%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM453+1 : 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 : 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 04:57:23 PM UTC 2026
% Result : Theorem 1.76s 1.89s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 13 unt; 0 def)
% Number of atoms : 89 ( 49 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 78 ( 31 ~; 33 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2171) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(c_0_8,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,plain,
! [X99,X100,X101] :
( ~ aInteger0(X99)
| ~ aInteger0(X100)
| ~ aInteger0(X101)
| sdtpldt0(X99,sdtpldt0(X100,X101)) = sdtpldt0(sdtpldt0(X99,X100),X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_10,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_14,plain,
! [X94] :
( ~ aInteger0(X94)
| aInteger0(smndt0(X94)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_15,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),X1)) = sdtpldt0(sz10,X1)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[m__2171]) ).
cnf(c_0_18,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),X1)) = sdtpldt0(sz10,X1)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_19,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_20,plain,
! [X104] :
( ( sdtpldt0(X104,sz00) = X104
| ~ aInteger0(X104) )
& ( X104 = sdtpldt0(sz00,X104)
| ~ aInteger0(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(c_0_21,plain,
! [X105] :
( ( sdtpldt0(X105,smndt0(X105)) = sz00
| ~ aInteger0(X105) )
& ( sz00 = sdtpldt0(smndt0(X105),X105)
| ~ aInteger0(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_22,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),sz00)) = sdtpldt0(sz10,sz00)
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,hypothesis,
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),xp)) = sdtpldt0(sz10,xp)
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_25,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,sz00)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,hypothesis,
( sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17])]) ).
cnf(c_0_28,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,sz00)
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_16]),c_0_17])]) ).
cnf(c_0_29,hypothesis,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,sz00) != sz10 ),
inference(ef,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
sdtpldt0(sz10,xp) = sz10,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_28]),c_0_29]) ).
cnf(c_0_31,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_19])]) ).
cnf(c_0_32,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(xp,X1)) = sdtpldt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_30]),c_0_17]),c_0_13])]) ).
cnf(c_0_33,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_16]),c_0_19])]) ).
cnf(c_0_34,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_25]),c_0_16]) ).
cnf(c_0_35,negated_conjecture,
sdtpldt0(sz10,sz00) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_23]),c_0_30]),c_0_19]),c_0_17])]) ).
cnf(c_0_36,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_33]),c_0_19])]) ).
cnf(c_0_37,negated_conjecture,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_19]),c_0_13])]) ).
cnf(c_0_38,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_39,negated_conjecture,
sdtpldt0(sz00,xp) = sz00,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_17]),c_0_13])]),c_0_37]) ).
cnf(c_0_40,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2171]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_17])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM453+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n005.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 00:35:15 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.76/1.89 % Version : CSE_E---1.7
% 1.76/1.89 % Problem : theBenchmark.p
% 1.76/1.89 % SZS status Theorem for theBenchmark.p
% 1.76/1.89 % SZS output start CNFRefutation
% See solution above
% 1.76/1.89 % Total time : 1.374s
%------------------------------------------------------------------------------