%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP778+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 01:35:24 PM UTC 2026
% Result : Theorem 64.08s 10.96s
% Output : CNFRefutation 64.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 178 ( 163 unt; 4 def)
% Number of atoms : 352 ( 175 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 28 ~; 21 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn 162 !; 0 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : difference(X1,product(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(f2,axiom,
! [X0,X1] : product(X1,difference(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
fof(f3,axiom,
! [X0,X1] : quotient(product(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(f4,axiom,
! [X0,X1] : product(quotient(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(f5,axiom,
! [X0,X1,X2,X3] : product(product(X3,X2),product(X1,X0)) = product(product(X3,X1),product(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(f6,axiom,
! [X0] : product(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(f7,axiom,
! [X0,X1] : product(product(product(X1,X0),X0),product(X0,product(X0,X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(f8,axiom,
! [X0,X1,X2] :
( d(X0,X1,X2)
<=> product(X0,X1) = product(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
fof(f9,axiom,
! [X0,X1,X2] :
( m(X0,X1,X2)
<=> product(product(X0,X1),product(X1,X2)) = product(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(f10,axiom,
d(a1,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(f11,axiom,
d(a,b1,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(f12,axiom,
d(a,b,c1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(f14,axiom,
d(a1,b2,c1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
fof(f16,conjecture,
m(b1,b,b2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f17,negated_conjecture,
~ m(b1,b,b2),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
~ m(b1,b,b2),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( product(product(X0,X1),product(X1,X2)) = product(X0,X2)
=> m(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f20,plain,
! [X0,X1,X2] :
( d(X0,X1,X2)
=> product(X0,X1) = product(X1,X2) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ d(X0,X1,X2)
| product(X0,X1) = product(X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( product(product(X0,X1),product(X1,X2)) != product(X0,X2)
| m(X0,X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f23,plain,
! [X0,X1] : difference(X1,product(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] : product(X1,difference(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0,X1] : quotient(product(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f26,plain,
! [X0,X1] : product(quotient(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : product(product(X3,X2),product(X1,X0)) = product(product(X3,X1),product(X2,X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1] : product(product(product(X1,X0),X0),product(X0,product(X0,X1))) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ d(X0,X1,X2)
| product(X0,X1) = product(X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X2,X0,X1] :
( product(product(X0,X1),product(X1,X2)) != product(X0,X2)
| m(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
d(a1,b,c),
inference(cnf_transformation,[],[f10]) ).
fof(f33,plain,
d(a,b1,c),
inference(cnf_transformation,[],[f11]) ).
fof(f34,plain,
d(a,b,c1),
inference(cnf_transformation,[],[f12]) ).
fof(f36,plain,
d(a1,b2,c1),
inference(cnf_transformation,[],[f14]) ).
fof(f38,plain,
~ m(b1,b,b2),
inference(cnf_transformation,[],[f18]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[],[f23]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[],[f24]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(product(X0,X1),product(X2,X3)) = product(product(X0,X2),product(X1,X3)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_54,plain,
! [X0: $i] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : product(product(product(X0,X1),X1),product(X1,product(X1,X0))) = X1,
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ~ d(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( m(X0,X1,X2)
| ( product(product(X0,X1),product(X1,X2)) != product(X0,X2) ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_58,plain,
d(a1,b,c),
inference(cnf_transformation,[],[f32]) ).
tcf(c_59,plain,
d(a,b1,c),
inference(cnf_transformation,[],[f33]) ).
tcf(c_60,plain,
d(a,b,c1),
inference(cnf_transformation,[],[f34]) ).
tcf(c_62,plain,
d(a1,b2,c1),
inference(cnf_transformation,[],[f36]) ).
tcf(c_64,negated_conjecture,
~ m(b1,b,b2),
inference(cnf_transformation,[],[f38]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 != b2 )
| ( X1 != b )
| ( X0 != b1 )
| ( product(product(X0,X1),product(X1,X2)) != product(X0,X2) ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_64]) ).
