%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG108+4 : TPTP v9.3.1. Released v4.0.0.
% 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 02:39:09 PM UTC 2026
% Result : Theorem 3.85s 1.36s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 21 unt; 2 def)
% Number of atoms : 355 ( 92 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 436 ( 159 ~; 149 |; 111 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 89 !; 32 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(f43,conjecture,
( ( aElementOf0(xb,slsdtgt0(xb))
| ? [X0] :
( sdtasdt0(xb,X0) = xb
& aElement0(X0) ) )
& ( aElementOf0(sz00,slsdtgt0(xb))
| ? [X0] :
( sdtasdt0(xb,X0) = sz00
& aElement0(X0) ) )
& ( aElementOf0(xa,slsdtgt0(xa))
| ? [X0] :
( sdtasdt0(xa,X0) = xa
& aElement0(X0) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ? [X0] :
( sdtasdt0(xa,X0) = sz00
& aElement0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
~ ( ( aElementOf0(xb,slsdtgt0(xb))
| ? [X0] :
( sdtasdt0(xb,X0) = xb
& aElement0(X0) ) )
& ( aElementOf0(sz00,slsdtgt0(xb))
| ? [X0] :
( sdtasdt0(xb,X0) = sz00
& aElement0(X0) ) )
& ( aElementOf0(xa,slsdtgt0(xa))
| ? [X0] :
( sdtasdt0(xa,X0) = xa
& aElement0(X0) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ? [X0] :
( sdtasdt0(xa,X0) = sz00
& aElement0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f53,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f42]) ).
fof(f54,plain,
~ ( ( aElementOf0(xb,slsdtgt0(xb))
| ? [X3] :
( xb = sdtasdt0(xb,X3)
& aElement0(X3) ) )
& ( aElementOf0(sz00,slsdtgt0(xb))
| ? [X2] :
( sz00 = sdtasdt0(xb,X2)
& aElement0(X2) ) )
& ( aElementOf0(xa,slsdtgt0(xa))
| ? [X1] :
( xa = sdtasdt0(xa,X1)
& aElement0(X1) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ? [X0] :
( sdtasdt0(xa,X0) = sz00
& aElement0(X0) ) ) ),
inference(rectify,[],[f44]) ).
fof(f72,plain,
! [X0] :
( ~ aElement0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f76,plain,
! [X0] :
( ~ aElement0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f108,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f53]) ).
fof(f109,plain,
( ( ~ aElementOf0(xb,slsdtgt0(xb))
& ! [X3] :
( xb != sdtasdt0(xb,X3)
| ~ aElement0(X3) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [X2] :
( sz00 != sdtasdt0(xb,X2)
| ~ aElement0(X2) ) )
| ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [X1] :
( xa != sdtasdt0(xa,X1)
| ~ aElement0(X1) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [X0] :
( sz00 != sdtasdt0(xa,X0)
| ~ aElement0(X0) ) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f157,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( ( ~ aElementOf0(X7,xI)
| ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ( ! [X8,X9] :
( sdtpldt0(X8,X9) != X7
| ~ aElementOf0(X9,slsdtgt0(xb))
| ~ aElementOf0(X8,slsdtgt0(xa)) )
| aElementOf0(X7,xI) ) )
& ! [X5] :
( ( ~ aElementOf0(X5,slsdtgt0(xb))
| ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ( ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(nnf_transformation,[],[f108]) ).
fof(f158,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ? [X12,X13] :
( sdtpldt0(X12,X13) = X9
& aElementOf0(X13,slsdtgt0(xb))
& aElementOf0(X12,slsdtgt0(xa)) ) )
& ( ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) )
| aElementOf0(X9,xI) ) )
& ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xb))
| ? [X8] :
( sdtasdt0(xb,X8) = X6
& aElement0(X8) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ? [X5] :
( sdtasdt0(xa,X5) = X3
& aElement0(X5) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f157]) ).
fof(f159,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ( sdtpldt0(sK30(X9),sK31(X9)) = X9
& aElementOf0(sK31(X9),slsdtgt0(xb))
& aElementOf0(sK30(X9),slsdtgt0(xa)) ) )
& ( ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) )
| aElementOf0(X9,xI) ) )
& ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xb))
| ( sdtasdt0(xb,sK29(X6)) = X6
& aElement0(sK29(X6)) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ( sdtasdt0(xa,sK28(X3)) = X3
& aElement0(sK28(X3)) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31]),skolemize(X5,sK28(X3)),skolemize(X8,sK29(X6)),skolemize(X12,sK30(X9)),skolemize(X13,sK31(X9))],[f158]) ).
fof(f162,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f163,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f176,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f182,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f76]) ).
fof(f252,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f253,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f282,plain,
! [X6,X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7)
| aElementOf0(X6,slsdtgt0(xb)) ),
inference(cnf_transformation,[],[f159]) ).
