%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP775+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 01:35:23 PM UTC 2026
% Result : Theorem 7.30s 6.97s
% Output : CNFRefutation 7.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 127 ( 52 unt; 4 def)
% Number of atoms : 401 ( 152 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 224 ( 91 ~; 101 |; 26 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 107 !; 9 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : product(product(X2,X1),X0) = product(X2,product(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
fof(f2,axiom,
! [X0] : product(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
fof(f3,axiom,
! [X0,X1] :
( l(X0,X1)
<=> ( product(X1,X0) = X1
& product(X0,X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(f4,axiom,
! [X0,X1] :
( r(X0,X1)
<=> ( product(X1,X0) = X0
& product(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
fof(f5,axiom,
! [X0,X1] :
( d(X0,X1)
<=> ? [X2] :
( l(X2,X1)
& r(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
fof(f6,conjecture,
! [X0,X1] :
( d(X0,X1)
<=> ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( d(X0,X1)
<=> ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( d(X0,X1)
<~> ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ( ~ l(X0,X1)
| ( product(X1,X0) = X1
& product(X0,X1) = X0 ) )
& ( product(X1,X0) != X1
| product(X0,X1) != X0
| l(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f10,plain,
! [X0,X1] :
( ( ~ l(X0,X1)
| ( product(X1,X0) = X1
& product(X0,X1) = X0 ) )
& ( product(X1,X0) != X1
| product(X0,X1) != X0
| l(X0,X1) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( ~ r(X0,X1)
| ( product(X1,X0) = X0
& product(X0,X1) = X1 ) )
& ( product(X1,X0) != X0
| product(X0,X1) != X1
| r(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f12,plain,
! [X0,X1] :
( ( ~ r(X0,X1)
| ( product(X1,X0) = X0
& product(X0,X1) = X1 ) )
& ( product(X1,X0) != X0
| product(X0,X1) != X1
| r(X0,X1) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( ~ d(X0,X1)
| ? [X2] :
( l(X2,X1)
& r(X0,X2) ) )
& ( ! [X2] :
( ~ l(X2,X1)
| ~ r(X0,X2) )
| d(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f14,plain,
! [X0,X1] :
( ( ~ d(X0,X1)
| ? [X3] :
( l(X3,X1)
& r(X0,X3) ) )
& ( ! [X2] :
( ~ l(X2,X1)
| ~ r(X0,X2) )
| d(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ d(X0,X1)
| ( l(sK0(X0,X1),X1)
& r(X0,sK0(X0,X1)) ) )
& ( ! [X2] :
( ~ l(X2,X1)
| ~ r(X0,X2) )
| d(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( ( d(X0,X1)
| ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) )
& ( ~ d(X0,X1)
| product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f17,plain,
? [X0,X1] :
( ( d(X0,X1)
| ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) )
& ( ~ d(X0,X1)
| product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0 ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( ( d(sK1,sK2)
| ( sK2 = product(sK2,product(sK1,sK2))
& sK1 = product(sK1,product(sK2,sK1)) ) )
& ( ~ d(sK1,sK2)
| sK2 != product(sK2,product(sK1,sK2))
| sK1 != product(sK1,product(sK2,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] : product(product(X2,X1),X0) = product(X2,product(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ~ l(X0,X1)
| product(X1,X0) = X1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X0,X1] :
( ~ l(X0,X1)
| product(X0,X1) = X0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0,X1] :
( product(X1,X0) != X1
| product(X0,X1) != X0
| l(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( ~ r(X0,X1)
| product(X1,X0) = X0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X0,X1] :
( ~ r(X0,X1)
| product(X0,X1) = X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( product(X1,X0) != X0
| product(X0,X1) != X1
| r(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( ~ d(X0,X1)
| l(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( ~ d(X0,X1)
| r(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ l(X2,X1)
| ~ r(X0,X2)
| d(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
( d(sK1,sK2)
| sK2 = product(sK2,product(sK1,sK2)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
( d(sK1,sK2)
