%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG061+2 : 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 : n004.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 02:38:32 PM UTC 2026
% Result : Theorem 2.40s 1.76s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 81 ( 26 unt; 0 def)
% Number of atoms : 197 ( 79 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 216 ( 100 ~; 95 |; 17 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
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(f12,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
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(f52,axiom,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(f54,axiom,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(f58,axiom,
( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
fof(f59,axiom,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2180) ).
fof(f60,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f61,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(negated_conjecture,[status(cth)],[f60]) ).
fof(f67,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(flattening,[],[f61]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ~ aScalar0(X0)
| aScalar0(smndt0(X0)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f80,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(f81,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,[],[f80]) ).
fof(f136,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f138,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f139,plain,
! [X0] :
( ~ aScalar0(X0)
| aScalar0(smndt0(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f210,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f214,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f219,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(cnf_transformation,[],[f58]) ).
fof(f221,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(cnf_transformation,[],[f58]) ).
fof(f222,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(cnf_transformation,[],[f59]) ).
fof(f223,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(cnf_transformation,[],[f67]) ).
tcf(c_56,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f136]) ).
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_59,plain,
! [X0: $i] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f139]) ).
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_129,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f210]) ).
tcf(c_133,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f214]) ).
tcf(c_139,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(cnf_transformation,[],[f221]) ).
tcf(c_141,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(cnf_transformation,[],[f219]) ).
tcf(c_142,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(cnf_transformation,[],[f222]) ).
tcf(c_143,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(cnf_transformation,[],[f223]) ).
tcf(c_1157,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(subtyping,[status(esa)],[c_143]) ).
tcf(c_1158,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(subtyping,[status(esa)],[c_142]) ).
tcf(c_1159,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(subtyping,[status(esa)],[c_141]) ).
tcf(c_1161,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(subtyping,[status(esa)],[c_139]) ).
tcf(c_1228,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtasdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) = sdtasdt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2) )
| ~ aScalar0(X2_iProver_sdtlseqdt0_2)
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_71]) ).
tcf(c_1230,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtpldt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) = sdtpldt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2) )
| ~ aScalar0(X2_iProver_sdtlseqdt0_2)
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_1239,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aScalar0(smndt0(X0_iProver_sdtlseqdt0_2))
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_59]) ).
tcf(c_1240,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aScalar0(sdtasdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2))
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_1241,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aScalar0(sdtpldt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2))
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_1249,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ~ iPr_def_10
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_1230]) ).
tcf(c_1250,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ~ iPr_def_11
| ( sdtpldt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) = sdtpldt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2) )
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_1230]) ).
tcf(c_1251,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1230]) ).
tcf(c_1252,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ~ iPr_def_12
| ( sdtasdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) = sdtasdt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2) )
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_1228]) ).
tcf(c_1253,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1228]) ).
tcf(c_1257,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] : X0_iProver_sdtlseqdt0_2 = X0_iProver_sdtlseqdt0_2,
theory(equality) ).
tcf(c_1260,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( X2_iProver_sdtlseqdt0_2 = X0_iProver_sdtlseqdt0_2 )
| ( X2_iProver_sdtlseqdt0_2 != X1_iProver_sdtlseqdt0_2 )
| ( X0_iProver_sdtlseqdt0_2 != X1_iProver_sdtlseqdt0_2 ) ),
theory(equality) ).
tcf(c_1264,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X3_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtpldt0(X0_iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2) = sdtpldt0(X1_iProver_sdtlseqdt0_2,X3_iProver_sdtlseqdt0_2) )
| ( X2_iProver_sdtlseqdt0_2 != X3_iProver_sdtlseqdt0_2 )
| ( X0_iProver_sdtlseqdt0_2 != X1_iProver_sdtlseqdt0_2 ) ),
theory(equality) ).
tcf(c_1314,plain,
( ~ iPr_def_10
| ~ aScalar0(sz0z00) ),
inference(instantiation,[status(thm)],[c_1249]) ).
tcf(c_1319,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ( sdtpldt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) = sdtpldt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_1250,c_56,c_1314,c_1250,c_1251]) ).
tcf(c_1320,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtpldt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) = sdtpldt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2) )
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(renaming,[status(thm)],[c_1319]) ).
tcf(c_1324,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ( sdtasdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) = sdtasdt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_1252,c_56,c_1314,c_1252,c_1253]) ).
tcf(c_1325,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtasdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) = sdtasdt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2) )
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(renaming,[status(thm)],[c_1324]) ).
tcf(c_2734,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) )
| ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != X0_iProver_sdtlseqdt0_2 )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) != X0_iProver_sdtlseqdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1260]) ).