fof(f293,plain,
! [X2] :
( sP4
| sz00 != sdtasdt0(xb,X2)
| ~ aElement0(X2)
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f294,plain,
! [X1] :
( sP4
| ~ aElementOf0(sz00,slsdtgt0(xb))
| xa != sdtasdt0(xa,X1)
| ~ aElement0(X1)
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f296,plain,
! [X0] :
( sP4
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| sz00 != sdtasdt0(xa,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f299,plain,
! [X2,X0,X1] :
( sP4
| sz00 != sdtasdt0(xb,X2)
| ~ aElement0(X2)
| xa != sdtasdt0(xa,X1)
| ~ aElement0(X1)
| sz00 != sdtasdt0(xa,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f313,plain,
! [X7] :
( ~ aElement0(X7)
| aElementOf0(sdtasdt0(xb,X7),slsdtgt0(xb)) ),
inference(equality_resolution,[],[f282]) ).
tcf(c_49,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f162]) ).
tcf(c_50,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f163]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_139,plain,
aElement0(xa),
inference(cnf_transformation,[],[f253]) ).
tcf(c_140,plain,
aElement0(xb),
inference(cnf_transformation,[],[f252]) ).
tcf(c_169,plain,
! [X0: $i] :
( aElementOf0(sdtasdt0(xb,X0),slsdtgt0(xb))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_179,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( sP4
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtasdt0(xb,X1) != sz00 )
| ( sdtasdt0(xa,X2) != xa )
| ( sdtasdt0(xa,X0) != sz00 ) ),
inference(cnf_transformation,[],[f299]) ).
tcf(c_182,negated_conjecture,
! [X0: $i] :
( sP4
| ~ aElement0(X0)
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ( sdtasdt0(xa,X0) != sz00 ) ),
inference(cnf_transformation,[],[f296]) ).
tcf(c_184,negated_conjecture,
! [X0: $i] :
( sP4
| ~ aElement0(X0)
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ( sdtasdt0(xa,X0) != xa ) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_185,negated_conjecture,
! [X0: $i] :
( sP4
| ~ aElement0(X0)
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ( sdtasdt0(xb,X0) != sz00 ) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_8062,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( sdtasdt0(xb,X0) != sz00 )
| ~ aElement0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_185]) ).
tcf(c_8064,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( sdtasdt0(xa,X0) != xa )
| ~ aElement0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_184]) ).
tcf(c_8067,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( sdtasdt0(xa,X0) != sz00 )
| ~ aElement0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_182]) ).
tcf(c_8071,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| sP4 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_179]) ).
tcf(c_8073,definition,
iPr_def_14 = slsdtgt0(xb),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_8090,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| sP4 ),
inference(demodulation,[status(thm)],[c_8071]) ).
tcf(c_8091,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ~ aElement0(X0)
| ( sdtasdt0(xa,X0) != sz00 ) ),
inference(demodulation,[status(thm)],[c_8067]) ).
tcf(c_8092,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ~ aElement0(X0)
| ( sdtasdt0(xa,X0) != xa ) ),
inference(demodulation,[status(thm)],[c_8064]) ).
tcf(c_8093,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ~ aElement0(X0)
| ( sdtasdt0(xb,X0) != sz00 ) ),
inference(demodulation,[status(thm)],[c_8062]) ).
tcf(c_10288,plain,
sdtasdt0(xa,sz10) = xa,
inference(superposition,[status(thm)],[c_139,c_62]) ).
tcf(c_10289,plain,
sdtasdt0(xb,sz10) = xb,
inference(superposition,[status(thm)],[c_140,c_62]) ).
tcf(c_10328,plain,
sdtasdt0(xa,sz00) = sz00,
inference(superposition,[status(thm)],[c_139,c_68]) ).
tcf(c_10329,plain,
sdtasdt0(xb,sz00) = sz00,
inference(superposition,[status(thm)],[c_140,c_68]) ).
tcf(c_10341,plain,
( ~ iPr_def_11
| ~ aElement0(sz10) ),
inference(superposition,[status(thm)],[c_10288,c_8092]) ).
tcf(c_10343,plain,
~ iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_10341,c_50]) ).
tcf(c_10350,plain,
( iPr_def_12
| iPr_def_10
| sP4 ),
inference(backward_subsumption_resolution,[status(thm)],[c_8090,c_10343]) ).
tcf(c_10463,plain,
! [X0: $i] :
( aElementOf0(sdtasdt0(xb,X0),iPr_def_14)
| ~ aElement0(X0) ),
inference(light_normalisation,[status(thm)],[c_169,c_8073]) ).
tcf(c_10470,plain,
( aElementOf0(xb,iPr_def_14)
| ~ aElement0(sz10) ),
inference(superposition,[status(thm)],[c_10289,c_10463]) ).