| sK1 = product(sK1,product(sK2,sK1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
( ~ d(sK1,sK2)
| sK2 != product(sK2,product(sK1,sK2))
| sK1 != product(sK1,product(sK2,sK1)) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),X2) = product(X0,product(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_50,plain,
! [X0: $i] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( l(X1,X0)
| ( product(X1,X0) != X1 )
| ( product(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( product(X0,X1) = X0 )
| ~ l(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( product(X1,X0) = X1 )
| ~ l(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( r(X1,X0)
| ( product(X1,X0) != X0 )
| ( product(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( product(X0,X1) = X1 )
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( product(X1,X0) = X0 )
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( d(X2,X1)
| ~ r(X2,X0)
| ~ l(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( r(X0,sK0(X0,X1))
| ~ d(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( l(sK0(X0,X1),X1)
| ~ d(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_60,negated_conjecture,
( ~ d(sK1,sK2)
| ( product(sK2,product(sK1,sK2)) != sK2 )
| ( product(sK1,product(sK2,sK1)) != sK1 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,negated_conjecture,
( d(sK1,sK2)
| ( product(sK1,product(sK2,sK1)) = sK1 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_62,negated_conjecture,
( d(sK1,sK2)
| ( product(sK2,product(sK1,sK2)) = sK2 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_400,definition,
iPr_def_10 = product(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_401,definition,
iPr_def_11 = product(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_402,definition,
iPr_def_12 = product(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_403,definition,
iPr_def_13 = product(sK1,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_404,negated_conjecture,
( d(sK1,sK2)
| ( iPr_def_11 = sK2 ) ),
inference(demodulation,[status(thm)],[c_62,c_400,c_401]) ).
tcf(c_405,negated_conjecture,
( d(sK1,sK2)
| ( iPr_def_13 = sK1 ) ),
inference(demodulation,[status(thm)],[c_61,c_402,c_403]) ).
tcf(c_406,negated_conjecture,
( ~ d(sK1,sK2)
| ( iPr_def_13 != sK1 )
| ( iPr_def_11 != sK2 ) ),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i] : product(X0,product(X0,X1)) = product(X0,X1),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_639,plain,
! [X0: $i] : product(sK1,product(sK2,X0)) = product(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_400,c_49]) ).
tcf(c_640,plain,
! [X0: $i] : product(sK2,product(iPr_def_10,X0)) = product(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_401,c_49]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i] :
( ( product(X1,sK0(X0,X1)) = X1 )
| ~ d(X0,X1) ),
inference(superposition,[status(thm)],[c_59,c_53]) ).
tcf(c_684,plain,
! [X0: $i,X1: $i] :
( ( product(sK0(X0,X1),X0) = X0 )
| ~ d(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_56]) ).
tcf(c_690,plain,
product(sK1,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_400,c_637]) ).
tcf(c_691,plain,
product(sK2,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_401,c_637]) ).
tcf(c_757,plain,
product(sK1,iPr_def_12) = product(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_402,c_639]) ).
tcf(c_758,plain,
product(sK1,iPr_def_11) = product(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_401,c_639]) ).
tcf(c_762,plain,
product(sK1,iPr_def_11) = product(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_691,c_639]) ).
tcf(c_767,plain,
product(iPr_def_10,sK1) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_757,c_403]) ).
tcf(c_796,plain,
! [X0: $i] :
( l(X0,X0)
| ( product(X0,X0) != X0 ) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_815,plain,
! [X0: $i] : l(X0,X0),
inference(ground_joinability,[status(thm)],[c_796,c_50]) ).
tcf(c_924,plain,
! [X0: $i] :
( r(X0,X0)
| ( product(X0,X0) != X0 ) ),
inference(superposition,[status(thm)],[c_50,c_54]) ).
tcf(c_952,plain,
! [X0: $i] : r(X0,X0),
inference(ground_joinability,[status(thm)],[c_924,c_50]) ).
