%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 01:35:22 PM UTC 2026
% Result : Unsatisfiable 11.53s 2.25s
% Output : CNFRefutation 11.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 21
% Syntax : Number of formulae : 146 ( 146 unt; 6 def)
% Number of atoms : 401 ( 145 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 127 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
fof(f2,axiom,
! [X0] : product(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
fof(f3,axiom,
! [X0,X1] : product(X0,difference(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(f4,axiom,
! [X0,X1] : difference(X0,product(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
fof(f5,axiom,
! [X0,X1] : quotient(product(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
fof(f6,axiom,
! [X0,X1] : product(quotient(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
fof(f7,axiom,
! [X2,X0,X1] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
fof(f9,axiom,
! [X0] : i(X0) = difference(X0,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
fof(f10,axiom,
! [X0] : j(X0) = quotient(one,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
fof(f11,axiom,
! [X0] : product(i(X0),X0) = product(X0,j(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
fof(f12,axiom,
! [X0] : eta(X0) = product(i(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
fof(f13,plain,
! [X0] : product(i(X0),X0) = eta(X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] : product(i(i(X0)),X1) = product(eta(X0),product(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
fof(f15,axiom,
! [X0,X1] : product(X0,product(eta(X0),X1)) = product(j(j(X0)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
fof(f17,axiom,
! [X2,X0,X1] : product(eta(X0),product(X1,X2)) = product(product(eta(X0),X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
fof(f23,negated_conjecture,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f24,plain,
! [X0] : eta(X0) = product(difference(X0,one),X0),
inference(definition_unfolding,[],[f13,f9]) ).
fof(f25,plain,
! [X0] : product(difference(X0,one),X0) = product(X0,quotient(one,X0)),
inference(definition_unfolding,[],[f11,f9,f10]) ).
fof(f26,plain,
! [X0,X1] : product(difference(difference(X0,one),one),X1) = product(product(difference(X0,one),X0),product(X0,X1)),
inference(definition_unfolding,[],[f14,f9,f9,f24]) ).
fof(f27,plain,
! [X0,X1] : product(X0,product(product(difference(X0,one),X0),X1)) = product(quotient(one,quotient(one,X0)),X1),
inference(definition_unfolding,[],[f15,f24,f10,f10]) ).
fof(f29,plain,
! [X2,X0,X1] : product(product(difference(X0,one),X0),product(X1,X2)) = product(product(product(difference(X0,one),X0),X1),X2),
inference(definition_unfolding,[],[f17,f24,f24]) ).
fof(f32,plain,
product(quotient(one,quotient(one,x0)),quotient(one,product(x1,x0))) != quotient(one,x1),
inference(definition_unfolding,[],[f23,f10,f10,f10,f10]) ).
tcf(c_70,plain,
! [X0: $i] : product(X0,one) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i] : product(one,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_78,plain,
! [X0: $i] : product(difference(X0,one),X0) = product(X0,quotient(one,X0)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] : product(product(difference(X0,one),X0),product(X0,X1)) = product(difference(difference(X0,one),one),X1),
inference(cnf_transformation,[],[f26]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] : product(X0,product(product(difference(X0,one),X0),X1)) = product(quotient(one,quotient(one,X0)),X1),
inference(cnf_transformation,[],[f27]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(product(difference(X0,one),X0),X1),X2) = product(product(difference(X0,one),X0),product(X1,X2)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_85,negated_conjecture,
product(quotient(one,quotient(one,x0)),quotient(one,product(x1,x0))) != quotient(one,x1),
inference(cnf_transformation,[],[f32]) ).
