%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG057+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 : n010.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 02:38:28 PM UTC 2026
% Result : Theorem 10.76s 2.77s
% Output : CNFRefutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 104 ( 32 unt; 0 def)
% Number of atoms : 314 ( 82 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 384 ( 174 ~; 176 |; 26 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn 120 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
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(f24,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
fof(f25,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
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(f46,axiom,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
fof(f47,axiom,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
fof(f48,axiom,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
fof(f51,axiom,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).
fof(f53,axiom,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
fof(f56,axiom,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1967) ).
fof(f57,axiom,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2027) ).
fof(f58,axiom,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2052) ).
fof(f59,conjecture,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f60,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f66,plain,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(flattening,[],[f60]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f75]) ).
fof(f79,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(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(flattening,[],[f79]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f103,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(f104,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(flattening,[],[f103]) ).
fof(f135,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f161,plain,
! [X2,X3,X0,X1] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f162,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f165,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f166,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f104]) ).
fof(f197,plain,
aScalar0(xC),
inference(cnf_transformation,[],[f46]) ).
fof(f199,plain,
aScalar0(xD),
inference(cnf_transformation,[],[f47]) ).
fof(f201,plain,
aScalar0(xE),
inference(cnf_transformation,[],[f48]) ).
fof(f207,plain,
aScalar0(xH),
inference(cnf_transformation,[],[f51]) ).
fof(f211,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f53]) ).
fof(f216,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(cnf_transformation,[],[f56]) ).
fof(f217,plain,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(cnf_transformation,[],[f57]) ).
fof(f218,plain,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(cnf_transformation,[],[f58]) ).
fof(f219,plain,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(cnf_transformation,[],[f66]) ).
tcf(c_56,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f135]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ 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,[],[f149]) ).
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,[],[f147]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_86,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f165]) ).
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,[],[f166]) ).
tcf(c_117,plain,
aScalar0(xC),
inference(cnf_transformation,[],[f197]) ).
tcf(c_119,plain,
aScalar0(xD),
inference(cnf_transformation,[],[f199]) ).
tcf(c_121,plain,
aScalar0(xE),
inference(cnf_transformation,[],[f201]) ).
tcf(c_127,plain,
aScalar0(xH),
inference(cnf_transformation,[],[f207]) ).
tcf(c_131,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f211]) ).
tcf(c_137,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(cnf_transformation,[],[f216]) ).
tcf(c_138,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(xP,xP),
inference(cnf_transformation,[],[f217]) ).
tcf(c_139,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) = xN,
inference(cnf_transformation,[],[f218]) ).
tcf(c_140,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(cnf_transformation,[],[f219]) ).
tcf(c_1147,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) = xN,
inference(subtyping,[status(esa)],[c_139]) ).
tcf(c_1148,plain,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) = sdtasdt0(xP,xP),
inference(subtyping,[status(esa)],[c_138]) ).
tcf(c_1196,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_1197,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_1200,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(X1_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2)
| sdtlseqdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2)
| ~ aScalar0(X1_iProver_sdtasdt0_2)
| ~ aScalar0(X0_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_83]) ).
tcf(c_1201,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(X0_iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2),sdtasdt0(X1_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)
| ~ sdtlseqdt0(sz0z00,X2_iProver_sdtasdt0_2)
| ~ sdtlseqdt0(X2_iProver_sdtasdt0_2,X3_iProver_sdtasdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2) ),
inference(subtyping,[status(esa)],[c_82]) ).
tcf(c_1212,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_1214,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_1224,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_1233,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_1214]) ).
tcf(c_1236,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_1212]) ).
tcf(c_1237,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1212]) ).
tcf(c_1241,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] : X0_iProver_sdtasdt0_2 = X0_iProver_sdtasdt0_2,
theory(equality) ).
tcf(c_1244,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_1251,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_1298,plain,
( ~ iPr_def_10
| ~ aScalar0(sz0z00) ),
inference(instantiation,[status(thm)],[c_1233]) ).
tcf(c_1308,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_1236,c_56,c_1298,c_1236,c_1237]) ).
tcf(c_1309,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_1308]) ).
tcf(c_2383,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ sdtlseqdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2)
| ( xN != X1_iProver_sdtasdt0_2 )
| ( sdtasdt0(xP,xP) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1251]) ).
tcf(c_2388,plain,
( aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(xP) ),
inference(instantiation,[status(thm)],[c_1224]) ).
tcf(c_2401,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( xN = X0_iProver_sdtasdt0_2 )
| ( xN != X1_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != X1_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1244]) ).
tcf(c_2402,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = X0_iProver_sdtasdt0_2 )
| ~ aScalar0(X0_iProver_sdtasdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtasdt0_2)
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xP,xP))
| ( sdtasdt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)) != sdtasdt0(X0_iProver_sdtasdt0_2,X0_iProver_sdtasdt0_2) ) ),
inference(instantiation,[status(thm)],[c_1196]) ).
tcf(c_2408,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = X1_iProver_sdtasdt0_2 )
| ( X1_iProver_sdtasdt0_2 != X0_iProver_sdtasdt0_2 )
| ( sdtasdt0(xP,xP) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1244]) ).
tcf(c_2429,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( xN = X0_iProver_sdtasdt0_2 )
| ( xN != xN )
| ( X0_iProver_sdtasdt0_2 != xN ) ),
inference(instantiation,[status(thm)],[c_2401]) ).
