%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG069+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 7.50s 1.77s
% Output : CNFRefutation 7.50s
% 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/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
fof(f27,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
fof(f52,axiom,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(f53,axiom,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(f54,axiom,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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(f137,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f138,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f154,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(f166,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f167,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(f206,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f208,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f53]) ).
fof(f210,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f218,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(f219,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,[],[f137]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f138]) ).
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,[],[f150]) ).
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,[],[f148]) ).
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,[],[f154]) ).
tcf(c_86,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f166]) ).
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,[],[f167]) ).
tcf(c_125,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f206]) ).
tcf(c_127,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f208]) ).
tcf(c_129,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f210]) ).
tcf(c_138,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,[],[f218]) ).
tcf(c_139,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(cnf_transformation,[],[f219]) ).
tcf(c_158,plain,
( aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(xP) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1181,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_1182,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_1194,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_1197,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_1199,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_1209,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_1210,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_1218,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_1199]) ).
tcf(c_1221,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_1197]) ).
tcf(c_1222,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1197]) ).
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] :
( ( 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_1236,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_1269,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_1194]) ).
tcf(c_1283,plain,
( ~ iPr_def_10
| ~ aScalar0(xP) ),
inference(instantiation,[status(thm)],[c_1218]) ).
tcf(c_1293,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_1221,c_127,c_1283,c_1221,c_1222]) ).
tcf(c_1294,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_1293]) ).
tcf(c_2357,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_1236]) ).
tcf(c_2365,plain,
( aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(instantiation,[status(thm)],[c_1210]) ).
tcf(c_2375,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_1229]) ).
tcf(c_2394,plain,
( aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(instantiation,[status(thm)],[c_1209]) ).
tcf(c_2414,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_2375]) ).
tcf(c_2448,plain,
( ( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(instantiation,[status(thm)],[c_1294]) ).
tcf(c_2485,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_2414]) ).
tcf(c_2486,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_2485]) ).
tcf(c_2508,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_1181]) ).
tcf(c_2514,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_1229]) ).
tcf(c_2667,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_2514]) ).
tcf(c_2816,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(instantiation,[status(thm)],[c_1182]) ).
tcf(c_2856,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_2357]) ).
tcf(c_3072,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_2508]) ).
tcf(c_3207,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_2667]) ).
tcf(c_3259,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_1294]) ).
tcf(c_5250,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_1194]) ).
tcf(c_10171,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_2856]) ).
tcf(c_10181,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_10171]) ).
tcf(c_10182,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10181,c_5250,c_3259,c_3207,c_3072,c_2816,c_2486,c_2448,c_2394,c_2365,c_1269,c_138,c_139,c_158,c_125,c_127,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG069+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 07:59:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 7.50/1.77 % SZS status Started for theBenchmark.p
% 7.50/1.77 % SZS status Theorem for theBenchmark.p
% 7.50/1.77
% 7.50/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.50/1.77
% 7.50/1.77 % ------ iProver source info
% 7.50/1.77
% 7.50/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 7.50/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.50/1.77 % git: non_committed_changes: false
% 7.50/1.77
% 7.50/1.77 % ------ Parsing...
% 7.50/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.50/1.77
% 7.50/1.77 % ------ Preprocessing... sup_sim: 2 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 %
% 7.50/1.77
% 7.50/1.77 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.50/1.77
% 7.50/1.77 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 7.50/1.77 % ------ Proving...
% 7.50/1.77 % ------ Problem Properties
% 7.50/1.77
% 7.50/1.77 %
% 7.50/1.77 % clauses 93
% 7.50/1.77 % conjectures 1
% 7.50/1.77 % EPR 25
% 7.50/1.77 % Horn 81
% 7.50/1.77 % unary 42
% 7.50/1.77 % binary 17
% 7.50/1.77 % lits 225
% 7.50/1.77 % lits eq 68
% 7.50/1.77 % fd_pure 0
% 7.50/1.77 % fd_pseudo 0
% 7.50/1.77 % fd_cond 1
% 7.50/1.77 % fd_pseudo_cond 5
% 7.50/1.77 % AC symbols 0
% 7.50/1.77
% 7.50/1.77 % ------ Input Options Time Limit: Unbounded
% 7.50/1.77
% 7.50/1.77
% 7.50/1.77 % ------
% 7.50/1.77 % Current options:
% 7.50/1.77 % ------
% 7.50/1.77
% 7.50/1.77
% 7.50/1.77 %
% 7.50/1.77
% 7.50/1.77 % ------ Proving...
% 7.50/1.77 %
% 7.50/1.77
% 7.50/1.77 % SZS status Theorem for theBenchmark.p
% 7.50/1.77
% 7.50/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.50/1.77
% 7.50/1.77
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