tcf(c_137,definition,
iPr_def_10 = quotient(one,x0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_138,definition,
iPr_def_11 = quotient(one,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_139,definition,
iPr_def_12 = product(x1,x0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_140,definition,
iPr_def_13 = quotient(one,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_141,definition,
iPr_def_14 = product(iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_142,definition,
iPr_def_15 = quotient(one,x1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_143,negated_conjecture,
iPr_def_14 != iPr_def_15,
inference(demodulation,[status(thm)],[c_85,c_142,c_139,c_140,c_137,c_138,c_141]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(product(difference(X0,one),X0),X1),X2) = product(product(difference(X0,one),X0),product(X1,X2)),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] : product(X0,product(product(difference(X0,one),X0),X1)) = product(quotient(one,quotient(one,X0)),X1),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] : product(product(difference(X0,one),X0),product(X0,X1)) = product(difference(difference(X0,one),one),X1),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_150,plain,
! [X0: $i] : product(difference(X0,one),X0) = product(X0,quotient(one,X0)),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : product(quotient(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : difference(X0,product(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : product(X0,difference(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_157,plain,
! [X0: $i] : product(one,X0) = X0,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_158,plain,
! [X0: $i] : product(X0,one) = X0,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i] : product(product(X0,quotient(one,X0)),product(X0,X1)) = product(difference(difference(X0,one),one),X1),
inference(demodulation,[status(thm)],[c_149,c_150]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : product(X0,product(product(X0,quotient(one,X0)),X1)) = product(quotient(one,quotient(one,X0)),X1),
inference(demodulation,[status(thm)],[c_148,c_150]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(product(X0,quotient(one,X0)),X1),X2) = product(product(X0,quotient(one,X0)),product(X1,X2)),
inference(demodulation,[status(thm)],[c_146,c_150]) ).
tcf(c_257,plain,
product(iPr_def_10,x0) = one,
inference(superposition,[status(thm)],[c_137,c_153]) ).
tcf(c_258,plain,
product(iPr_def_15,x1) = one,
inference(superposition,[status(thm)],[c_142,c_153]) ).
tcf(c_259,plain,
product(iPr_def_11,iPr_def_10) = one,
inference(superposition,[status(thm)],[c_138,c_153]) ).
tcf(c_260,plain,
product(iPr_def_13,iPr_def_12) = one,
inference(superposition,[status(thm)],[c_140,c_153]) ).
tcf(c_263,plain,
! [X0: $i] : quotient(X0,X0) = one,
inference(superposition,[status(thm)],[c_157,c_154]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i] : difference(quotient(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_153,c_155]) ).
tcf(c_269,plain,
difference(x1,iPr_def_12) = x0,
inference(superposition,[status(thm)],[c_139,c_155]) ).
tcf(c_270,plain,
difference(iPr_def_11,iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_141,c_155]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : quotient(X0,difference(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_156,c_154]) ).
tcf(c_308,plain,
! [X0: $i] : product(X0,product(X0,quotient(one,X0))) = product(quotient(one,quotient(one,X0)),one),
inference(superposition,[status(thm)],[c_158,c_239]) ).
tcf(c_313,plain,
! [X0: $i] : product(x0,product(product(x0,iPr_def_10),X0)) = product(quotient(one,iPr_def_10),X0),
inference(superposition,[status(thm)],[c_137,c_239]) ).
tcf(c_605,plain,
! [X0: $i] : product(x0,product(product(x0,iPr_def_10),X0)) = product(iPr_def_11,X0),
inference(demodulation,[status(thm)],[c_313,c_138]) ).
tcf(c_611,plain,
! [X0: $i] : product(X0,product(X0,quotient(one,X0))) = quotient(one,quotient(one,X0)),
inference(demodulation,[status(thm)],[c_308,c_158]) ).
tcf(c_1013,plain,
product(product(iPr_def_10,quotient(one,iPr_def_10)),one) = product(difference(difference(iPr_def_10,one),one),x0),
inference(superposition,[status(thm)],[c_257,c_238]) ).
tcf(c_1015,plain,
quotient(one,x0) = iPr_def_10,
inference(superposition,[status(thm)],[c_257,c_154]) ).
tcf(c_1016,plain,
! [X0: $i] : difference(x0,product(product(x0,X0),iPr_def_10)) = quotient(product(X0,one),x0),
inference(superposition,[status(thm)],[c_257,c_152]) ).
tcf(c_1022,plain,
quotient(one,x1) = iPr_def_15,
inference(superposition,[status(thm)],[c_258,c_154]) ).
tcf(c_1027,plain,
product(product(iPr_def_11,quotient(one,iPr_def_11)),one) = product(difference(difference(iPr_def_11,one),one),iPr_def_10),
inference(superposition,[status(thm)],[c_259,c_238]) ).