tcf(c_2478,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( ( sdtasdt0(xP,xP) = X0_iProver_sdtasdt0_2 )
| ( X0_iProver_sdtasdt0_2 != sdtasdt0(xP,xP) )
| ( sdtasdt0(xP,xP) != sdtasdt0(xP,xP) ) ),
inference(instantiation,[status(thm)],[c_2408]) ).
tcf(c_2487,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(xP,xP))
| ~ aScalar0(xP) ),
inference(instantiation,[status(thm)],[c_1197]) ).
tcf(c_2506,plain,
xN = xN,
inference(instantiation,[status(thm)],[c_1241]) ).
tcf(c_2547,plain,
( ( sdtasdt0(xP,xP) = sdtasdt0(xP,xP) )
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xP,xP))
| ( sdtasdt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)) != sdtasdt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)) ) ),
inference(instantiation,[status(thm)],[c_2402]) ).
tcf(c_2590,plain,
( ( sdtasdt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)) = sdtasdt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)) )
| ~ aScalar0(sdtasdt0(xP,xP)) ),
inference(instantiation,[status(thm)],[c_1309]) ).
tcf(c_2594,plain,
( ( sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) )
| ( sdtasdt0(xP,xP) != sdtasdt0(xP,xP) )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) != sdtasdt0(xP,xP) ) ),
inference(instantiation,[status(thm)],[c_2478]) ).
tcf(c_2719,plain,
( ( xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) )
| ( xN != xN )
| ( sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) != xN ) ),
inference(instantiation,[status(thm)],[c_2429]) ).
tcf(c_2759,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2: iProver_sdtasdt0_2,X2_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(X2_iProver_sdtasdt0_2,sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2))
| sdtlseqdt0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2),X2_iProver_sdtasdt0_2)
| ~ aScalar0(X2_iProver_sdtasdt0_2)
| ~ aScalar0(sdtasdt0(X0_iProver_sdtasdt0_2,X1_iProver_sdtasdt0_2)) ),
inference(instantiation,[status(thm)],[c_1200]) ).
tcf(c_2918,plain,
! [X0_iProver_sdtasdt0_2: iProver_sdtasdt0_2] :
( sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ sdtlseqdt0(X0_iProver_sdtasdt0_2,sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ( xN != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) )
| ( sdtasdt0(xP,xP) != X0_iProver_sdtasdt0_2 ) ),
inference(instantiation,[status(thm)],[c_2383]) ).
tcf(c_2996,plain,
( aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(xE) ),
inference(instantiation,[status(thm)],[c_1224]) ).
tcf(c_3796,plain,
( aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(xD)
| ~ aScalar0(xC) ),
inference(instantiation,[status(thm)],[c_1224]) ).
tcf(c_4089,plain,
( sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ( xN != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) )
| ( sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)) ) ),
inference(instantiation,[status(thm)],[c_2918]) ).
tcf(c_6506,plain,
( aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(xH) ),
inference(instantiation,[status(thm)],[c_1224]) ).
tcf(c_7128,plain,
( sdtlseqdt0(sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(instantiation,[status(thm)],[c_1201]) ).
tcf(c_14296,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(xE,xE))
| ~ aScalar0(xE) ),
inference(instantiation,[status(thm)],[c_1197]) ).
tcf(c_16225,plain,
( sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(instantiation,[status(thm)],[c_2759]) ).
tcf(c_16226,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16225,c_14296,c_7128,c_6506,c_4089,c_3796,c_2996,c_2719,c_2594,c_2590,c_2547,c_2506,c_2487,c_2388,c_1148,c_1147,c_137,c_140,c_117,c_119,c_121,c_127,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG057+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 08:00:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 10.76/2.77 % SZS status Started for theBenchmark.p
% 10.76/2.77 % SZS status Theorem for theBenchmark.p
% 10.76/2.77
% 10.76/2.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.76/2.77
% 10.76/2.77 % ------ iProver source info
% 10.76/2.77
% 10.76/2.77 % git: date: 2026-07-19 20:42:38 +0200
% 10.76/2.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.76/2.77 % git: non_committed_changes: false
% 10.76/2.77
% 10.76/2.77 % ------ Parsing...
% 10.76/2.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.76/2.77
% 10.76/2.77 % ------ 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 %
% 10.76/2.77
% 10.76/2.77 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.76/2.77
% 10.76/2.77 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 10.76/2.77 % ------ Proving...
% 10.76/2.77 % ------ Problem Properties
% 10.76/2.77
% 10.76/2.77 %
% 10.76/2.77 % clauses 94
% 10.76/2.77 % conjectures 1
% 10.76/2.77 % EPR 25
% 10.76/2.77 % Horn 82
% 10.76/2.77 % unary 41
% 10.76/2.77 % binary 19
% 10.76/2.77 % lits 228
% 10.76/2.77 % lits eq 73
% 10.76/2.77 % fd_pure 0
% 10.76/2.77 % fd_pseudo 0
% 10.76/2.77 % fd_cond 1
% 10.76/2.77 % fd_pseudo_cond 5
% 10.76/2.77 % AC symbols 0
% 10.76/2.77
% 10.76/2.77 % ------ Input Options Time Limit: Unbounded
% 10.76/2.77
% 10.76/2.77
% 10.76/2.77 % ------
% 10.76/2.77 % Current options:
% 10.76/2.77 % ------
% 10.76/2.77
% 10.76/2.77
% 10.76/2.77 %
% 10.76/2.77
% 10.76/2.77 % ------ Proving...
% 10.76/2.77 %
% 10.76/2.77
% 10.76/2.77 % SZS status Theorem for theBenchmark.p
% 10.76/2.77
% 10.76/2.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.76/2.77
% 10.76/2.77
%------------------------------------------------------------------------------