tcf(c_1045,plain,
! [X0: $i,X1: $i] :
( d(X0,X1)
| ~ r(X0,X1) ),
inference(superposition,[status(thm)],[c_815,c_57]) ).
tcf(c_1085,plain,
( r(sK1,iPr_def_10)
| ( sK1 != iPr_def_13 )
| ( product(sK1,iPr_def_10) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_767,c_54]) ).
tcf(c_1093,plain,
( r(sK1,iPr_def_10)
| ( sK1 != iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_1085,c_690]) ).
tcf(c_1151,plain,
! [X0: $i] : d(X0,X0),
inference(superposition,[status(thm)],[c_952,c_1045]) ).
tcf(c_1202,plain,
product(sK1,iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_758,c_50]) ).
tcf(c_1239,plain,
product(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_762,c_1202]) ).
tcf(c_1254,plain,
product(sK2,iPr_def_10) = product(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_50,c_640]) ).
tcf(c_1271,plain,
product(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1254,c_401]) ).
tcf(c_1296,plain,
( l(iPr_def_10,iPr_def_11)
| ( product(iPr_def_10,iPr_def_11) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1271,c_51]) ).
tcf(c_1299,plain,
l(iPr_def_10,iPr_def_11),
inference(ground_joinability,[status(thm)],[c_1296,c_1239]) ).
tcf(c_1327,plain,
! [X0: $i] :
( d(X0,iPr_def_11)
| ~ r(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1299,c_57]) ).
tcf(c_1332,plain,
( d(sK1,iPr_def_11)
| ~ r(sK1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_1327]) ).
tcf(c_4166,plain,
( ( sK1 = iPr_def_13 )
| ( product(sK0(sK1,sK2),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_405,c_684]) ).
tcf(c_4167,plain,
( ( sK2 = iPr_def_11 )
| ( product(sK0(sK1,sK2),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_404,c_684]) ).
tcf(c_4169,plain,
! [X0: $i] : product(sK0(X0,X0),X0) = X0,
inference(superposition,[status(thm)],[c_1151,c_684]) ).
tcf(c_4232,plain,
! [X0: $i] :
( ( sK1 = iPr_def_13 )
| ( product(sK0(sK1,sK2),product(sK1,X0)) = product(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_4166,c_49]) ).
tcf(c_4834,plain,
( ( sK1 = iPr_def_13 )
| ( product(sK0(sK1,sK2),iPr_def_10) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1202,c_4232]) ).
tcf(c_7267,plain,
! [X0: $i,X1: $i] : product(sK0(X0,X0),product(X0,X1)) = product(X0,X1),
inference(superposition,[status(thm)],[c_4169,c_49]) ).
tcf(c_8774,plain,
! [X0: $i,X1: $i] :
( ( product(sK0(X0,X1),X1) = sK0(X0,X1) )
| ~ d(X0,X1) ),
inference(superposition,[status(thm)],[c_59,c_52]) ).
tcf(c_8781,plain,
! [X0: $i,X1: $i] :
( ( product(X1,sK0(X0,X1)) = X1 )
| ~ d(X0,X1) ),
inference(superposition,[status(thm)],[c_59,c_53]) ).
tcf(c_8789,plain,
( ( sK2 = iPr_def_11 )
| ( product(sK2,sK0(sK1,sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_404,c_8781]) ).
tcf(c_8808,plain,
! [X0: $i,X1: $i] :
( ( product(X0,sK0(X0,X1)) = sK0(X0,X1) )
| ~ d(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_55]) ).
tcf(c_8846,plain,
! [X0: $i,X1: $i] : product(X0,product(X0,X1)) = product(X0,X1),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_8847,plain,
! [X0: $i] : product(sK2,product(sK1,X0)) = product(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_402,c_49]) ).
tcf(c_9216,plain,
( ( sK2 = iPr_def_11 )
| ( product(sK1,sK0(sK1,sK2)) = sK0(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_404,c_8808]) ).
