%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG073+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 05:05:14 PM UTC 2026
% Result : Theorem 2.49s 2.09s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 18 unt; 0 def)
% Number of atoms : 124 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 133 ( 56 ~; 53 |; 17 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDistr) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1911,hypothesis,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
fof(m__1873,hypothesis,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).
fof(m__1820,hypothesis,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
fof(m__2405,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2405) ).
fof(m__2654,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2654) ).
fof(mSqrt,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X2)
& sdtasdt0(X1,X1) = sdtasdt0(X2,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).
fof(m__2628,hypothesis,
( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
& sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2628) ).
fof(m__,conjecture,
sdtpldt0(xR,xS) = sdtpldt0(xP,xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1930,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(m__1892,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(c_0_14,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])])]) ).
fof(c_0_15,plain,
! [X105,X106] :
( ~ aScalar0(X105)
| ~ aScalar0(X106)
| ~ sdtlseqdt0(X105,X106)
| ~ sdtlseqdt0(X106,X105)
| X105 = X106 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])]) ).
fof(c_0_16,plain,
! [X84,X85] :
( ~ aScalar0(X84)
| ~ aScalar0(X85)
| aScalar0(sdtpldt0(X84,X85)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])]) ).
fof(c_0_17,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_18,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_14]) ).
cnf(c_0_19,hypothesis,
xP = sdtasdt0(xE,xH),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_20,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_21,hypothesis,
aScalar0(xE),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_22,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(split_conjunct,[status(thm)],[m__2405]) ).
cnf(c_0_24,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(split_conjunct,[status(thm)],[m__2654]) ).
fof(c_0_25,plain,
! [X123,X124] :
( ~ aScalar0(X123)
| ~ aScalar0(X124)
| ~ sdtlseqdt0(sz0z00,X123)
| ~ sdtlseqdt0(sz0z00,X124)
| sdtasdt0(X123,X123) != sdtasdt0(X124,X124)
| X123 = X124 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqrt])]) ).
cnf(c_0_26,plain,
( aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,hypothesis,
( sdtpldt0(sdtasdt0(xE,X1),xP) = sdtasdt0(xE,sdtpldt0(X1,xH))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_29,hypothesis,
( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))
| ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| sdtasdt0(X1,X1) != sdtasdt0(X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,hypothesis,
sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
inference(split_conjunct,[status(thm)],[m__2628]) ).
cnf(c_0_32,plain,
( aScalar0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_27]),c_0_27]) ).
cnf(c_0_33,hypothesis,
sdtasdt0(xE,sdtpldt0(xH,xH)) = sdtpldt0(xP,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_20])]) ).
cnf(c_0_34,hypothesis,
( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))
| ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_35,hypothesis,
( X1 = sdtpldt0(xP,xP)
| sdtasdt0(X1,X1) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,hypothesis,
aScalar0(sdtpldt0(xP,xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_20]),c_0_21])]) ).
cnf(c_0_37,hypothesis,
( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
fof(c_0_38,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_39,hypothesis,
( X1 = sdtpldt0(xP,xP)
| sdtasdt0(X1,X1) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_40,hypothesis,
( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_36])]) ).
cnf(c_0_41,hypothesis,
sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
inference(split_conjunct,[status(thm)],[m__2628]) ).
cnf(c_0_42,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,hypothesis,
~ aScalar0(sdtpldt0(xR,xS)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_44,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_45,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_46,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_26]),c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG073+2 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:49:20 EDT 2026
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % start to proof: theBenchmark
% 2.49/2.09 % Version : CSE_E---1.7
% 2.49/2.09 % Problem : theBenchmark.p
% 2.49/2.09 % SZS status Theorem for theBenchmark.p
% 2.49/2.09 % SZS output start CNFRefutation
% See solution above
% 2.49/2.10 % Total time : 1.370s
%------------------------------------------------------------------------------