%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG060+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:10 PM UTC 2026
% Result : Theorem 32.68s 20.24s
% Output : CNFRefutation 32.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 43 unt; 0 def)
% Number of atoms : 240 ( 102 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 238 ( 96 ~; 91 |; 43 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 81 ( 1 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMNeg,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
fof(m__2144,hypothesis,
( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
fof(m__1892,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(mMDNeg,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMDNeg) ).
fof(mScZero,axiom,
! [X1] :
( aScalar0(X1)
=> ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(m__1930,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1854,hypothesis,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(m__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
fof(m__1800,hypothesis,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(m__1837,hypothesis,
( aScalar0(xF)
& xF = sdtasdt0(xA,xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mDistr,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
fof(mArith,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(m__,conjecture,
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__) ).
fof(mDistr2,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
fof(c_0_17,plain,
! [X100,X101] :
( ( sdtasdt0(X100,smndt0(X101)) = smndt0(sdtasdt0(X100,X101))
| ~ aScalar0(X100)
| ~ aScalar0(X101) )
& ( sdtasdt0(smndt0(X100),X101) = smndt0(sdtasdt0(X100,X101))
| ~ aScalar0(X100)
| ~ aScalar0(X101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])]) ).
cnf(c_0_18,plain,
( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_19,hypothesis,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_20,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
fof(c_0_21,plain,
! [X102,X103] :
( ~ aScalar0(X102)
| ~ aScalar0(X103)
| sdtasdt0(smndt0(X102),smndt0(X103)) = sdtasdt0(X102,X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])]) ).
fof(c_0_22,plain,
! [X89] :
( ( sdtpldt0(X89,sz0z00) = X89
| ~ aScalar0(X89) )
& ( sdtpldt0(sz0z00,X89) = X89
| ~ aScalar0(X89) )
& ( sdtasdt0(X89,sz0z00) = sz0z00
| ~ aScalar0(X89) )
& ( sdtasdt0(sz0z00,X89) = sz0z00
| ~ aScalar0(X89) )
& ( sdtpldt0(X89,smndt0(X89)) = sz0z00
| ~ aScalar0(X89) )
& ( sdtpldt0(smndt0(X89),X89) = sz0z00
| ~ aScalar0(X89) )
& ( smndt0(smndt0(X89)) = X89
| ~ aScalar0(X89) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).
cnf(c_0_23,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(xR)) = smndt0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,plain,
( sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
fof(c_0_26,plain,
! [X86,X87] :
( ~ aScalar0(X86)
| ~ aScalar0(X87)
| aScalar0(sdtasdt0(X86,X87)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).
cnf(c_0_27,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_28,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_29,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_30,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,hypothesis,
( smndt0(smndt0(xN)) = sdtasdt0(xS,xR)
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20]),c_0_25])]) ).
cnf(c_0_32,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
fof(c_0_33,plain,
! [X88] :
( ~ aScalar0(X88)
| aScalar0(smndt0(X88)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).
cnf(c_0_34,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,hypothesis,
sdtasdt0(xC,smndt0(xG)) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_36,hypothesis,
( sdtasdt0(xS,xR) = xN
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_37,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_39,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_40,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_41,plain,
! [X93,X94,X95] :
( ( sdtasdt0(X93,sdtpldt0(X94,X95)) = sdtpldt0(sdtasdt0(X93,X94),sdtasdt0(X93,X95))
| ~ aScalar0(X93)
| ~ aScalar0(X94)
| ~ aScalar0(X95) )
& ( sdtasdt0(sdtpldt0(X93,X94),X95) = sdtpldt0(sdtasdt0(X93,X95),sdtasdt0(X94,X95))
| ~ aScalar0(X93)
| ~ aScalar0(X94)
| ~ aScalar0(X95) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])]) ).
cnf(c_0_42,plain,
( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_43,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_44,hypothesis,
( aScalar0(smndt0(xR))
| ~ aScalar0(smndt0(xG)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_29])]) ).
cnf(c_0_45,hypothesis,
sdtasdt0(xS,xR) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_25])]) ).
cnf(c_0_46,hypothesis,
sdtasdt0(xF,smndt0(xD)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_47,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,hypothesis,
sdtasdt0(smndt0(xR),xS) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_25]),c_0_20])]) ).
cnf(c_0_49,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_28])]) ).