tcf(c_9618,plain,
product(sK2,iPr_def_10) = product(iPr_def_12,sK2),
inference(superposition,[status(thm)],[c_400,c_8847]) ).
tcf(c_9626,plain,
( ( sK2 = iPr_def_11 )
| ( product(sK2,sK0(sK1,sK2)) = product(iPr_def_12,sK0(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_9216,c_8847]) ).
tcf(c_9639,plain,
product(iPr_def_12,sK2) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_9618,c_401]) ).
tcf(c_10020,plain,
( ( sK2 = iPr_def_11 )
| ( product(sK0(sK0(sK1,sK2),sK0(sK1,sK2)),sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_4167,c_7267]) ).
tcf(c_10189,plain,
( ( sK2 = iPr_def_11 )
| ( product(iPr_def_12,sK0(sK1,sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_9626,c_8789]) ).
tcf(c_10221,plain,
( ( sK2 = iPr_def_11 )
| ( product(iPr_def_12,sK2) = sK2 ) ),
inference(superposition,[status(thm)],[c_10189,c_8846]) ).
tcf(c_10226,plain,
sK2 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_10221,c_9639]) ).
tcf(c_10247,plain,
( ~ d(sK1,iPr_def_11)
| ( iPr_def_11 != iPr_def_11 )
| ( sK1 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_406,c_10226]) ).
tcf(c_10248,plain,
( d(sK1,iPr_def_11)
| ( sK1 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_405,c_10226]) ).
tcf(c_10252,plain,
( ~ d(sK1,iPr_def_11)
| ( sK1 != iPr_def_13 ) ),
inference(equality_resolution_simp,[status(thm)],[c_10247]) ).
tcf(c_10289,plain,
d(sK1,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_10248,c_1093,c_1332,c_10248]) ).
tcf(c_10293,plain,
product(sK0(sK1,iPr_def_11),iPr_def_11) = sK0(sK1,iPr_def_11),
inference(superposition,[status(thm)],[c_10289,c_8774]) ).
tcf(c_10294,plain,
product(iPr_def_11,sK0(sK1,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_10289,c_8781]) ).
tcf(c_10307,plain,
( l(sK0(sK1,iPr_def_11),iPr_def_11)
| ( product(sK0(sK1,iPr_def_11),iPr_def_11) != sK0(sK1,iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_10294,c_51]) ).
tcf(c_10314,plain,
l(sK0(sK1,iPr_def_11),iPr_def_11),
inference(ground_joinability,[status(thm)],[c_10307,c_10293]) ).
tcf(c_10746,plain,
sK2 = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_10020,c_10226]) ).
tcf(c_10771,plain,
( ( sK1 = iPr_def_13 )
| ( product(sK0(sK1,iPr_def_11),iPr_def_10) = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_4834,c_10746]) ).
tcf(c_10825,plain,
( ~ d(sK1,iPr_def_11)
| ( iPr_def_11 != iPr_def_11 )
| ( sK1 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_406,c_10746]) ).
tcf(c_10826,plain,
( d(sK1,iPr_def_11)
| ( sK1 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_405,c_10746]) ).
tcf(c_10855,plain,
( ~ d(sK1,iPr_def_11)
| ( sK1 != iPr_def_13 ) ),
inference(equality_resolution_simp,[status(thm)],[c_10825]) ).
tcf(c_10898,plain,
d(sK1,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_10826,c_10289]) ).
tcf(c_10900,plain,
product(sK0(sK1,iPr_def_11),sK1) = sK1,
inference(superposition,[status(thm)],[c_10898,c_684]) ).
tcf(c_10901,plain,
product(iPr_def_11,sK0(sK1,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_10898,c_670]) ).
tcf(c_10916,plain,
( l(sK0(sK1,iPr_def_11),iPr_def_11)
| ( product(sK0(sK1,iPr_def_11),iPr_def_11) != sK0(sK1,iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_10901,c_51]) ).