tcf(c_1029,plain,
quotient(one,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_259,c_154]) ).
tcf(c_1030,plain,
! [X0: $i] : difference(iPr_def_10,product(product(iPr_def_10,X0),iPr_def_11)) = quotient(product(X0,one),iPr_def_10),
inference(superposition,[status(thm)],[c_259,c_152]) ).
tcf(c_1037,plain,
! [X0: $i] : difference(iPr_def_12,product(product(iPr_def_12,X0),iPr_def_13)) = quotient(product(X0,one),iPr_def_12),
inference(superposition,[status(thm)],[c_260,c_152]) ).
tcf(c_1059,plain,
product(x1,x0) = iPr_def_12,
inference(superposition,[status(thm)],[c_269,c_156]) ).
tcf(c_1060,plain,
product(iPr_def_11,iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_270,c_156]) ).
tcf(c_1067,plain,
difference(iPr_def_10,one) = x0,
inference(superposition,[status(thm)],[c_137,c_268]) ).
tcf(c_1069,plain,
difference(iPr_def_11,one) = iPr_def_10,
inference(superposition,[status(thm)],[c_138,c_268]) ).
tcf(c_1118,plain,
! [X0: $i] : product(iPr_def_11,difference(product(x0,iPr_def_10),X0)) = product(x0,X0),
inference(superposition,[status(thm)],[c_156,c_605]) ).
tcf(c_1124,plain,
! [X0: $i] : product(product(x0,iPr_def_10),X0) = difference(x0,product(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_605,c_155]) ).
tcf(c_1127,plain,
! [X0: $i] : difference(X0,product(product(X0,x0),product(x0,iPr_def_10))) = quotient(product(iPr_def_11,X0),X0),
inference(superposition,[status(thm)],[c_605,c_152]) ).
tcf(c_1181,plain,
product(x0,product(x0,iPr_def_10)) = quotient(one,iPr_def_10),
inference(superposition,[status(thm)],[c_137,c_611]) ).
tcf(c_1250,plain,
product(x0,product(x0,iPr_def_10)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1181,c_1029]) ).
tcf(c_1262,plain,
! [X0: $i] : difference(iPr_def_12,product(product(iPr_def_12,X0),iPr_def_13)) = quotient(X0,iPr_def_12),
inference(demodulation,[status(thm)],[c_1037,c_158]) ).
tcf(c_1263,plain,
! [X0: $i] : difference(iPr_def_10,product(product(iPr_def_10,X0),iPr_def_11)) = quotient(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_1030,c_158]) ).
tcf(c_1265,plain,
! [X0: $i] : difference(x0,product(product(x0,X0),iPr_def_10)) = quotient(X0,x0),
inference(demodulation,[status(thm)],[c_1016,c_158]) ).
tcf(c_1266,plain,
! [X0: $i] : difference(X0,product(product(X0,x0),product(x0,iPr_def_10))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1127,c_154]) ).
tcf(c_1271,plain,
product(product(iPr_def_11,quotient(one,iPr_def_11)),one) = product(x0,iPr_def_10),
inference(demodulation,[status(thm)],[c_1027,c_1067,c_1069]) ).
tcf(c_1272,plain,
product(iPr_def_11,quotient(one,iPr_def_11)) = product(x0,iPr_def_10),
inference(demodulation,[status(thm)],[c_1271,c_158]) ).
tcf(c_1275,plain,
product(product(iPr_def_10,iPr_def_11),one) = product(difference(x0,one),x0),
inference(demodulation,[status(thm)],[c_1013,c_1067,c_1029]) ).
tcf(c_1276,plain,
product(x0,iPr_def_10) = product(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_1275,c_158,c_150,c_137]) ).
tcf(c_1912,plain,
difference(iPr_def_10,product(product(iPr_def_10,x0),x0)) = quotient(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_1250,c_152]) ).
tcf(c_2002,plain,
product(iPr_def_11,quotient(one,iPr_def_11)) = product(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_1272,c_1276]) ).
tcf(c_2017,plain,
! [X0: $i] : product(difference(difference(iPr_def_11,one),one),X0) = product(product(iPr_def_10,iPr_def_11),product(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_2002,c_238]) ).