tcf(c_125,plain,
product(product(b1,b),product(b,b2)) != product(b1,b2),
inference(unflattening,[status(thm)],[c_124]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ( X2 != c )
| ( X1 != b )
| ( X0 != a1 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_58]) ).
tcf(c_131,plain,
product(a1,b) = product(b,c),
inference(unflattening,[status(thm)],[c_130]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ( X2 != c )
| ( X1 != b1 )
| ( X0 != a ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_59]) ).
tcf(c_136,plain,
product(a,b1) = product(b1,c),
inference(unflattening,[status(thm)],[c_135]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ( X2 != c1 )
| ( X1 != b )
| ( X0 != a ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_60]) ).
tcf(c_141,plain,
product(a,b) = product(b,c1),
inference(unflattening,[status(thm)],[c_140]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ( X2 != c1 )
| ( X1 != b2 )
| ( X0 != a1 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_62]) ).
tcf(c_151,plain,
product(a1,b2) = product(b2,c1),
inference(unflattening,[status(thm)],[c_150]) ).
tcf(c_199,definition,
iPr_def_10 = product(b1,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_200,definition,
iPr_def_11 = product(b,b2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_201,definition,
iPr_def_12 = product(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_202,definition,
iPr_def_13 = product(b1,b2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_203,plain,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_125,c_202,c_200,c_199,c_201]) ).
tcf(c_271,plain,
! [X0: $i] : difference(X0,X0) = X0,
inference(superposition,[status(thm)],[c_54,c_49]) ).
tcf(c_272,plain,
difference(b1,iPr_def_10) = b,
inference(superposition,[status(thm)],[c_199,c_49]) ).
tcf(c_273,plain,
difference(b,iPr_def_11) = b2,
inference(superposition,[status(thm)],[c_200,c_49]) ).
tcf(c_274,plain,
difference(b1,iPr_def_13) = b2,
inference(superposition,[status(thm)],[c_202,c_49]) ).
tcf(c_275,plain,
difference(iPr_def_10,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_201,c_49]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),product(X1,product(X1,quotient(X0,X1)))) = X1,
inference(superposition,[status(thm)],[c_52,c_55]) ).
tcf(c_298,plain,
product(product(product(b,b1),b1),product(b1,iPr_def_10)) = b1,
inference(superposition,[status(thm)],[c_199,c_55]) ).
tcf(c_299,plain,
product(product(product(b2,b),b),product(b,iPr_def_11)) = b,
inference(superposition,[status(thm)],[c_200,c_55]) ).
tcf(c_307,plain,
product(b1,b) = iPr_def_10,
inference(superposition,[status(thm)],[c_272,c_50]) ).
tcf(c_308,plain,
product(b,b2) = iPr_def_11,
inference(superposition,[status(thm)],[c_273,c_50]) ).
tcf(c_309,plain,
product(b1,b2) = iPr_def_13,
inference(superposition,[status(thm)],[c_274,c_50]) ).
tcf(c_310,plain,
product(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_275,c_50]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),product(X0,X2)) = product(X0,product(X1,X2)),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i] : product(product(b1,X0),product(b,X1)) = product(iPr_def_10,product(X0,X1)),
inference(superposition,[status(thm)],[c_307,c_53]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),product(X2,X1)) = product(product(X0,X2),X1),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i] : product(product(X0,b1),product(X1,b)) = product(product(X0,X1),iPr_def_10),
inference(superposition,[status(thm)],[c_307,c_53]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] : product(product(X0,b),product(X1,b2)) = product(product(X0,X1),iPr_def_11),
inference(superposition,[status(thm)],[c_308,c_53]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),product(b1,c)) = product(product(X0,a),product(X1,b1)),
inference(superposition,[status(thm)],[c_136,c_53]) ).
tcf(c_426,plain,
quotient(product(b,c1),b) = a,
inference(superposition,[status(thm)],[c_141,c_51]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),product(b,c1)) = product(product(X0,a),product(X1,b)),
inference(superposition,[status(thm)],[c_141,c_53]) ).