tcf(c_10932,plain,
sK1 != iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_10855,c_1093,c_1332,c_10248,c_10252]) ).
tcf(c_11205,plain,
product(sK0(sK1,iPr_def_11),iPr_def_10) = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_10771,c_1093,c_1332,c_10248,c_10252,c_10771]) ).
tcf(c_12465,plain,
l(sK0(sK1,iPr_def_11),iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_10916,c_10314]) ).
tcf(c_12469,plain,
product(sK0(sK1,iPr_def_11),iPr_def_11) = sK0(sK1,iPr_def_11),
inference(superposition,[status(thm)],[c_12465,c_52]) ).
tcf(c_12548,plain,
! [X0: $i] : product(sK0(sK1,iPr_def_11),product(iPr_def_11,X0)) = product(sK0(sK1,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_12469,c_49]) ).
tcf(c_16497,plain,
product(sK0(sK1,iPr_def_11),iPr_def_10) = product(sK0(sK1,iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_1271,c_12548]) ).
tcf(c_16536,plain,
sK0(sK1,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_16497,c_12469,c_11205]) ).
tcf(c_16605,plain,
product(iPr_def_10,sK1) = sK1,
inference(demodulation,[status(thm)],[c_10900,c_16536]) ).
tcf(c_16606,plain,
sK1 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_16605,c_767]) ).
tcf(c_16607,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16606,c_10932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP775+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/5.45 % Computer : n016.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Wed Sep 23 16:06:03 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/5.52 Running first-order theorem proving
% 0.22/5.52 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/5.53
% 0.22/5.53 % ======== iProver multi-core TPTP/SMT =========
% 0.22/5.53
% 0.22/5.53 % Detected problem language: tptp
% 0.22/5.56 % Proving...
% 7.30/6.97 % SZS status Started for theBenchmark.p
% 7.30/6.97 % SZS status Theorem for theBenchmark.p
% 7.30/6.97
% 7.30/6.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.30/6.97
% 7.30/6.97 % ------ iProver source info
% 7.30/6.97
% 7.30/6.97 % git: date: 2026-07-19 20:42:38 +0200
% 7.30/6.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.30/6.97 % git: non_committed_changes: false
% 7.30/6.97
% 7.30/6.97 % ------ Parsing...
% 7.30/6.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.30/6.97
% 7.30/6.97 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 7.30/6.97
% 7.30/6.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.30/6.97
% 7.30/6.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.30/6.97 % ------ Proving...
% 7.30/6.97 % ------ Problem Properties
% 7.30/6.97
% 7.30/6.97 %
% 7.30/6.97 % clauses 18
% 7.30/6.97 % conjectures 3
% 7.30/6.97 % EPR 4
% 7.30/6.97 % Horn 16
% 7.30/6.97 % unary 6
% 7.30/6.97 % binary 8
% 7.30/6.97 % lits 34
% 7.30/6.97 % lits eq 18
% 7.30/6.97 % fd_pure 0
% 7.30/6.97 % fd_pseudo 0
% 7.30/6.97 % fd_cond 0
% 7.30/6.97 % fd_pseudo_cond 0
% 7.30/6.97 % AC symbols 0
% 7.30/6.97
% 7.30/6.97 % ------ Schedule dynamic 5 is on
% 7.30/6.97
% 7.30/6.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.30/6.97
% 7.30/6.97
% 7.30/6.97 % ------
% 7.30/6.97 % Current options:
% 7.30/6.97 % ------
% 7.30/6.97
% 7.30/6.97
% 7.30/6.97 %
% 7.30/6.97
% 7.30/6.97 % ------ Proving...
% 7.30/6.97 %
% 7.30/6.97
% 7.30/6.97 % SZS status Theorem for theBenchmark.p
% 7.30/6.97
% 7.30/6.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.30/6.97
% 7.30/6.97
%------------------------------------------------------------------------------