tcf(c_2035,plain,
! [X0: $i] : product(iPr_def_11,difference(product(iPr_def_10,iPr_def_11),X0)) = product(x0,X0),
inference(light_normalisation,[status(thm)],[c_1118,c_1276]) ).
tcf(c_2041,plain,
! [X0: $i] : difference(product(iPr_def_10,iPr_def_11),X0) = difference(iPr_def_11,product(x0,X0)),
inference(superposition,[status(thm)],[c_2035,c_155]) ).
tcf(c_2045,plain,
! [X0: $i] : product(product(iPr_def_10,iPr_def_11),X0) = difference(x0,product(iPr_def_11,X0)),
inference(light_normalisation,[status(thm)],[c_1124,c_1276]) ).
tcf(c_2047,plain,
! [X0: $i] : product(product(iPr_def_10,iPr_def_11),difference(iPr_def_11,X0)) = difference(x0,X0),
inference(superposition,[status(thm)],[c_156,c_2045]) ).
tcf(c_2084,plain,
difference(iPr_def_10,x0) = quotient(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_1912,c_157,c_257]) ).
tcf(c_2092,plain,
! [X0: $i] : product(product(iPr_def_10,iPr_def_11),product(iPr_def_11,X0)) = product(x0,X0),
inference(demodulation,[status(thm)],[c_2017,c_1067,c_1069]) ).
tcf(c_2317,plain,
! [X0: $i] : product(product(iPr_def_12,X0),iPr_def_13) = product(iPr_def_12,quotient(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_1262,c_156]) ).
tcf(c_2327,plain,
! [X0: $i] : product(product(iPr_def_10,X0),iPr_def_11) = product(iPr_def_10,quotient(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_1263,c_156]) ).
tcf(c_2351,plain,
! [X0: $i] : difference(X0,product(product(X0,x0),product(iPr_def_10,iPr_def_11))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1266,c_1276]) ).
tcf(c_2355,plain,
! [X0: $i] : difference(quotient(X0,x0),product(X0,product(iPr_def_10,iPr_def_11))) = iPr_def_11,
inference(superposition,[status(thm)],[c_153,c_2351]) ).
tcf(c_2356,plain,
difference(x1,product(iPr_def_12,product(iPr_def_10,iPr_def_11))) = iPr_def_11,
inference(superposition,[status(thm)],[c_1059,c_2351]) ).
tcf(c_2363,plain,
! [X0: $i] : product(product(X0,x0),product(iPr_def_10,iPr_def_11)) = product(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_2351,c_156]) ).
tcf(c_2366,plain,
product(x0,product(product(product(iPr_def_10,iPr_def_11),x0),product(iPr_def_10,iPr_def_11))) = product(iPr_def_11,iPr_def_11),
inference(superposition,[status(thm)],[c_2351,c_2035]) ).
tcf(c_2399,plain,
! [X0: $i] : quotient(difference(x0,X0),difference(iPr_def_11,X0)) = product(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_2047,c_154]) ).
tcf(c_2439,plain,
product(x0,product(iPr_def_10,quotient(iPr_def_11,iPr_def_10))) = product(iPr_def_11,iPr_def_11),
inference(demodulation,[status(thm)],[c_2366,c_2327,c_2363]) ).
tcf(c_2440,plain,
product(x0,x0) = product(iPr_def_11,iPr_def_11),
inference(demodulation,[status(thm)],[c_2439,c_156,c_2084]) ).
tcf(c_2593,plain,
difference(x0,product(product(iPr_def_11,iPr_def_11),iPr_def_10)) = quotient(x0,x0),
inference(superposition,[status(thm)],[c_2440,c_1265]) ).
tcf(c_2643,plain,
! [X0: $i] : product(product(iPr_def_10,iPr_def_11),X0) = product(x0,difference(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_156,c_2092]) ).
tcf(c_2675,plain,
product(iPr_def_12,product(iPr_def_10,iPr_def_11)) = product(x1,iPr_def_11),
inference(superposition,[status(thm)],[c_2356,c_156]) ).
tcf(c_2736,plain,
! [X0: $i] : quotient(product(iPr_def_12,quotient(X0,iPr_def_12)),iPr_def_13) = product(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_2317,c_154]) ).