tcf(c_2862,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = X1_iProver_sdtlseqdt0_2 )
| ( X1_iProver_sdtlseqdt0_2 != X0_iProver_sdtlseqdt0_2 )
| ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != X0_iProver_sdtlseqdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1260]) ).
tcf(c_3131,plain,
( aScalar0(sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS)) ),
inference(instantiation,[status(thm)],[c_1241]) ).
tcf(c_3143,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = X0_iProver_sdtlseqdt0_2 )
| ( X0_iProver_sdtlseqdt0_2 != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) )
| ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ) ),
inference(instantiation,[status(thm)],[c_2862]) ).
tcf(c_3144,plain,
( ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) )
| ~ aScalar0(sdtpldt0(xR,smndt0(xS))) ),
inference(instantiation,[status(thm)],[c_1325]) ).
tcf(c_3596,plain,
( aScalar0(smndt0(xS))
| ~ aScalar0(xS) ),
inference(instantiation,[status(thm)],[c_1239]) ).
tcf(c_3726,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtpldt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) )
| ( sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)) != X1_iProver_sdtlseqdt0_2 )
| ( sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) != X0_iProver_sdtlseqdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1264]) ).
tcf(c_4606,plain,
( aScalar0(smndt0(xN))
| ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS)) ),
inference(superposition,[status(thm)],[c_1161,c_1240]) ).
tcf(c_4608,plain,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(superposition,[status(thm)],[c_1159,c_1240]) ).
tcf(c_5213,plain,
( ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) )
| ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ) ),
inference(instantiation,[status(thm)],[c_3143]) ).
tcf(c_5705,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtpldt0(X0_iProver_sdtlseqdt0_2,sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) )
| ( sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)) != sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) )
| ( sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) != X0_iProver_sdtlseqdt0_2 ) ),
inference(instantiation,[status(thm)],[c_3726]) ).
tcf(c_5706,plain,
( ( sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)) = sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) )
| ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xS,xS)) ),
inference(instantiation,[status(thm)],[c_1320]) ).
tcf(c_9488,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) )
| ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) ) ),
inference(instantiation,[status(thm)],[c_2734]) ).
tcf(c_11442,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) )
| ( sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)) != sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) )
| ( sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) != sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) ) ),
inference(instantiation,[status(thm)],[c_5705]) ).
tcf(c_11443,plain,
sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
inference(instantiation,[status(thm)],[c_1257]) ).
tcf(c_11444,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11443,c_11442,c_9488,c_5706,c_5213,c_4606,c_4608,c_3596,c_3144,c_3131,c_1158,c_1157,c_129,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG061+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n004.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 08:02:08 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.44 % Proving...
% 2.40/1.76 % SZS status Started for theBenchmark.p
% 2.40/1.76 % SZS status Theorem for theBenchmark.p
% 2.40/1.76
% 2.40/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.40/1.76
% 2.40/1.76 % ------ iProver source info
% 2.40/1.76
% 2.40/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 2.40/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.40/1.76 % git: non_committed_changes: false
% 2.40/1.76
% 2.40/1.76 % ------ Parsing...
% 2.40/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.40/1.76
% 2.40/1.76 % ------ Preprocessing... sup_sim: 0 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 %
% 2.40/1.76
% 2.40/1.76 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.40/1.76
% 2.40/1.76 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 2.40/1.76 % ------ Proving...
% 2.40/1.76 % ------ Problem Properties
% 2.40/1.76
% 2.40/1.76 %
% 2.40/1.76 % clauses 97
% 2.40/1.76 % conjectures 1
% 2.40/1.76 % EPR 25
% 2.40/1.76 % Horn 85
% 2.40/1.76 % unary 44
% 2.40/1.76 % binary 19
% 2.40/1.76 % lits 231
% 2.40/1.76 % lits eq 76
% 2.40/1.76 % fd_pure 0
% 2.40/1.76 % fd_pseudo 0
% 2.40/1.76 % fd_cond 1
% 2.40/1.76 % fd_pseudo_cond 5
% 2.40/1.76 % AC symbols 0
% 2.40/1.76
% 2.40/1.76 % ------ Input Options Time Limit: Unbounded
% 2.40/1.76
% 2.40/1.76
% 2.40/1.76 % ------
% 2.40/1.76 % Current options:
% 2.40/1.76 % ------
% 2.40/1.76
% 2.40/1.76
% 2.40/1.76 %
% 2.40/1.76
% 2.40/1.76 % ------ Proving...
% 2.40/1.76 %
% 2.40/1.76
% 2.40/1.76 % SZS status Theorem for theBenchmark.p
% 2.40/1.76
% 2.40/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.40/1.76
% 2.40/1.76
%------------------------------------------------------------------------------