%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG069+2 : 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 02:38:43 PM UTC 2026
% Result : Theorem 8.47s 1.81s
% Output : CNFRefutation 8.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 15 unt; 0 def)
% Number of atoms : 266 ( 84 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 338 ( 157 ~; 152 |; 22 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn 130 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr2) ).
fof(f27,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
fof(f28,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtasdt0(X0,X0) = sdtasdt0(X1,X1)
& sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).
fof(f52,axiom,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(f53,axiom,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
fof(f54,axiom,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(f61,axiom,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2580) ).
fof(f62,conjecture,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f63,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(negated_conjecture,[status(cth)],[f62]) ).
fof(f69,plain,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(flattening,[],[f63]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f78]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
inference(flattening,[],[f82]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
inference(ennf_transformation,[],[f16]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
inference(flattening,[],[f86]) ).
fof(f105,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f28]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(flattening,[],[f106]) ).
fof(f139,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f168,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f169,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f212,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f214,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f53]) ).
fof(f216,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f224,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(cnf_transformation,[],[f61]) ).
fof(f225,plain,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(cnf_transformation,[],[f69]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) = sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_86,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ( sdtasdt0(X0,X0) != sdtasdt0(X1,X1) ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_129,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f212]) ).
tcf(c_131,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f214]) ).
tcf(c_133,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f216]) ).
tcf(c_142,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(cnf_transformation,[],[f224]) ).
tcf(c_143,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(cnf_transformation,[],[f225]) ).
tcf(c_162,plain,
( aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(xP) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1216,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( X0_iProver_sdtasdt0_2 = X1_iProver_sdtasdt0_2 )
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2)
| ~ sdtlseqdt0(sz0z00,X1_iProver_sdtasdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtasdt0_2)
| ( sdtasdt0(X0_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) != sdtasdt0(X1_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) ) ),
inference(subtyping,[status(esa)],[c_87]) ).
tcf(c_1217,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2))
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_86]) ).
tcf(c_1229,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(X0_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2),sdtasdt0(X0_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2)),sdtpldt0(sdtasdt0(X1_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2),sdtasdt0(X1_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2))) = sdtasdt0(sdtpldt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtpldt0(X2_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2)) )
| ~ aScalar0(X3_iProver_sdtasdt0_2)
| ~ aScalar0(X2_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_74]) ).
tcf(c_1232,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) )
| ~ aScalar0(X2_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_71]) ).
tcf(c_1234,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtpldt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtpldt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) )
| ~ aScalar0(X2_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_1244,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( aScalar0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2))
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_1245,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( aScalar0(sdtpldt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2))
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_1253,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ~ iPr_def_10
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_1234]) ).
tcf(c_1256,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ~ iPr_def_12
| ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) )
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_1232]) ).
tcf(c_1257,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1232]) ).
tcf(c_1264,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( X2_iProver_sdtasdt0_2 = X0_iProver_sdtasdt0_2 )
| ( X2_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 ) ),
theory(equality) ).
tcf(c_1271,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(X0_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2)
| ~ sdtlseqdt0(X1_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2)
| ( X2_iProver_sdtasdt0_2 != X3_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 ) ),
theory(equality) ).
tcf(c_1306,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(xP) ),
inference(instantiation,[status(thm)],[c_1229]) ).
tcf(c_1320,plain,
( ~ iPr_def_10
| ~ aScalar0(xP) ),
inference(instantiation,[status(thm)],[c_1253]) ).
tcf(c_1330,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ~ aScalar0(X0_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_1256,c_131,c_1320,c_1256,c_1257]) ).
tcf(c_1331,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) = sdtasdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) )
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(renaming,[status(thm)],[c_1330]) ).
tcf(c_2418,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2)
| ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) != X1_iProver_sdtasdt0_2 )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1271]) ).
tcf(c_2426,plain,
( aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(instantiation,[status(thm)],[c_1245]) ).
tcf(c_2436,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = X1_iProver_sdtasdt0_2 )
| ( X1_iProver_sdtasdt0_2 != X0_iProver_sdtasdt0_2 )
| ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1264]) ).
tcf(c_2455,plain,
( aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(instantiation,[status(thm)],[c_1244]) ).
tcf(c_2475,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = X2_iProver_sdtasdt0_2 )
| ( X2_iProver_sdtasdt0_2 != sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) )
| ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) != sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) ) ),
inference(instantiation,[status(thm)],[c_2436]) ).
tcf(c_2509,plain,
( ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(instantiation,[status(thm)],[c_1331]) ).
tcf(c_2546,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = sdtpldt0(sdtpldt0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtasdt0(X0_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2)),sdtpldt0(sdtasdt0(X3_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtasdt0(X3_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2))) )
| ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) != sdtasdt0(sdtpldt0(X0_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2),sdtpldt0(X1_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2)) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtasdt0(X0_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2)),sdtpldt0(sdtasdt0(X3_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtasdt0(X3_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2))) != sdtasdt0(sdtpldt0(X0_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2),sdtpldt0(X1_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2)) ) ),
inference(instantiation,[status(thm)],[c_2475]) ).