tcf(c_481,plain,
product(b,c1) = product(a,b),
inference(superposition,[status(thm)],[c_426,c_52]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i] : product(X0,product(X0,quotient(X1,X0))) = difference(product(X1,X0),X0),
inference(superposition,[status(thm)],[c_288,c_49]) ).
tcf(c_856,plain,
! [X0: $i] : product(b1,product(b,X0)) = product(iPr_def_10,product(b1,X0)),
inference(superposition,[status(thm)],[c_307,c_369]) ).
tcf(c_858,plain,
! [X0: $i] : product(b,product(b2,X0)) = product(iPr_def_11,product(b,X0)),
inference(superposition,[status(thm)],[c_308,c_369]) ).
tcf(c_863,plain,
! [X0: $i] : product(product(b1,c),product(a,X0)) = product(a,product(b1,X0)),
inference(superposition,[status(thm)],[c_136,c_369]) ).
tcf(c_864,plain,
! [X0: $i] : product(product(b,c1),product(a,X0)) = product(a,product(b,X0)),
inference(superposition,[status(thm)],[c_481,c_369]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i,X2: $i] : product(X0,product(X1,difference(X0,X2))) = product(product(X0,X1),X2),
inference(superposition,[status(thm)],[c_50,c_369]) ).
tcf(c_889,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c_54,c_369]) ).
tcf(c_897,plain,
! [X0: $i] : product(product(b,X0),product(a1,b)) = product(b,product(X0,c)),
inference(superposition,[status(thm)],[c_131,c_369]) ).
tcf(c_903,plain,
! [X0: $i] : product(product(b2,X0),product(a1,b2)) = product(b2,product(X0,c1)),
inference(superposition,[status(thm)],[c_151,c_369]) ).
tcf(c_926,plain,
! [X0: $i,X1: $i,X2: $i] : difference(product(X0,X1),product(X0,product(X1,X2))) = product(X0,X2),
inference(superposition,[status(thm)],[c_369,c_49]) ).
tcf(c_982,plain,
! [X0: $i] : difference(b1,product(iPr_def_10,product(b1,X0))) = product(b,X0),
inference(superposition,[status(thm)],[c_856,c_49]) ).
tcf(c_1009,plain,
! [X0: $i] : product(iPr_def_10,product(b2,X0)) = product(iPr_def_13,product(b,X0)),
inference(superposition,[status(thm)],[c_309,c_371]) ).
tcf(c_1015,plain,
! [X0: $i] : product(product(b1,X0),iPr_def_11) = product(iPr_def_10,product(X0,b2)),
inference(superposition,[status(thm)],[c_308,c_371]) ).
tcf(c_1083,plain,
! [X0: $i,X1: $i] : quotient(product(X0,product(X1,X0)),X0) = product(X0,X1),
inference(superposition,[status(thm)],[c_889,c_51]) ).
tcf(c_1154,plain,
! [X0: $i] : difference(b,product(iPr_def_11,product(b,X0))) = product(b2,X0),
inference(superposition,[status(thm)],[c_858,c_49]) ).
tcf(c_1264,plain,
! [X0: $i] : product(b,difference(b1,X0)) = difference(b1,product(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_50,c_982]) ).
tcf(c_1500,plain,
! [X0: $i,X1: $i] : product(X0,quotient(X1,X0)) = quotient(product(X0,X1),X0),
inference(superposition,[status(thm)],[c_52,c_1083]) ).
tcf(c_1824,plain,
! [X0: $i] : difference(iPr_def_13,product(iPr_def_10,product(b2,X0))) = product(b,X0),
inference(superposition,[status(thm)],[c_1009,c_49]) ).
tcf(c_1894,plain,
! [X0: $i] : product(b2,difference(b,X0)) = difference(b,product(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_50,c_1154]) ).
tcf(c_2342,plain,
! [X0: $i] : product(product(X0,b),iPr_def_13) = product(product(X0,b1),iPr_def_11),
inference(superposition,[status(thm)],[c_309,c_388]) ).
tcf(c_2379,plain,
! [X0: $i] : product(b,difference(b1,difference(iPr_def_10,X0))) = difference(b1,X0),
inference(superposition,[status(thm)],[c_50,c_1264]) ).