cnf(c_0_50,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,hypothesis,
sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_45]),c_0_20]),c_0_25])]) ).
fof(c_0_52,plain,
! [X90,X91,X92] :
( ( sdtpldt0(sdtpldt0(X90,X91),X92) = sdtpldt0(X90,sdtpldt0(X91,X92))
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtpldt0(X90,X91) = sdtpldt0(X91,X90)
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtasdt0(sdtasdt0(X90,X91),X92) = sdtasdt0(X90,sdtasdt0(X91,X92))
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtasdt0(X90,X91) = sdtasdt0(X91,X90)
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).
cnf(c_0_53,hypothesis,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xD)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_46]),c_0_40])]) ).
cnf(c_0_54,hypothesis,
( sdtpldt0(sdtasdt0(smndt0(xR),X1),smndt0(xN)) = sdtasdt0(smndt0(xR),sdtpldt0(X1,xS))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_25])]),c_0_49])]) ).
cnf(c_0_55,hypothesis,
( sdtpldt0(sdtasdt0(X1,smndt0(xR)),smndt0(xN)) = sdtasdt0(sdtpldt0(X1,xS),smndt0(xR))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_25])]),c_0_49])]) ).
cnf(c_0_56,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_37]),c_0_39])]) ).
cnf(c_0_58,hypothesis,
sdtasdt0(sdtpldt0(smndt0(xR),xS),smndt0(xR)) = sdtasdt0(smndt0(xR),sdtpldt0(smndt0(xR),xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_49])]) ).
cnf(c_0_59,hypothesis,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_32]) ).
cnf(c_0_60,hypothesis,
( sdtpldt0(sdtasdt0(smndt0(xS),X1),smndt0(xN)) = sdtasdt0(smndt0(xS),sdtpldt0(X1,xR))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_19]),c_0_20])]),c_0_57])]) ).
cnf(c_0_61,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_62,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_63,plain,
( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X3,smndt0(X2))) = sdtasdt0(sdtpldt0(smndt0(X1),X3),smndt0(X2))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_24]),c_0_37]),c_0_37]) ).
cnf(c_0_64,hypothesis,
sdtasdt0(sdtpldt0(xS,smndt0(xR)),smndt0(xR)) = sdtasdt0(smndt0(xR),sdtpldt0(xS,smndt0(xR))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_25]),c_0_49])]) ).
cnf(c_0_65,plain,
( sdtpldt0(sdtasdt0(X1,smndt0(X2)),sdtasdt0(X3,X2)) = sdtasdt0(sdtpldt0(X1,smndt0(X3)),smndt0(X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_24]),c_0_37]),c_0_37]) ).
cnf(c_0_66,hypothesis,
sdtasdt0(smndt0(xS),sdtpldt0(smndt0(xS),xR)) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_57])]) ).
fof(c_0_67,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_68,hypothesis,
( aScalar0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_62]),c_0_20])]) ).
cnf(c_0_69,hypothesis,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_34,c_0_61]) ).
cnf(c_0_70,hypothesis,
sdtasdt0(smndt0(xR),sdtpldt0(smndt0(xR),xS)) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_63]),c_0_51]),c_0_25]),c_0_20])]) ).
cnf(c_0_71,hypothesis,
sdtasdt0(smndt0(xR),sdtpldt0(xS,smndt0(xR))) = sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_51]),c_0_25]),c_0_20])]) ).
cnf(c_0_72,hypothesis,
( sdtpldt0(smndt0(xN),sdtasdt0(xR,X1)) = sdtasdt0(xR,sdtpldt0(smndt0(xS),X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_62]),c_0_20])]),c_0_57])]) ).
cnf(c_0_73,hypothesis,
( sdtpldt0(smndt0(xN),sdtasdt0(X1,xR)) = sdtasdt0(sdtpldt0(smndt0(xS),X1),xR)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_19]),c_0_20])]),c_0_57])]) ).
cnf(c_0_74,plain,
( sdtpldt0(sdtasdt0(smndt0(X1),X2),sdtasdt0(X1,X3)) = sdtasdt0(smndt0(X1),sdtpldt0(X2,smndt0(X3)))
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_24]),c_0_37]),c_0_37]) ).
cnf(c_0_75,hypothesis,
sdtasdt0(smndt0(xS),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_59]),c_0_20]),c_0_57])]) ).
