%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM435+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 : n001.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 04:57:19 PM UTC 2026
% Result : Theorem 1.56s 1.80s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 23 unt; 0 def)
% Number of atoms : 137 ( 47 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 55 ~; 49 |; 18 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 34 !; 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(m__1032,hypothesis,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1032) ).
fof(m__979,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
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(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__,conjecture,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_12,plain,
! [X51,X52,X53] :
( ~ aInteger0(X51)
| ~ aInteger0(X52)
| ~ aInteger0(X53)
| sdtpldt0(X51,sdtpldt0(X52,X53)) = sdtpldt0(sdtpldt0(X51,X52),X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_13,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_14,hypothesis,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__1032]) ).
cnf(c_0_15,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__979]) ).
fof(c_0_16,plain,
! [X46] :
( ~ aInteger0(X46)
| aInteger0(smndt0(X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_17,plain,
! [X47,X48] :
( ~ aInteger0(X47)
| ~ aInteger0(X48)
| aInteger0(sdtpldt0(X47,X48)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_18,hypothesis,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(sdtasdt0(xp,xq),xm),X1)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__979]) ).
fof(c_0_21,plain,
! [X57] :
( ( sdtpldt0(X57,smndt0(X57)) = sz00
| ~ aInteger0(X57) )
& ( sz00 = sdtpldt0(smndt0(X57),X57)
| ~ aInteger0(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_22,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(sdtasdt0(xp,xq),xm),X1)
| ~ aInteger0(X1) ),
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,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,plain,
! [X61,X62] :
( ~ aInteger0(X61)
| ~ aInteger0(X62)
| sdtasdt0(X61,X62) = sdtasdt0(X62,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_26,hypothesis,
( aInteger0(sdtasdt0(sdtasdt0(xp,xq),xm))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_14]),c_0_15])]) ).
cnf(c_0_27,hypothesis,
sdtpldt0(sdtasdt0(sdtasdt0(xp,xq),xm),xb) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20])]) ).
cnf(c_0_28,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,hypothesis,
aInteger0(xm),
inference(split_conjunct,[status(thm)],[m__1032]) ).
fof(c_0_30,plain,
! [X49,X50] :
( ~ aInteger0(X49)
| ~ aInteger0(X50)
| aInteger0(sdtasdt0(X49,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_31,hypothesis,
aInteger0(sdtasdt0(sdtasdt0(xp,xq),xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_20])]) ).
fof(c_0_32,plain,
! [X54,X55] :
( ~ aInteger0(X54)
| ~ aInteger0(X55)
| sdtpldt0(X54,X55) = sdtpldt0(X55,X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_33,hypothesis,
( sdtpldt0(sdtasdt0(xm,sdtasdt0(xp,xq)),xb) = sdtpldt0(xa,sz00)
| ~ aInteger0(sdtasdt0(xp,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_34,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_36,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[m__979]) ).
cnf(c_0_37,hypothesis,
( aInteger0(sdtasdt0(xm,sdtasdt0(xp,xq)))
| ~ aInteger0(sdtasdt0(xp,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_29])]) ).
cnf(c_0_38,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,hypothesis,
sdtpldt0(sdtasdt0(xm,sdtasdt0(xp,xq)),xb) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_40,hypothesis,
aInteger0(sdtasdt0(xm,sdtasdt0(xp,xq))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_41,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_24]),c_0_19]) ).
cnf(c_0_42,hypothesis,
sdtpldt0(xb,sdtasdt0(xm,sdtasdt0(xp,xq))) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_20]),c_0_40])]) ).
fof(c_0_43,plain,
! [X56] :
( ( sdtpldt0(X56,sz00) = X56
| ~ aInteger0(X56) )
& ( X56 = sdtpldt0(sz00,X56)
| ~ aInteger0(X56) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_44,hypothesis,
sdtpldt0(smndt0(xb),sdtpldt0(xa,sz00)) = sdtpldt0(sz00,sdtasdt0(xm,sdtasdt0(xp,xq))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40]),c_0_20])]) ).
cnf(c_0_45,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_46,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,hypothesis,
sdtpldt0(sz00,sdtasdt0(xm,sdtasdt0(xp,xq))) = sdtpldt0(smndt0(xb),xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_15])]) ).
cnf(c_0_48,hypothesis,
sdtpldt0(smndt0(xb),xa) = sdtasdt0(xm,sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_40])]) ).
fof(c_0_49,plain,
! [X58,X59,X60] :
( ~ aInteger0(X58)
| ~ aInteger0(X59)
| ~ aInteger0(X60)
| sdtasdt0(X58,sdtasdt0(X59,X60)) = sdtasdt0(sdtasdt0(X58,X59),X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_50,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtasdt0(xm,sdtasdt0(xp,xq))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_48]),c_0_14]),c_0_15])]) ).
fof(c_0_51,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_52,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,hypothesis,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtasdt0(xm,sdtasdt0(xp,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_19]),c_0_20])]) ).
cnf(c_0_54,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,hypothesis,
sdtasdt0(xm,sdtasdt0(xp,xq)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_29]),c_0_35]),c_0_36])]) ).
cnf(c_0_56,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_52]),c_0_34]) ).
cnf(c_0_57,negated_conjecture,
sdtasdt0(sdtasdt0(xp,xq),xm) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(rw,[status(thm)],[c_0_54,c_0_14]) ).
cnf(c_0_58,hypothesis,
sdtasdt0(xq,sdtasdt0(xm,xp)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_35]),c_0_36]),c_0_29])]) ).
cnf(c_0_59,negated_conjecture,
sdtasdt0(xq,sdtasdt0(xp,xm)) != sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_52]),c_0_29]),c_0_35]),c_0_36])]) ).
cnf(c_0_60,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_28]),c_0_36]),c_0_29])]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM435+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
% 0.14/0.33 % Computer : n001.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 00:35:18 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.56/1.80 % Version : CSE_E---1.7
% 1.56/1.80 % Problem : theBenchmark.p
% 1.56/1.80 % SZS status Theorem for theBenchmark.p
% 1.56/1.80 % SZS output start CNFRefutation
% See solution above
% 1.56/1.80 % Total time : 1.373s
%------------------------------------------------------------------------------