%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG082+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 : n012.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 05:05:16 PM UTC 2026
% Result : Theorem 89.28s 50.05s
% Output : CNFRefutation 89.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 28 unt; 0 def)
% Number of atoms : 161 ( 65 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 156 ( 68 ~; 64 |; 15 &)
% ( 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 : 71 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(m__444,hypothesis,
aElement0(xx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__444) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__,conjecture,
sdtasdt0(smndt0(sz10),xx) = smndt0(xx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_13,plain,
! [X43] :
( ( sdtasdt0(X43,sz10) = X43
| ~ aElement0(X43) )
& ( X43 = sdtasdt0(sz10,X43)
| ~ aElement0(X43) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
fof(c_0_14,plain,
! [X38,X39] :
( ~ aElement0(X38)
| ~ aElement0(X39)
| sdtasdt0(X38,X39) = sdtasdt0(X39,X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_15,plain,
! [X37] :
( ( sdtpldt0(X37,smndt0(X37)) = sz00
| ~ aElement0(X37) )
& ( sz00 = sdtpldt0(smndt0(X37),X37)
| ~ aElement0(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
fof(c_0_16,plain,
! [X44,X45,X46] :
( ( sdtasdt0(X44,sdtpldt0(X45,X46)) = sdtpldt0(sdtasdt0(X44,X45),sdtasdt0(X44,X46))
| ~ aElement0(X44)
| ~ aElement0(X45)
| ~ aElement0(X46) )
& ( sdtasdt0(sdtpldt0(X45,X46),X44) = sdtpldt0(sdtasdt0(X45,X44),sdtasdt0(X46,X44))
| ~ aElement0(X44)
| ~ aElement0(X45)
| ~ aElement0(X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_17,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__444]) ).
cnf(c_0_19,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X36] :
( ( sdtpldt0(X36,sz00) = X36
| ~ aElement0(X36) )
& ( X36 = sdtpldt0(sz00,X36)
| ~ aElement0(X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(c_0_21,plain,
! [X33,X34,X35] :
( ~ aElement0(X33)
| ~ aElement0(X34)
| ~ aElement0(X35)
| sdtpldt0(sdtpldt0(X33,X34),X35) = sdtpldt0(X33,sdtpldt0(X34,X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_22,plain,
! [X29,X30] :
( ~ aElement0(X29)
| ~ aElement0(X30)
| aElement0(sdtasdt0(X29,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_23,plain,
! [X26] :
( ~ aElement0(X26)
| aElement0(smndt0(X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
cnf(c_0_24,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,hypothesis,
sdtasdt0(xx,sz10) = xx,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_28,hypothesis,
( sdtasdt0(X1,xx) = sdtasdt0(xx,X1)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_29,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_30,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,hypothesis,
sdtpldt0(smndt0(xx),xx) = sz00,
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
fof(c_0_35,plain,
! [X31,X32] :
( ~ aElement0(X31)
| ~ aElement0(X32)
| sdtpldt0(X31,X32) = sdtpldt0(X32,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_36,hypothesis,
( sdtpldt0(sdtasdt0(xx,X1),xx) = sdtasdt0(xx,sdtpldt0(X1,sz10))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_18])]) ).
cnf(c_0_37,hypothesis,
sdtasdt0(xx,sz00) = sdtasdt0(sz00,xx),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_39,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_40,plain,
( sdtpldt0(sdtpldt0(X1,X2),sdtasdt0(X3,X4)) = sdtpldt0(X1,sdtpldt0(X2,sdtasdt0(X3,X4)))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X4)
| ~ aElement0(X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,plain,
( sdtasdt0(smndt0(X1),sz10) = smndt0(X1)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_42,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_43,hypothesis,
( sdtpldt0(smndt0(xx),sdtpldt0(xx,X1)) = sdtpldt0(sz00,X1)
| ~ aElement0(smndt0(xx))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_34]),c_0_18])]) ).
cnf(c_0_44,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,hypothesis,
sdtpldt0(sdtasdt0(sz00,xx),xx) = xx,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_29]),c_0_37]),c_0_38]),c_0_26]) ).
cnf(c_0_46,hypothesis,
aElement0(sdtasdt0(sz00,xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_29]),c_0_18])]) ).
cnf(c_0_47,plain,
( sdtpldt0(sdtasdt0(X1,X2),sz00) = sdtasdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_48,hypothesis,
( sdtpldt0(sdtpldt0(X1,xx),sdtasdt0(X2,X3)) = sdtpldt0(X1,sdtpldt0(xx,sdtasdt0(X2,X3)))
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_49,hypothesis,
sdtasdt0(smndt0(xx),sz10) = smndt0(xx),
inference(spm,[status(thm)],[c_0_41,c_0_18]) ).