tcf(c_2777,plain,
difference(x0,product(product(iPr_def_11,iPr_def_11),iPr_def_10)) = one,
inference(demodulation,[status(thm)],[c_2593,c_263]) ).
tcf(c_3043,plain,
! [X0: $i] : quotient(product(iPr_def_10,quotient(X0,iPr_def_10)),iPr_def_11) = product(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_2327,c_154]) ).
tcf(c_3377,plain,
! [X0: $i] : quotient(product(X0,product(iPr_def_10,iPr_def_11)),iPr_def_11) = quotient(X0,x0),
inference(superposition,[status(thm)],[c_2355,c_273]) ).
tcf(c_3411,plain,
quotient(one,difference(iPr_def_11,product(product(iPr_def_11,iPr_def_11),iPr_def_10))) = product(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_2777,c_2399]) ).
tcf(c_3546,plain,
! [X0: $i] : difference(iPr_def_11,product(product(iPr_def_11,X0),iPr_def_10)) = quotient(X0,x0),
inference(demodulation,[status(thm)],[c_3377,c_152]) ).
tcf(c_3549,plain,
quotient(one,quotient(iPr_def_11,x0)) = product(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_3411,c_3546]) ).
tcf(c_3866,plain,
difference(product(iPr_def_10,iPr_def_11),one) = quotient(iPr_def_11,x0),
inference(superposition,[status(thm)],[c_3549,c_268]) ).
tcf(c_3867,plain,
product(product(iPr_def_10,iPr_def_11),quotient(iPr_def_11,x0)) = one,
inference(superposition,[status(thm)],[c_3549,c_153]) ).
tcf(c_3900,plain,
product(x0,difference(iPr_def_11,quotient(iPr_def_11,x0))) = one,
inference(demodulation,[status(thm)],[c_3867,c_2643]) ).
tcf(c_3901,plain,
difference(iPr_def_11,x0) = quotient(iPr_def_11,x0),
inference(demodulation,[status(thm)],[c_3866,c_158,c_2041]) ).
tcf(c_4084,plain,
product(x0,difference(iPr_def_11,difference(iPr_def_11,x0))) = one,
inference(light_normalisation,[status(thm)],[c_3900,c_3901]) ).
tcf(c_4088,plain,
difference(iPr_def_11,difference(iPr_def_11,x0)) = difference(x0,one),
inference(superposition,[status(thm)],[c_4084,c_155]) ).
tcf(c_4089,plain,
quotient(one,difference(iPr_def_11,difference(iPr_def_11,x0))) = x0,
inference(superposition,[status(thm)],[c_4084,c_154]) ).
tcf(c_4169,plain,
! [X0: $i] : product(iPr_def_12,product(X0,iPr_def_12)) = quotient(product(iPr_def_12,X0),iPr_def_13),
inference(superposition,[status(thm)],[c_154,c_2736]) ).
tcf(c_4378,plain,
quotient(one,difference(x0,one)) = x0,
inference(light_normalisation,[status(thm)],[c_4089,c_4088]) ).
tcf(c_4385,plain,
! [X0: $i,X1: $i] : product(product(product(difference(x0,one),x0),X0),X1) = product(product(difference(x0,one),x0),product(X0,X1)),
inference(superposition,[status(thm)],[c_4378,c_242]) ).
tcf(c_4534,plain,
! [X0: $i] : product(iPr_def_10,product(X0,iPr_def_10)) = quotient(product(iPr_def_10,X0),iPr_def_11),
inference(superposition,[status(thm)],[c_154,c_3043]) ).
tcf(c_4606,plain,
! [X0: $i,X1: $i] : product(product(x0,difference(iPr_def_11,X0)),X1) = product(x0,difference(iPr_def_11,product(X0,X1))),
inference(demodulation,[status(thm)],[c_4385,c_150,c_1015,c_1276,c_2643]) ).
tcf(c_5743,plain,
! [X0: $i] : product(iPr_def_12,product(product(X0,iPr_def_13),iPr_def_12)) = difference(iPr_def_13,product(product(iPr_def_13,iPr_def_12),X0)),
inference(superposition,[status(thm)],[c_4169,c_152]) ).
