%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG061+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 : n011.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 10.33s 22.33s
% Output : CNFRefutation 10.33s
% 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(f134,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f135,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f136,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f137,plain,
! [X0] :
( ~ aScalar0(X0)
| aScalar0(smndt0(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f204,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f208,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f213,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(cnf_transformation,[],[f58]) ).
fof(f215,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(cnf_transformation,[],[f58]) ).
fof(f216,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(f217,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,[],[f134]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_59,plain,
! [X0: $i] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f137]) ).
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,[],[f148]) ).
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,[],[f146]) ).
tcf(c_125,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f204]) ).
tcf(c_129,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f208]) ).
tcf(c_135,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(cnf_transformation,[],[f215]) ).
tcf(c_137,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(cnf_transformation,[],[f213]) ).
tcf(c_138,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,[],[f216]) ).
tcf(c_139,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,[],[f217]) ).
tcf(c_1127,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_139]) ).
tcf(c_1128,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_138]) ).
tcf(c_1129,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(subtyping,[status(esa)],[c_137]) ).
tcf(c_1131,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(subtyping,[status(esa)],[c_135]) ).
tcf(c_1194,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_1196,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_1205,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_1206,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_1207,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_1215,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_1196]) ).
tcf(c_1216,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_1196]) ).
tcf(c_1217,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1196]) ).
tcf(c_1218,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_1194]) ).
tcf(c_1219,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1194]) ).
tcf(c_1223,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] : X0_iProver_sdtlseqdt0_2 = X0_iProver_sdtlseqdt0_2,
theory(equality) ).
tcf(c_1226,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_1230,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_1278,plain,
( ~ iPr_def_10
| ~ aScalar0(sz0z00) ),
inference(instantiation,[status(thm)],[c_1215]) ).
tcf(c_1283,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_1216,c_56,c_1278,c_1216,c_1217]) ).
tcf(c_1284,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_1283]) ).
tcf(c_1288,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_1218,c_56,c_1278,c_1218,c_1219]) ).
tcf(c_1289,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_1288]) ).
tcf(c_2663,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_1226]) ).
tcf(c_2772,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_1226]) ).
tcf(c_3033,plain,
( aScalar0(sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS)) ),
inference(instantiation,[status(thm)],[c_1207]) ).
tcf(c_3045,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_2772]) ).
tcf(c_3046,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_1289]) ).
tcf(c_3409,plain,
( aScalar0(smndt0(xS))
| ~ aScalar0(xS) ),
inference(instantiation,[status(thm)],[c_1205]) ).
tcf(c_3521,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_3045]) ).
tcf(c_3825,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_1230]) ).
tcf(c_4279,plain,
( aScalar0(smndt0(xN))
| ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS)) ),
inference(superposition,[status(thm)],[c_1131,c_1206]) ).
tcf(c_4281,plain,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(superposition,[status(thm)],[c_1129,c_1206]) ).
tcf(c_5063,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_2663]) ).
tcf(c_5963,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_3825]) ).
tcf(c_5964,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_1284]) ).
tcf(c_11759,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_5963]) ).
tcf(c_11760,plain,
sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
inference(instantiation,[status(thm)],[c_1223]) ).
tcf(c_11761,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11760,c_11759,c_5964,c_5063,c_4279,c_4281,c_3521,c_3409,c_3046,c_3033,c_1128,c_1127,c_125,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG061+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/20.43 % CPULimit : 300
% 0.08/20.43 % WCLimit : 300
% 0.08/20.43 % DateTime : Thu Sep 24 08:02:33 UTC 2026
% 0.08/20.43 % CPUTime :
% 0.08/20.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/20.47 Running first-order theorem proving
% 0.08/20.47 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
% 0.08/20.48
% 0.08/20.48 % ======== iProver multi-core TPTP/SMT =========
% 0.08/20.48
% 0.08/20.48 % Detected problem language: tptp
% 0.08/20.50 % Proving...
% 10.33/22.33 % SZS status Started for theBenchmark.p
% 10.33/22.33 % SZS status Theorem for theBenchmark.p
% 10.33/22.33
% 10.33/22.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.33/22.33
% 10.33/22.33 % ------ iProver source info
% 10.33/22.33
% 10.33/22.33 % git: date: 2026-07-19 20:42:38 +0200
% 10.33/22.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.33/22.33 % git: non_committed_changes: false
% 10.33/22.33
% 10.33/22.33 % ------ Parsing...
% 10.33/22.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.33/22.33
% 10.33/22.33 % ------ 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 %
% 10.33/22.33
% 10.33/22.33 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.33/22.33
% 10.33/22.33 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 10.33/22.33 % ------ Proving...
% 10.33/22.33 % ------ Problem Properties
% 10.33/22.33
% 10.33/22.33 %
% 10.33/22.33 % clauses 93
% 10.33/22.33 % conjectures 1
% 10.33/22.33 % EPR 25
% 10.33/22.33 % Horn 81
% 10.33/22.33 % unary 42
% 10.33/22.33 % binary 17
% 10.33/22.33 % lits 225
% 10.33/22.33 % lits eq 72
% 10.33/22.33 % fd_pure 0
% 10.33/22.33 % fd_pseudo 0
% 10.33/22.33 % fd_cond 1
% 10.33/22.33 % fd_pseudo_cond 5
% 10.33/22.33 % AC symbols 0
% 10.33/22.33
% 10.33/22.33 % ------ Input Options Time Limit: Unbounded
% 10.33/22.33
% 10.33/22.33
% 10.33/22.33 % ------
% 10.33/22.33 % Current options:
% 10.33/22.33 % ------
% 10.33/22.33
% 10.33/22.33
% 10.33/22.33 %
% 10.33/22.33
% 10.33/22.33 % ------ Proving...
% 10.33/22.33 %
% 10.33/22.33
% 10.33/22.33 % SZS status Theorem for theBenchmark.p
% 10.33/22.33
% 10.33/22.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.33/22.33
% 10.33/22.33
%------------------------------------------------------------------------------