tcf(c_10473,plain,
aElementOf0(xb,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_10470,c_50]) ).
tcf(c_10740,plain,
( ~ iPr_def_10
| ~ aElement0(sz00)
| ( sdtasdt0(xb,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_8093]) ).
tcf(c_10744,plain,
( ~ iPr_def_12
| ~ aElement0(sz00) ),
inference(superposition,[status(thm)],[c_10328,c_8091]) ).
tcf(c_10745,plain,
~ iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_10744,c_49]) ).
fof(f116,definition,
( ~ sP4
| ( ~ aElementOf0(xb,slsdtgt0(xb))
& ! [X3] :
( xb != sdtasdt0(xb,X3)
| ~ aElement0(X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f117,plain,
( sP4
| ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [X2] :
( sz00 != sdtasdt0(xb,X2)
| ~ aElement0(X2) ) )
| ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [X1] :
( xa != sdtasdt0(xa,X1)
| ~ aElement0(X1) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [X0] :
( sz00 != sdtasdt0(xa,X0)
| ~ aElement0(X0) ) ) ),
inference(definition_folding,[],[f109,f116]) ).
fof(f160,plain,
( ~ sP4
| ( ~ aElementOf0(xb,slsdtgt0(xb))
& ! [X3] :
( xb != sdtasdt0(xb,X3)
| ~ aElement0(X3) ) ) ),
inference(nnf_transformation,[],[f116]) ).
fof(f161,plain,
( ~ sP4
| ( ~ aElementOf0(xb,slsdtgt0(xb))
& ! [X0] :
( xb != sdtasdt0(xb,X0)
| ~ aElement0(X0) ) ) ),
inference(rectify,[],[f160]) ).
fof(f290,plain,
( ~ sP4
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_178,plain,
( ~ sP4
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_10199,plain,
( ~ sP4
| ~ aElementOf0(xb,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_178,c_8073]) ).
tcf(c_10479,plain,
~ sP4,
inference(backward_subsumption_resolution,[status(thm)],[c_10199,c_10473]) ).
tcf(c_10480,plain,
( iPr_def_12
| iPr_def_10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_10350,c_10479]) ).
tcf(c_10748,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_10480,c_10745]) ).
tcf(c_10753,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10748,c_10740,c_10329,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG108+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 % Computer : n005.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Thu Sep 24 08:16:33 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 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
% 0.18/0.46
% 0.18/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.46
% 0.18/0.46 % Detected problem language: tptp
% 0.18/0.48 % Proving...
% 3.85/1.36 % SZS status Started for theBenchmark.p
% 3.85/1.36 % SZS status Theorem for theBenchmark.p
% 3.85/1.36
% 3.85/1.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.85/1.36
% 3.85/1.36 % ------ iProver source info
% 3.85/1.36
% 3.85/1.36 % git: date: 2026-07-19 20:42:38 +0200
% 3.85/1.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.85/1.36 % git: non_committed_changes: false
% 3.85/1.36
% 3.85/1.36 % ------ Parsing...
% 3.85/1.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.85/1.36
% 3.85/1.36 % ------ 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: 2 0s sf_e pe_s pe_e %
% 3.85/1.36
% 3.85/1.36 % ------ Preprocessing... gs_s sp: 12 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.85/1.36
% 3.85/1.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.85/1.36 % ------ Proving...
% 3.85/1.36 % ------ Problem Properties
% 3.85/1.36
% 3.85/1.36 %
% 3.85/1.36 % clauses 137
% 3.85/1.36 % conjectures 11
% 3.85/1.36 % EPR 38
% 3.85/1.36 % Horn 104
% 3.85/1.36 % unary 20
% 3.85/1.36 % binary 29
% 3.85/1.36 % lits 438
% 3.85/1.36 % lits eq 59
% 3.85/1.36 % fd_pure 0
% 3.85/1.36 % fd_pseudo 0
% 3.85/1.36 % fd_cond 3
% 3.85/1.36 % fd_pseudo_cond 11
% 3.85/1.36 % AC symbols 0
% 3.85/1.36
% 3.85/1.36 % ------ Schedule dynamic 5 is on
% 3.85/1.36
% 3.85/1.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.85/1.36
% 3.85/1.36
% 3.85/1.36 % ------
% 3.85/1.36 % Current options:
% 3.85/1.36 % ------
% 3.85/1.36
% 3.85/1.36
% 3.85/1.36 %
% 3.85/1.36
% 3.85/1.36 % ------ Proving...
% 3.85/1.36 %
% 3.85/1.36
% 3.85/1.36 % SZS status Theorem for theBenchmark.p
% 3.85/1.36
% 3.85/1.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.85/1.36
% 3.85/1.36
%------------------------------------------------------------------------------