%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM524+3 : 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 : n005.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 04:57:41 PM UTC 2026
% Result : Theorem 4.10s 3.26s
% Output : CNFRefutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 20 unt; 0 def)
% Number of atoms : 175 ( 69 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 207 ( 82 ~; 81 |; 32 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(m__3046,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(m__3059,hypothesis,
( aNaturalNumber0(xq)
& xn = sdtasdt0(xp,xq)
& xq = sdtsldt0(xn,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(c_0_11,plain,
! [X156,X157,X159] :
( ( aNaturalNumber0(esk2_2(X156,X157))
| ~ doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) )
& ( X157 = sdtasdt0(X156,esk2_2(X156,X157))
| ~ doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) )
& ( ~ aNaturalNumber0(X159)
| X157 != sdtasdt0(X156,X159)
| doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_12,plain,
! [X102,X103] :
( ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| aNaturalNumber0(sdtasdt0(X102,X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_13,plain,
! [X160,X161,X162] :
( ( aNaturalNumber0(X162)
| X162 != sdtsldt0(X161,X160)
| X160 = sz00
| ~ doDivides0(X160,X161)
| ~ aNaturalNumber0(X160)
| ~ aNaturalNumber0(X161) )
& ( X161 = sdtasdt0(X160,X162)
| X162 != sdtsldt0(X161,X160)
| X160 = sz00
| ~ doDivides0(X160,X161)
| ~ aNaturalNumber0(X160)
| ~ aNaturalNumber0(X161) )
& ( ~ aNaturalNumber0(X162)
| X161 != sdtasdt0(X160,X162)
| X162 = sdtsldt0(X161,X160)
| X160 = sz00
| ~ doDivides0(X160,X161)
| ~ aNaturalNumber0(X160)
| ~ aNaturalNumber0(X161) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_14,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_14]),c_0_15]) ).
fof(c_0_18,plain,
! [X112,X113,X114] :
( ~ aNaturalNumber0(X112)
| ~ aNaturalNumber0(X113)
| ~ aNaturalNumber0(X114)
| sdtasdt0(sdtasdt0(X112,X113),X114) = sdtasdt0(X112,sdtasdt0(X113,X114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_19,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_15]),c_0_17]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_21,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_22,hypothesis,
( aNaturalNumber0(esk7_0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
& doDivides0(xp,sdtasdt0(xn,xn))
& aNaturalNumber0(esk8_0)
& xn = sdtasdt0(xp,esk8_0)
& doDivides0(xp,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__3046])]) ).
cnf(c_0_23,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,hypothesis,
xn = sdtasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
fof(c_0_26,plain,
! [X110,X111] :
( ~ aNaturalNumber0(X110)
| ~ aNaturalNumber0(X111)
| sdtasdt0(X110,X111) = sdtasdt0(X111,X110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_27,hypothesis,
( sdtsldt0(sdtasdt0(xp,X1),xp) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
( sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_20])]) ).
cnf(c_0_31,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_33,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_34,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
fof(c_0_35,plain,
! [X123,X124,X125] :
( ( sdtasdt0(X123,X124) != sdtasdt0(X123,X125)
| X124 = X125
| ~ aNaturalNumber0(X124)
| ~ aNaturalNumber0(X125)
| X123 = sz00
| ~ aNaturalNumber0(X123) )
& ( sdtasdt0(X124,X123) != sdtasdt0(X125,X123)
| X124 = X125
| ~ aNaturalNumber0(X124)
| ~ aNaturalNumber0(X125)
| X123 = sz00
| ~ aNaturalNumber0(X123) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_36,hypothesis,
( sdtasdt0(xp,sdtasdt0(X1,xq)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_25])]) ).
cnf(c_0_37,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,hypothesis,
( sdtasdt0(xm,xm) = esk7_0
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_33]),c_0_34]) ).
cnf(c_0_39,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_40,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,hypothesis,
( sdtasdt0(xp,sdtasdt0(X1,sdtasdt0(X2,xq))) = sdtasdt0(xn,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_25])]),c_0_15]) ).
cnf(c_0_42,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_25])]) ).
cnf(c_0_43,hypothesis,
sdtasdt0(xm,xm) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_15]),c_0_39])]) ).
cnf(c_0_44,hypothesis,
( X1 = esk7_0
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,esk7_0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_29]) ).
cnf(c_0_45,hypothesis,
sdtasdt0(xp,sdtasdt0(xn,xq)) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_30]),c_0_24]),c_0_25]),c_0_20])]) ).
cnf(c_0_46,negated_conjecture,
sdtasdt0(xn,xq) != esk7_0,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,hypothesis,
~ aNaturalNumber0(sdtasdt0(xn,xq)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_28]),c_0_20])]),c_0_46]),c_0_21]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_49,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_15]),c_0_25]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM524+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:41:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.10/3.26 % Version : CSE_E---1.7
% 4.10/3.26 % Problem : theBenchmark.p
% 4.10/3.26 % SZS status Theorem for theBenchmark.p
% 4.10/3.26 % SZS output start CNFRefutation
% See solution above
% 4.10/3.28 % Total time : 2.372s
%------------------------------------------------------------------------------