tcf(c_2834,plain,
! [X0: $i,X1: $i] : product(X0,quotient(difference(X0,X1),X0)) = quotient(X1,X0),
inference(superposition,[status(thm)],[c_50,c_1500]) ).
tcf(c_2840,plain,
product(b1,quotient(b,b1)) = quotient(iPr_def_10,b1),
inference(superposition,[status(thm)],[c_307,c_1500]) ).
tcf(c_2842,plain,
product(b,quotient(b2,b)) = quotient(iPr_def_11,b),
inference(superposition,[status(thm)],[c_308,c_1500]) ).
tcf(c_3224,plain,
! [X0: $i] : product(b,difference(b2,X0)) = difference(iPr_def_13,product(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_50,c_1824]) ).
tcf(c_3233,plain,
! [X0: $i] : product(b2,difference(b,difference(iPr_def_11,X0))) = difference(b,X0),
inference(superposition,[status(thm)],[c_50,c_1894]) ).
tcf(c_3939,plain,
product(product(b,c1),iPr_def_13) = product(product(a,b1),iPr_def_11),
inference(superposition,[status(thm)],[c_481,c_2342]) ).
tcf(c_3963,plain,
product(product(b,c1),iPr_def_13) = product(product(b1,c),iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3939,c_136]) ).
tcf(c_4016,plain,
! [X0: $i] : difference(b,difference(b1,X0)) = difference(b1,difference(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_2379,c_49]) ).
tcf(c_4845,plain,
! [X0: $i,X1: $i] : difference(X0,quotient(X1,X0)) = quotient(difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_2834,c_49]) ).
tcf(c_4927,plain,
product(b,difference(b2,iPr_def_11)) = difference(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_310,c_3224]) ).
tcf(c_4975,plain,
difference(b,difference(iPr_def_13,iPr_def_12)) = difference(b2,iPr_def_11),
inference(superposition,[status(thm)],[c_4927,c_49]) ).
tcf(c_5127,plain,
! [X0: $i] : difference(b,difference(iPr_def_11,X0)) = difference(b2,difference(b,X0)),
inference(superposition,[status(thm)],[c_3233,c_49]) ).
tcf(c_7443,plain,
! [X0: $i] : difference(b1,difference(iPr_def_10,product(b1,X0))) = difference(b,X0),
inference(superposition,[status(thm)],[c_49,c_4016]) ).
tcf(c_7444,plain,
difference(b1,difference(iPr_def_10,b1)) = difference(b,b1),
inference(superposition,[status(thm)],[c_271,c_4016]) ).
tcf(c_7464,plain,
product(b1,difference(b,b1)) = difference(iPr_def_10,b1),
inference(superposition,[status(thm)],[c_7444,c_50]) ).
tcf(c_7631,plain,
product(product(b,c1),iPr_def_13) = product(iPr_def_10,product(c,b2)),
inference(demodulation,[status(thm)],[c_3963,c_1015]) ).
tcf(c_7641,plain,
difference(product(b,c1),product(iPr_def_10,product(c,b2))) = iPr_def_13,
inference(superposition,[status(thm)],[c_7631,c_49]) ).
tcf(c_8526,plain,
! [X0: $i,X1: $i] : product(difference(X0,quotient(X1,X0)),X0) = difference(X0,X1),
inference(superposition,[status(thm)],[c_4845,c_52]) ).
tcf(c_8710,plain,
! [X0: $i] : difference(b,difference(iPr_def_11,product(b,X0))) = difference(b2,X0),
inference(superposition,[status(thm)],[c_49,c_5127]) ).
tcf(c_8711,plain,
difference(b,difference(iPr_def_11,b)) = difference(b2,b),
inference(superposition,[status(thm)],[c_271,c_5127]) ).
tcf(c_8728,plain,
product(b,difference(b2,b)) = difference(iPr_def_11,b),
inference(superposition,[status(thm)],[c_8711,c_50]) ).