cnf(c_0_50,hypothesis,
sdtpldt0(xx,smndt0(xx)) = sz00,
inference(spm,[status(thm)],[c_0_42,c_0_18]) ).
cnf(c_0_51,hypothesis,
( sdtasdt0(smndt0(X1),xx) = sdtasdt0(xx,smndt0(X1))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_52,hypothesis,
( sdtpldt0(smndt0(xx),sdtpldt0(xx,X1)) = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_33]),c_0_18])]) ).
cnf(c_0_53,hypothesis,
sdtpldt0(xx,sdtasdt0(sz00,xx)) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_18]),c_0_46])]) ).
cnf(c_0_54,hypothesis,
sdtpldt0(sz00,sdtasdt0(sz00,xx)) = sdtasdt0(sz00,xx),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_55,hypothesis,
( sdtpldt0(sdtasdt0(X1,xx),sz00) = sdtasdt0(X1,xx)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_18]) ).
fof(c_0_56,negated_conjecture,
sdtasdt0(smndt0(sz10),xx) != smndt0(xx),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_57,hypothesis,
( sdtpldt0(sdtpldt0(X1,xx),smndt0(xx)) = sdtpldt0(X1,sz00)
| ~ aElement0(smndt0(xx))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_27])]) ).
cnf(c_0_58,hypothesis,
sdtasdt0(smndt0(sz10),xx) = sdtasdt0(xx,smndt0(sz10)),
inference(spm,[status(thm)],[c_0_51,c_0_27]) ).
cnf(c_0_59,hypothesis,
( sdtpldt0(sdtasdt0(xx,smndt0(X1)),xx) = sdtasdt0(xx,sdtpldt0(smndt0(X1),sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_60,plain,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_61,hypothesis,
sdtasdt0(sz00,xx) = sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_46]),c_0_53]),c_0_34]),c_0_54]) ).
cnf(c_0_62,plain,
( sdtpldt0(sz00,smndt0(X1)) = smndt0(X1)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_63,hypothesis,
( sdtpldt0(sdtasdt0(smndt0(X1),xx),sz00) = sdtasdt0(smndt0(X1),xx)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_33]) ).
cnf(c_0_64,negated_conjecture,
sdtasdt0(smndt0(sz10),xx) != smndt0(xx),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_65,hypothesis,
( sdtpldt0(sdtpldt0(X1,xx),smndt0(xx)) = sdtpldt0(X1,sz00)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_33]),c_0_18])]) ).
cnf(c_0_66,hypothesis,
( aElement0(sdtasdt0(xx,smndt0(sz10)))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_58]),c_0_18])]) ).
cnf(c_0_67,hypothesis,
sdtpldt0(sdtasdt0(xx,smndt0(sz10)),xx) = sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_27]),c_0_60]),c_0_37]),c_0_61]) ).
cnf(c_0_68,hypothesis,
sdtpldt0(sz00,smndt0(xx)) = smndt0(xx),
inference(spm,[status(thm)],[c_0_62,c_0_18]) ).
cnf(c_0_69,hypothesis,
sdtpldt0(sdtasdt0(xx,smndt0(sz10)),sz00) = sdtasdt0(xx,smndt0(sz10)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_27]),c_0_58]),c_0_58]) ).
cnf(c_0_70,negated_conjecture,
sdtasdt0(xx,smndt0(sz10)) != smndt0(xx),
inference(rw,[status(thm)],[c_0_64,c_0_58]) ).
cnf(c_0_71,hypothesis,
~ aElement0(smndt0(sz10)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]),c_0_69]),c_0_70]) ).
cnf(c_0_72,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_33]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : RNG082+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.06/0.28 % Computer : n012.cluster.edu
% 0.06/0.28 % Model : x86_64 x86_64
% 0.06/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.28 % Memory : 8042.1875MB
% 0.06/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.28 % CPULimit : 300
% 0.06/0.28 % WCLimit : 300
% 0.06/0.28 % DateTime : Tue May 5 01:50:16 EDT 2026
% 0.06/0.28 % CPUTime :
% 0.06/0.29 % start to proof: theBenchmark
% 89.28/50.05 % Version : CSE_E---1.7
% 89.28/50.05 % Problem : theBenchmark.p
% 89.28/50.05 % SZS status Theorem for theBenchmark.p
% 89.28/50.05 % SZS output start CNFRefutation
% See solution above
% 89.67/50.45 % Total time : 34.822s
%------------------------------------------------------------------------------