a11) = X0,
inference(demodulation,[status(thm)],[c_3596,c_69]) ).
tcf(c_3604,plain,
! [X0: $i] : product(X0,a10) = product(X0,a11),
inference(superposition,[status(thm)],[c_3597,c_69]) ).
tcf(c_3606,plain,
product(a11,product(a10,a11)) = a11,
inference(superposition,[status(thm)],[c_3597,c_245]) ).
tcf(c_3607,plain,
product(a10,a9) = a11,
inference(light_normalisation,[status(thm)],[c_3606,c_3513,c_3534]) ).
tcf(c_3619,plain,
product(a11,a10) = a11,
inference(superposition,[status(thm)],[c_3604,c_68]) ).
tcf(c_3661,plain,
a10 = a11,
inference(demodulation,[status(thm)],[c_3619,c_3516]) ).
tcf(c_3663,plain,
tuple(a2,a3,a4,a3,a4,a3,a8,a9,a10,a10,a10,a13,a10,a13) != tuple(a10,a2,a3,a4,a3,a4,a3,a8,a9,a10,a10,a10,a13,a10),
inference(demodulation,[status(thm)],[c_3593,c_3661]) ).
tcf(c_3664,plain,
product(a2,a10) = a10,
inference(light_normalisation,[status(thm)],[c_3297,c_3415,c_3429,c_3453,c_3505,c_3607,c_3661]) ).
tcf(c_3665,plain,
product(a2,product(a10,a2)) = product(a10,a2),
inference(superposition,[status(thm)],[c_3664,c_245]) ).
tcf(c_3667,plain,
product(a10,a10) = a2,
inference(superposition,[status(thm)],[c_3664,c_69]) ).
tcf(c_3669,plain,
product(a2,a3) = a3,
inference(light_normalisation,[status(thm)],[c_3665,c_3518]) ).
tcf(c_3690,plain,
a2 = a10,
inference(demodulation,[status(thm)],[c_3667,c_68]) ).
tcf(c_3693,plain,
a2 = a12,
inference(demodulation,[status(thm)],[c_3519,c_3690]) ).
tcf(c_3696,plain,
tuple(a2,a2,a3,a4,a3,a4,a3,a8,a9,a2,a2,a2,a13,a2) != tuple(a2,a3,a4,a3,a4,a3,a8,a9,a2,a2,a2,a13,a2,a13),
inference(light_normalisation,[status(thm)],[c_3663,c_3690]) ).
tcf(c_3708,plain,
a3 = a4,
inference(light_normalisation,[status(thm)],[c_3460,c_3465,c_3669]) ).
tcf(c_3710,plain,
tuple(a2,a2,a3,a3,a3,a3,a3,a8,a9,a2,a2,a2,a13,a2) != tuple(a2,a3,a3,a3,a3,a3,a8,a9,a2,a2,a2,a13,a2,a13),
inference(demodulation,[status(thm)],[c_3696,c_3708]) ).
tcf(c_3713,plain,
! [X0: $i] : product(product(X0,a2),a3) = product(product(X0,a3),a13),
inference(light_normalisation,[status(thm)],[c_280,c_3693]) ).
tcf(c_3715,plain,
product(product(a2,a3),a13) = product(a2,a3),
inference(superposition,[status(thm)],[c_68,c_3713]) ).
tcf(c_3730,plain,
a3 = a13,
inference(light_normalisation,[status(thm)],[c_3715,c_3434,c_3669]) ).
tcf(c_3736,plain,
tuple(a2,a2,a3,a3,a3,a3,a3,a8,a9,a2,a2,a2,a3,a2) != tuple(a2,a3,a3,a3,a3,a3,a8,a9,a2,a2,a2,a3,a2,a3),
inference(demodulation,[status(thm)],[c_3710,c_3730]) ).
tcf(c_3799,plain,
a2 = a3,
inference(light_normalisation,[status(thm)],[c_3462,c_3465,c_3466,c_3567,c_3693,c_3708]) ).
tcf(c_3800,plain,
tuple(a3,a3,a3,a3,a3,a3,a3,a8,a9,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a8,a9,a3,a3,a3,a3,a3,a3),
inference(demodulation,[status(thm)],[c_3736,c_3799]) ).
tcf(c_3811,plain,
product(a8,a3) = a9,
inference(demodulation,[status(thm)],[c_75,c_3799]) ).
tcf(c_3812,plain,
a3 = a9,
inference(light_normalisation,[status(thm)],[c_3811,c_3493]) ).
tcf(c_3819,plain,
tuple(a3,a3,a3,a3,a3,a3,a3,a8,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a8,a3,a3,a3,a3,a3,a3,a3),
inference(light_normalisation,[status(thm)],[c_3800,c_3812]) ).
tcf(c_3837,plain,
a3 = a8,
inference(demodulation,[status(thm)],[c_3495,c_68]) ).
tcf(c_3839,plain,
tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3) != tuple(a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3,a3),
inference(demodulation,[status(thm)],[c_3819,c_3837]) ).
tcf(c_3841,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_3839]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP053-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 04:18:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.39 Running UEQ theorem proving
% 0.08/0.39 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
% 0.08/0.40
% 0.08/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.40
% 0.08/0.40 % Detected problem language: tptp
% 0.08/0.41 % Proving...
% 3.55/1.08 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.55/1.08 % SZS status Started for theBenchmark.p
% 3.55/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 3.55/1.08
% 3.55/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.55/1.08
% 3.55/1.08 % ------ iProver source info
% 3.55/1.08
% 3.55/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 3.55/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.55/1.08 % git: non_committed_changes: false
% 3.55/1.08
% 3.55/1.08 % ------ Parsing...% successful
% 3.55/1.08
% 3.55/1.08
% 3.55/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.55/1.08
% 3.55/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.55/1.08
% 3.55/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.55/1.08
% 3.55/1.08 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.55/1.08 % ------ Proving...
% 3.55/1.08 % ------ Problem Properties
% 3.55/1.08
% 3.55/1.08 %
% 3.55/1.08 % clauses 19
% 3.55/1.08 % conjectures 1
% 3.55/1.08 % EPR 0
% 3.55/1.08 % Horn 19
% 3.55/1.08 % unary 19
% 3.55/1.08 % binary 0
% 3.55/1.08 % lits 19
% 3.55/1.08 % lits eq 19
% 3.55/1.08 % fd_pure 0
% 3.55/1.08 % fd_pseudo 0
% 3.55/1.08 % fd_cond 0
% 3.55/1.08 % fd_pseudo_cond 0
% 3.55/1.08 % AC symbols 0
% 3.55/1.08
% 3.55/1.08 % ------ Input Options Time Limit: Unbounded
% 3.55/1.08
% 3.55/1.08
% 3.55/1.08 % ------
% 3.55/1.08 % Current options:
% 3.55/1.08 % ------
% 3.55/1.08
% 3.55/1.08
% 3.55/1.08 %
% 3.55/1.08
% 3.55/1.08 % ------ Proving...
% 3.55/1.08 %
% 3.55/1.08
% 3.55/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 3.55/1.08
% 3.55/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/1.08
% 3.55/1.08
%------------------------------------------------------------------------------