tcf(c_10844,plain,
! [X0: $i] : product(b1,difference(b,X0)) = difference(iPr_def_10,product(b1,X0)),
inference(superposition,[status(thm)],[c_7443,c_50]) ).
tcf(c_12078,plain,
! [X0: $i,X1: $i] : product(difference(X0,X1),X0) = difference(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c_51,c_8526]) ).
tcf(c_13100,plain,
! [X0: $i] : product(b,difference(b2,X0)) = difference(iPr_def_11,product(b,X0)),
inference(superposition,[status(thm)],[c_8710,c_50]) ).
tcf(c_16618,plain,
product(difference(iPr_def_10,b1),iPr_def_10) = product(b1,difference(b,iPr_def_10)),
inference(superposition,[status(thm)],[c_12078,c_10844]) ).
tcf(c_16821,plain,
product(difference(iPr_def_11,b),iPr_def_11) = product(b,difference(b2,iPr_def_11)),
inference(superposition,[status(thm)],[c_13100,c_12078]) ).
tcf(c_16822,plain,
product(difference(iPr_def_11,b),iPr_def_11) = difference(iPr_def_13,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_16821,c_4927]) ).
tcf(c_16887,plain,
! [X0: $i,X1: $i] : product(product(X0,difference(iPr_def_11,b)),product(X1,iPr_def_11)) = product(product(X0,X1),difference(iPr_def_13,iPr_def_12)),
inference(superposition,[status(thm)],[c_16822,c_53]) ).
tcf(c_22115,plain,
! [X0: $i,X1: $i] : product(product(X0,difference(iPr_def_10,b1)),product(X1,iPr_def_10)) = product(product(X0,X1),product(b1,difference(b,iPr_def_10))),
inference(superposition,[status(thm)],[c_16618,c_53]) ).
tcf(c_30221,plain,
! [X0: $i] : product(product(X0,iPr_def_10),iPr_def_11) = product(product(X0,iPr_def_11),iPr_def_12),
inference(superposition,[status(thm)],[c_310,c_384]) ).
tcf(c_33032,plain,
product(b1,quotient(iPr_def_10,b1)) = difference(product(b,b1),b1),
inference(superposition,[status(thm)],[c_2840,c_655]) ).
tcf(c_33033,plain,
product(b,quotient(iPr_def_11,b)) = difference(product(b2,b),b),
inference(superposition,[status(thm)],[c_2842,c_655]) ).
tcf(c_35739,plain,
product(product(b,b1),b1) = product(b,difference(iPr_def_10,b1)),
inference(superposition,[status(thm)],[c_7464,c_885]) ).
tcf(c_35753,plain,
product(product(b2,b),b) = product(b2,difference(iPr_def_11,b)),
inference(superposition,[status(thm)],[c_8728,c_885]) ).
tcf(c_36310,plain,
product(product(b,difference(iPr_def_10,b1)),product(b1,iPr_def_10)) = b1,
inference(demodulation,[status(thm)],[c_298,c_35739]) ).
tcf(c_36322,plain,
product(product(b2,difference(iPr_def_11,b)),product(b,iPr_def_11)) = b,
inference(demodulation,[status(thm)],[c_299,c_35753]) ).
tcf(c_37921,plain,
! [X0: $i,X1: $i,X2: $i] : difference(product(X0,X1),product(X0,X2)) = product(X0,difference(X1,X2)),
inference(superposition,[status(thm)],[c_50,c_926]) ).
tcf(c_39757,plain,
product(product(b1,c),product(b1,c)) = product(a,product(b1,b1)),
inference(superposition,[status(thm)],[c_136,c_863]) ).
tcf(c_39992,plain,
product(product(b,c1),product(b,c1)) = product(a,product(b,b)),
inference(superposition,[status(thm)],[c_481,c_864]) ).
tcf(c_40161,plain,
product(product(b,b1),product(b1,difference(b,iPr_def_10))) = b1,
inference(demodulation,[status(thm)],[c_36310,c_22115]) ).
tcf(c_40178,plain,
product(b1,difference(b,iPr_def_10)) = difference(product(b,b1),b1),
inference(superposition,[status(thm)],[c_40161,c_49]) ).