cnf(c_0_76,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_57])]) ).
cnf(c_0_78,hypothesis,
aScalar0(sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_37]),c_0_25])]) ).
fof(c_0_79,plain,
! [X96,X97,X98,X99] :
( ~ aScalar0(X96)
| ~ aScalar0(X97)
| ~ aScalar0(X98)
| ~ aScalar0(X99)
| sdtasdt0(sdtpldt0(X96,X97),sdtpldt0(X98,X99)) = sdtpldt0(sdtpldt0(sdtasdt0(X96,X98),sdtasdt0(X96,X99)),sdtpldt0(sdtasdt0(X97,X98),sdtasdt0(X97,X99))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr2])]) ).
cnf(c_0_80,hypothesis,
sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_59]),c_0_71]),c_0_25]),c_0_49])]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(sdtpldt0(smndt0(xS),xR),xR) = sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_20])]) ).
cnf(c_0_82,hypothesis,
( sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(X1,smndt0(xS)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_62]),c_0_20])]),c_0_57])]) ).
cnf(c_0_83,hypothesis,
( sdtpldt0(sdtasdt0(X1,xR),smndt0(xN)) = sdtasdt0(sdtpldt0(X1,smndt0(xS)),xR)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_19]),c_0_20])]),c_0_57])]) ).
cnf(c_0_84,hypothesis,
sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_19]),c_0_20]),c_0_25])]) ).
cnf(c_0_85,hypothesis,
( sdtpldt0(smndt0(xN),sdtasdt0(xS,X1)) = sdtasdt0(xS,sdtpldt0(smndt0(xR),X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_51]),c_0_25])]),c_0_49])]) ).
cnf(c_0_86,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_59]),c_0_77]),c_0_78])]) ).
cnf(c_0_87,hypothesis,
( sdtpldt0(sdtasdt0(xS,X1),smndt0(xN)) = sdtasdt0(xS,sdtpldt0(X1,smndt0(xR)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_51]),c_0_25])]),c_0_49])]) ).
cnf(c_0_88,plain,
( sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4)))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,hypothesis,
sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_80]),c_0_81]),c_0_20])]) ).
cnf(c_0_90,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),xR) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_20])]) ).
cnf(c_0_91,hypothesis,
sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)) = sdtasdt0(xS,sdtpldt0(smndt0(xR),xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_25])]) ).
cnf(c_0_92,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtasdt0(xS,sdtpldt0(xS,smndt0(xR)))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_25])]) ).
cnf(c_0_93,hypothesis,
( sdtpldt0(sdtpldt0(sdtasdt0(X1,xR),sdtasdt0(X1,X2)),sdtpldt0(smndt0(xN),sdtasdt0(smndt0(xS),X2))) = sdtasdt0(sdtpldt0(X1,smndt0(xS)),sdtpldt0(xR,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_19]),c_0_20])]),c_0_57])]) ).
cnf(c_0_94,hypothesis,
sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_89]),c_0_90]),c_0_20])]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(xS,sdtpldt0(smndt0(xR),xS)) = sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_91]),c_0_25])]) ).
cnf(c_0_96,hypothesis,
sdtpldt0(sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),sdtasdt0(xS,sdtpldt0(xS,smndt0(xR)))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_82]),c_0_20])]) ).
cnf(c_0_97,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_62]),c_0_89]),c_0_94]),c_0_61]),c_0_84]),c_0_91]),c_0_95]),c_0_57]),c_0_20])]),c_0_96]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : RNG060+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.27 % Computer : n012.cluster.edu
% 0.06/0.27 % Model : x86_64 x86_64
% 0.06/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.27 % Memory : 8042.1875MB
% 0.06/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.27 % CPULimit : 300
% 0.06/0.27 % WCLimit : 300
% 0.06/0.27 % DateTime : Tue May 5 01:48:31 EDT 2026
% 0.06/0.27 % CPUTime :
% 0.06/0.28 % start to proof: theBenchmark
% 32.68/20.24 % Version : CSE_E---1.7
% 32.68/20.24 % Problem : theBenchmark.p
% 32.68/20.24 % SZS status Theorem for theBenchmark.p
% 32.68/20.24 % SZS output start CNFRefutation
% See solution above
% 32.78/20.39 % Total time : 14.375s
%------------------------------------------------------------------------------