%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM422+1 : 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 : n004.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 04:57:16 PM UTC 2026
% Result : Theorem 94.03s 51.49s
% Output : CNFRefutation 94.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 19 unt; 0 def)
% Number of atoms : 147 ( 59 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 149 ( 64 ~; 60 |; 16 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(m__446,hypothesis,
aInteger0(xa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__446) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(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',mDistrib) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(m__,conjecture,
sdtasdt0(smndt0(sz10),xa) = smndt0(xa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_12,plain,
! [X32,X33,X34] :
( ~ aInteger0(X32)
| ~ aInteger0(X33)
| ~ aInteger0(X34)
| sdtpldt0(X32,sdtpldt0(X33,X34)) = sdtpldt0(sdtpldt0(X32,X33),X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_13,plain,
! [X30,X31] :
( ~ aInteger0(X30)
| ~ aInteger0(X31)
| aInteger0(sdtasdt0(X30,X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
fof(c_0_14,plain,
! [X44] :
( ( sdtasdt0(X44,sz10) = X44
| ~ aInteger0(X44) )
& ( X44 = sdtasdt0(sz10,X44)
| ~ aInteger0(X44) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
fof(c_0_15,plain,
! [X27] :
( ~ aInteger0(X27)
| aInteger0(smndt0(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_16,plain,
! [X42,X43] :
( ~ aInteger0(X42)
| ~ aInteger0(X43)
| sdtasdt0(X42,X43) = sdtasdt0(X43,X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_17,plain,
! [X37] :
( ( sdtpldt0(X37,sz00) = X37
| ~ aInteger0(X37) )
& ( X37 = sdtpldt0(sz00,X37)
| ~ aInteger0(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_18,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X38] :
( ( sdtpldt0(X38,smndt0(X38)) = sz00
| ~ aInteger0(X38) )
& ( sz00 = sdtpldt0(smndt0(X38),X38)
| ~ aInteger0(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_23,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__446]) ).
fof(c_0_25,plain,
! [X45,X46,X47] :
( ( sdtasdt0(X45,sdtpldt0(X46,X47)) = sdtpldt0(sdtasdt0(X45,X46),sdtasdt0(X45,X47))
| ~ aInteger0(X45)
| ~ aInteger0(X46)
| ~ aInteger0(X47) )
& ( sdtasdt0(sdtpldt0(X45,X46),X47) = sdtpldt0(sdtasdt0(X45,X47),sdtasdt0(X46,X47))
| ~ aInteger0(X45)
| ~ aInteger0(X46)
| ~ aInteger0(X47) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
cnf(c_0_26,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( sdtpldt0(sdtpldt0(X1,X2),sdtasdt0(X3,X4)) = sdtpldt0(X1,sdtpldt0(X2,sdtasdt0(X3,X4)))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X4)
| ~ aInteger0(X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,plain,
( sdtasdt0(smndt0(X1),sz10) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
( sdtasdt0(X1,xa) = sdtasdt0(xa,X1)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
sdtasdt0(xa,sz10) = xa,
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_33,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_34,plain,
! [X48] :
( ( sdtasdt0(X48,sz00) = sz00
| ~ aInteger0(X48) )
& ( sz00 = sdtasdt0(sz00,X48)
| ~ aInteger0(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
cnf(c_0_35,plain,
( sdtpldt0(sdtasdt0(X1,X2),sz00) = sdtasdt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_36,hypothesis,
( sdtpldt0(sdtpldt0(X1,xa),sdtasdt0(X2,X3)) = sdtpldt0(X1,sdtpldt0(xa,sdtasdt0(X2,X3)))
| ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_37,hypothesis,
sdtasdt0(smndt0(xa),sz10) = smndt0(xa),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_38,hypothesis,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_39,hypothesis,
( sdtasdt0(smndt0(X1),xa) = sdtasdt0(xa,smndt0(X1))
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_40,hypothesis,
( sdtpldt0(sdtasdt0(xa,X1),xa) = sdtasdt0(xa,sdtpldt0(X1,sz10))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_24])]) ).
cnf(c_0_41,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_44,hypothesis,
( sdtpldt0(sdtasdt0(X1,xa),sz00) = sdtasdt0(X1,xa)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
fof(c_0_45,negated_conjecture,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_46,hypothesis,
( sdtpldt0(sdtpldt0(X1,xa),smndt0(xa)) = sdtpldt0(X1,sz00)
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_33])]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(smndt0(sz10),xa) = sdtasdt0(xa,smndt0(sz10)),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_48,hypothesis,
( sdtpldt0(sdtasdt0(xa,smndt0(X1)),xa) = sdtasdt0(xa,sdtpldt0(smndt0(X1),sz10))
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_49,plain,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(spm,[status(thm)],[c_0_41,c_0_33]) ).
cnf(c_0_50,hypothesis,
sdtasdt0(xa,sz00) = sz00,
inference(spm,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_51,plain,
( sdtpldt0(sz00,smndt0(X1)) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_21]) ).
cnf(c_0_52,hypothesis,
( sdtpldt0(sdtasdt0(smndt0(X1),xa),sz00) = sdtasdt0(smndt0(X1),xa)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_53,negated_conjecture,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,hypothesis,
( sdtpldt0(sdtpldt0(X1,xa),smndt0(xa)) = sdtpldt0(X1,sz00)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_21]),c_0_24])]) ).
cnf(c_0_55,hypothesis,
( aInteger0(sdtasdt0(xa,smndt0(sz10)))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_47]),c_0_24])]) ).
cnf(c_0_56,hypothesis,
sdtpldt0(sdtasdt0(xa,smndt0(sz10)),xa) = sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_49]),c_0_50]) ).
cnf(c_0_57,hypothesis,
sdtpldt0(sz00,smndt0(xa)) = smndt0(xa),
inference(spm,[status(thm)],[c_0_51,c_0_24]) ).
cnf(c_0_58,hypothesis,
sdtpldt0(sdtasdt0(xa,smndt0(sz10)),sz00) = sdtasdt0(xa,smndt0(sz10)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_33]),c_0_47]),c_0_47]) ).
cnf(c_0_59,negated_conjecture,
sdtasdt0(xa,smndt0(sz10)) != smndt0(xa),
inference(rw,[status(thm)],[c_0_53,c_0_47]) ).
cnf(c_0_60,hypothesis,
~ aInteger0(smndt0(sz10)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]),c_0_58]),c_0_59]) ).
cnf(c_0_61,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_21]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM422+1 : 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 : n004.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 00:32:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 94.03/51.49 % Version : CSE_E---1.7
% 94.03/51.49 % Problem : theBenchmark.p
% 94.03/51.49 % SZS status Theorem for theBenchmark.p
% 94.03/51.49 % SZS output start CNFRefutation
% See solution above
% 94.42/51.89 % Total time : 36.843s
%------------------------------------------------------------------------------