tcf(c_2547,plain,
( ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) )
| ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) ),
inference(instantiation,[status(thm)],[c_2546]) ).
tcf(c_2569,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = X0_iProver_sdtasdt0_2 )
| ~ aScalar0(X0_iProver_sdtasdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtasdt0_2)
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ( sdtasdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) != sdtasdt0(X0_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) ) ),
inference(instantiation,[status(thm)],[c_1216]) ).
tcf(c_2575,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = X1_iProver_sdtasdt0_2 )
| ( X1_iProver_sdtasdt0_2 != X0_iProver_sdtasdt0_2 )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1264]) ).
tcf(c_2728,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = X0_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) ) ),
inference(instantiation,[status(thm)],[c_2575]) ).
tcf(c_2877,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(instantiation,[status(thm)],[c_1217]) ).
tcf(c_2917,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X4_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(X1_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2),sdtasdt0(X1_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2)),sdtpldt0(sdtasdt0(X4_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2),sdtasdt0(X4_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2))),X0_iProver_sdtasdt0_2)
| ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) != sdtpldt0(sdtpldt0(sdtasdt0(X1_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2),sdtasdt0(X1_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2)),sdtpldt0(sdtasdt0(X4_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2),sdtasdt0(X4_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2))) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_2418]) ).
tcf(c_3133,plain,
( ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) )
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ( sdtasdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) != sdtasdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ) ),
inference(instantiation,[status(thm)],[c_2569]) ).
tcf(c_3268,plain,
( ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS))) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS))) != sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) ) ),
inference(instantiation,[status(thm)],[c_2728]) ).
tcf(c_3320,plain,
( ( sdtasdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) = sdtasdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) )
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
inference(instantiation,[status(thm)],[c_1331]) ).
tcf(c_5302,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) )
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(instantiation,[status(thm)],[c_1229]) ).
tcf(c_10116,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtasdt0(X0_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2)),sdtpldt0(sdtasdt0(X3_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtasdt0(X3_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS))))
| ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) != sdtpldt0(sdtpldt0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtasdt0(X0_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2)),sdtpldt0(sdtasdt0(X3_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),sdtasdt0(X3_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2))) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS))) ) ),
inference(instantiation,[status(thm)],[c_2917]) ).
tcf(c_10126,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS))))
| ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) != sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) )
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS))) ) ),
inference(instantiation,[status(thm)],[c_10116]) ).
tcf(c_10127,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10126,c_5302,c_3320,c_3268,c_3133,c_2877,c_2547,c_2509,c_2455,c_2426,c_1306,c_142,c_143,c_162,c_129,c_131,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG069+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 % Computer : n005.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Thu Sep 24 08:04:32 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.15/0.47
% 0.15/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.47
% 0.15/0.47 % Detected problem language: tptp
% 0.15/0.48 % Proving...
% 8.47/1.81 % SZS status Started for theBenchmark.p
% 8.47/1.81 % SZS status Theorem for theBenchmark.p
% 8.47/1.81
% 8.47/1.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.47/1.81
% 8.47/1.81 % ------ iProver source info
% 8.47/1.81
% 8.47/1.81 % git: date: 2026-07-19 20:42:38 +0200
% 8.47/1.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.47/1.81 % git: non_committed_changes: false
% 8.47/1.81
% 8.47/1.81 % ------ Parsing...
% 8.47/1.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.47/1.81
% 8.47/1.81 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 8.47/1.81
% 8.47/1.81 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.47/1.81
% 8.47/1.81 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 8.47/1.81 % ------ Proving...
% 8.47/1.81 % ------ Problem Properties
% 8.47/1.81
% 8.47/1.81 %
% 8.47/1.81 % clauses 97
% 8.47/1.81 % conjectures 1
% 8.47/1.81 % EPR 25
% 8.47/1.81 % Horn 85
% 8.47/1.81 % unary 44
% 8.47/1.81 % binary 19
% 8.47/1.81 % lits 231
% 8.47/1.81 % lits eq 72
% 8.47/1.81 % fd_pure 0
% 8.47/1.81 % fd_pseudo 0
% 8.47/1.81 % fd_cond 1
% 8.47/1.81 % fd_pseudo_cond 5
% 8.47/1.81 % AC symbols 0
% 8.47/1.81
% 8.47/1.81 % ------ Input Options Time Limit: Unbounded
% 8.47/1.81
% 8.47/1.81
% 8.47/1.81 % ------
% 8.47/1.81 % Current options:
% 8.47/1.81 % ------
% 8.47/1.81
% 8.47/1.81
% 8.47/1.81 %
% 8.47/1.81
% 8.47/1.81 % ------ Proving...
% 8.47/1.81 %
% 8.47/1.81
% 8.47/1.81 % SZS status Theorem for theBenchmark.p
% 8.47/1.81
% 8.47/1.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.47/1.81
% 8.47/1.81
%------------------------------------------------------------------------------