tcf(c_40190,plain,
product(b1,difference(b,iPr_def_10)) = product(b1,quotient(iPr_def_10,b1)),
inference(demodulation,[status(thm)],[c_33032,c_40178]) ).
tcf(c_40268,plain,
product(product(b2,b),difference(iPr_def_13,iPr_def_12)) = b,
inference(demodulation,[status(thm)],[c_36322,c_16887]) ).
tcf(c_40285,plain,
difference(product(b2,b),b) = difference(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_40268,c_49]) ).
tcf(c_40298,plain,
product(b,quotient(iPr_def_11,b)) = difference(iPr_def_13,iPr_def_12),
inference(demodulation,[status(thm)],[c_33033,c_40285]) ).
tcf(c_40450,plain,
difference(b,difference(iPr_def_13,iPr_def_12)) = quotient(iPr_def_11,b),
inference(superposition,[status(thm)],[c_40298,c_49]) ).
tcf(c_40471,plain,
difference(b2,iPr_def_11) = quotient(iPr_def_11,b),
inference(light_normalisation,[status(thm)],[c_40450,c_4975]) ).
tcf(c_40516,plain,
product(difference(b2,iPr_def_11),b) = iPr_def_11,
inference(superposition,[status(thm)],[c_40471,c_52]) ).
tcf(c_42677,plain,
difference(b1,product(b1,difference(b,iPr_def_10))) = quotient(iPr_def_10,b1),
inference(superposition,[status(thm)],[c_40190,c_49]) ).
tcf(c_44124,plain,
difference(b,iPr_def_10) = quotient(iPr_def_10,b1),
inference(demodulation,[status(thm)],[c_42677,c_49]) ).
tcf(c_44152,plain,
product(difference(b,iPr_def_10),b1) = iPr_def_10,
inference(superposition,[status(thm)],[c_44124,c_52]) ).
tcf(c_45123,plain,
product(product(b,a1),iPr_def_10) = product(b,product(b1,c)),
inference(superposition,[status(thm)],[c_897,c_386]) ).
tcf(c_46859,plain,
product(product(b2,a1),iPr_def_11) = product(b2,product(b,c1)),
inference(superposition,[status(thm)],[c_903,c_388]) ).
tcf(c_49934,plain,
difference(product(b,a1),product(b,product(b1,c))) = iPr_def_10,
inference(superposition,[status(thm)],[c_45123,c_49]) ).
tcf(c_52894,plain,
difference(product(b2,a1),product(b2,product(b,c1))) = iPr_def_11,
inference(superposition,[status(thm)],[c_46859,c_49]) ).
tcf(c_57937,plain,
product(b,difference(a1,product(b1,c))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_49934,c_37921]) ).
tcf(c_57955,plain,
difference(a1,product(b1,c)) = difference(b,iPr_def_10),
inference(superposition,[status(thm)],[c_57937,c_49]) ).
tcf(c_58004,plain,
product(a1,difference(b,iPr_def_10)) = product(b1,c),
inference(superposition,[status(thm)],[c_57955,c_50]) ).
tcf(c_58015,plain,
product(product(a1,a),product(difference(b,iPr_def_10),b1)) = product(product(b1,c),product(b1,c)),
inference(superposition,[status(thm)],[c_58004,c_393]) ).
tcf(c_58037,plain,
product(product(a1,a),iPr_def_10) = product(a,product(b1,b1)),
inference(light_normalisation,[status(thm)],[c_58015,c_39757,c_44152]) ).
tcf(c_62092,plain,
product(b2,difference(a1,product(b,c1))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_52894,c_37921]) ).
tcf(c_62111,plain,
difference(a1,product(b,c1)) = difference(b2,iPr_def_11),
inference(superposition,[status(thm)],[c_62092,c_49]) ).
tcf(c_62145,plain,
product(a1,difference(b2,iPr_def_11)) = product(b,c1),
inference(superposition,[status(thm)],[c_62111,c_50]) ).