tcf(c_5956,plain,
! [X0: $i] : product(iPr_def_12,product(product(X0,iPr_def_13),iPr_def_12)) = difference(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_5743,c_157,c_260]) ).
tcf(c_7463,plain,
product(iPr_def_12,product(product(x0,difference(iPr_def_11,iPr_def_13)),iPr_def_12)) = difference(iPr_def_13,product(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_2643,c_5956]) ).
tcf(c_7499,plain,
difference(iPr_def_13,product(iPr_def_10,iPr_def_11)) = product(x1,iPr_def_11),
inference(demodulation,[status(thm)],[c_7463,c_260,c_1069,c_1276,c_2675,c_4606]) ).
tcf(c_8083,plain,
product(iPr_def_13,product(x1,iPr_def_11)) = product(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_7499,c_156]) ).
tcf(c_8393,plain,
difference(iPr_def_11,product(product(iPr_def_11,iPr_def_13),x1)) = quotient(product(iPr_def_10,iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_8083,c_152]) ).
tcf(c_8610,plain,
difference(iPr_def_11,product(iPr_def_14,x1)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_8393,c_158,c_259,c_1060,c_4534]) ).
tcf(c_8701,plain,
product(iPr_def_11,iPr_def_10) = product(iPr_def_14,x1),
inference(superposition,[status(thm)],[c_8610,c_156]) ).
tcf(c_8937,plain,
product(iPr_def_14,x1) = one,
inference(demodulation,[status(thm)],[c_8701,c_259]) ).
tcf(c_9014,plain,
quotient(one,x1) = iPr_def_14,
inference(superposition,[status(thm)],[c_8937,c_154]) ).
tcf(c_9242,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_9014,c_1022]) ).
tcf(c_9243,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9242,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.35 % Computer : n016.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Wed Sep 23 16:04:41 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.39 Running UEQ theorem proving
% 0.15/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40
% 0.15/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.40
% 0.15/0.40 % Detected problem language: tptp
% 0.15/0.42 % Proving...
% 11.53/2.25 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 11.53/2.25 % SZS status Started for theBenchmark.p
% 11.53/2.25 % SZS status Unsatisfiable for theBenchmark.p
% 11.53/2.25
% 11.53/2.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.53/2.25
% 11.53/2.25 % ------ iProver source info
% 11.53/2.25
% 11.53/2.25 % git: date: 2026-07-19 20:42:38 +0200
% 11.53/2.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.53/2.25 % git: non_committed_changes: false
% 11.53/2.25
% 11.53/2.25 % ------ Parsing...% successful
% 11.53/2.25
% 11.53/2.25
% 11.53/2.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.53/2.25
% 11.53/2.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 11.53/2.25
% 11.53/2.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.53/2.25
% 11.53/2.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 11.53/2.25 % ------ Proving...
% 11.53/2.25 % ------ Problem Properties
% 11.53/2.25
% 11.53/2.25 %
% 11.53/2.25 % clauses 22
% 11.53/2.25 % conjectures 1
% 11.53/2.25 % EPR 1
% 11.53/2.25 % Horn 22
% 11.53/2.25 % unary 22
% 11.53/2.25 % binary 0
% 11.53/2.25 % lits 22
% 11.53/2.25 % lits eq 22
% 11.53/2.25 % fd_pure 0
% 11.53/2.25 % fd_pseudo 0
% 11.53/2.25 % fd_cond 0
% 11.53/2.25 % fd_pseudo_cond 0
% 11.53/2.25 % AC symbols 0
% 11.53/2.25
% 11.53/2.25 % ------ Input Options Time Limit: Unbounded
% 11.53/2.25
% 11.53/2.25
% 11.53/2.25 % ------
% 11.53/2.25 % Current options:
% 11.53/2.25 % ------
% 11.53/2.25
% 11.53/2.25
% 11.53/2.25 %
% 11.53/2.25
% 11.53/2.25 % ------ Proving...
% 11.53/2.25 %
% 11.53/2.25
% 11.53/2.25 % SZS status Unsatisfiable for theBenchmark.p
% 11.53/2.25
% 11.53/2.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.53/2.25
% 11.53/2.25
%------------------------------------------------------------------------------