tcf(c_62165,plain,
product(product(a1,a),product(difference(b2,iPr_def_11),b)) = product(product(b,c1),product(b,c1)),
inference(superposition,[status(thm)],[c_62145,c_430]) ).
tcf(c_62189,plain,
product(product(a1,a),iPr_def_11) = product(a,product(b,b)),
inference(light_normalisation,[status(thm)],[c_62165,c_39992,c_40516]) ).
tcf(c_74382,plain,
product(product(a1,a),iPr_def_10) = product(b1,c),
inference(demodulation,[status(thm)],[c_58037,c_54,c_136]) ).
tcf(c_76606,plain,
product(product(a1,a),iPr_def_11) = product(b,c1),
inference(demodulation,[status(thm)],[c_62189,c_54,c_481]) ).
tcf(c_76630,plain,
product(product(product(a1,a),iPr_def_10),iPr_def_11) = product(product(b,c1),iPr_def_12),
inference(superposition,[status(thm)],[c_76606,c_30221]) ).
tcf(c_76645,plain,
product(product(b,c1),iPr_def_12) = product(product(b1,c),iPr_def_11),
inference(light_normalisation,[status(thm)],[c_76630,c_74382]) ).
tcf(c_93216,plain,
product(product(b,c1),iPr_def_12) = product(iPr_def_10,product(c,b2)),
inference(demodulation,[status(thm)],[c_76645,c_1015]) ).
tcf(c_93228,plain,
difference(product(b,c1),product(iPr_def_10,product(c,b2))) = iPr_def_12,
inference(superposition,[status(thm)],[c_93216,c_49]) ).
tcf(c_93249,plain,
iPr_def_12 = iPr_def_13,
inference(demodulation,[status(thm)],[c_7641,c_93228]) ).
tcf(c_93250,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_93249,c_203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP778+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 16:01:18 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 64.08/10.96 % SZS status Started for theBenchmark.p
% 64.08/10.96 % SZS status Theorem for theBenchmark.p
% 64.08/10.96
% 64.08/10.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 64.08/10.96
% 64.08/10.96 % ------ iProver source info
% 64.08/10.96
% 64.08/10.96 % git: date: 2026-07-19 20:42:38 +0200
% 64.08/10.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 64.08/10.96 % git: non_committed_changes: false
% 64.08/10.96
% 64.08/10.96 % ------ Parsing...
% 64.08/10.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 64.08/10.96
% 64.08/10.96 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 64.08/10.96
% 64.08/10.96 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 64.08/10.96 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 64.08/10.96
% 64.08/10.96 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 64.08/10.96 % ------ Proving...
% 64.08/10.96 % ------ Problem Properties
% 64.08/10.96
% 64.08/10.96 %
% 64.08/10.96 % clauses 18
% 64.08/10.96 % conjectures 0
% 64.08/10.96 % EPR 1
% 64.08/10.96 % Horn 18
% 64.08/10.96 % unary 18
% 64.08/10.96 % binary 0
% 64.08/10.96 % lits 18
% 64.08/10.96 % lits eq 18
% 64.08/10.96 % fd_pure 0
% 64.08/10.96 % fd_pseudo 0
% 64.08/10.96 % fd_cond 0
% 64.08/10.96 % fd_pseudo_cond 0
% 64.08/10.96 % AC symbols 0
% 64.08/10.96
% 64.08/10.96 % ------ Schedule UEQ
% 64.08/10.96
% 64.08/10.96 % ------ Option_UEQ Time Limit: 10.
% 64.08/10.96
% 64.08/10.96
% 64.08/10.96 % ------
% 64.08/10.96 % Current options:
% 64.08/10.96 % ------
% 64.08/10.96
% 64.08/10.96
% 64.08/10.96 %
% 64.08/10.96
% 64.08/10.96 % ------ Proving...
% 64.08/10.96 %
% 64.08/10.96
% 64.08/10.96 % SZS status Theorem for theBenchmark.p
% 64.08/10.96
% 64.08/10.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 64.08/10.96
% 64.08/10.96
%------------------------------------------------------------------------------