%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM835+2 : TPTP v9.2.1. Released v4.1.0.
% 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 : n007.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 04:58:39 PM UTC 2026
% Result : Theorem 0.27s 1.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_33)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(conseq(110), 2), 1)',axiom,
! [X1] :
( vd165 = vplus(vd151,X1)
=> vsucc(vplus(vd151,X1)) = vplus(vd151,vsucc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 1)') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X15,X16] :
( vplus(X15,vsucc(X16)) = vsucc(vplus(X15,X16))
& vplus(X15,v1) = vsucc(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof('ass(cond(52, 0), 0)',axiom,
! [X9,X10] : vplus(vsucc(X9),X10) = vsucc(vplus(X9,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof('ass(cond(conseq(110), 1), 6)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 = v1
=> m(vsucc(vd165)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 6)') ).
fof('ass(cond(conseq(110), 1), 0)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> m(vsucc(vd165)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 0)') ).
fof('ass(cond(conseq(110), 2), 0)',axiom,
! [X1] :
( vd165 = vplus(vd151,X1)
=> m(vsucc(vd165)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 0)') ).
fof('ass(cond(conseq(110), 1), 4)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> vsucc(vskolem3) = vplus(v1,vskolem3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 4)') ).
fof('ass(cond(conseq(110), 1), 5)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> X2 = vsucc(vskolem3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 5)') ).
fof('ass(cond(conseq(110), 0), 0)',axiom,
( vd151 = vd165
=> m(vsucc(vd165)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 0)') ).
fof('ass(cond(43, 0), 0)',axiom,
! [X11] : vplus(v1,X11) = vsucc(X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof('ass(cond(12, 0), 0)',axiom,
! [X18] : vsucc(X18) != X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof('ass(cond(20, 0), 0)',axiom,
! [X17] :
( X17 != v1
=> X17 = vsucc(vskolem2(X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof('dis(case_distinction(conseq(110)))',conjecture,
( ? [X1] : vd165 = vplus(vd151,X1)
| ? [X2] : vd151 = vplus(vd165,X2)
| vd151 = vd165 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(case_distinction(conseq(110)))') ).
fof('def(cond(conseq(105), 0), 1)',axiom,
! [X3,X4] :
( m(X4)
<=> ( X3 = X4
| ? [X5] : X3 = vplus(X4,X5)
| ? [X6] : X4 = vplus(X3,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(105), 0), 1)') ).
fof('ass(cond(conseq(110), 1), 2)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> vplus(vd165,vplus(v1,vskolem3)) = vplus(vplus(vd165,v1),vskolem3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 2)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X12,X13,X14] : vplus(vplus(X12,X13),X14) = vplus(X12,vplus(X13,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(conseq(110), 1), 3)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> vd151 = vplus(vd165,vplus(v1,vskolem3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 3)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X7,X8] : vplus(X8,X7) = vplus(X7,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(i_0_18,plain,
! [X52] :
( vd165 != vplus(vd151,X52)
| vsucc(vplus(vd151,X52)) = vplus(vd151,vsucc(X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 2), 1)'])]) ).
fof(i_0_19,plain,
! [X79,X80] :
( vplus(X79,vsucc(X80)) = vsucc(vplus(X79,X80))
& vplus(X79,v1) = vsucc(X79) ),
inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).
fof(i_0_20,plain,
! [X73,X74] : vplus(vsucc(X73),X74) = vsucc(vplus(X73,X74)),
inference(variable_rename,[status(thm)],['ass(cond(52, 0), 0)']) ).
fof(i_0_21,plain,
! [X60] :
( vd151 != vplus(vd165,X60)
| X60 != v1
| m(vsucc(vd165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 6)'])]) ).
fof(i_0_22,plain,
! [X54] :
( vd151 != vplus(vd165,X54)
| X54 = v1
| m(vsucc(vd165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 0)'])]) ).
fof(i_0_23,plain,
! [X51] :
( vd165 != vplus(vd151,X51)
| m(vsucc(vd165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 2), 0)'])]) ).
fof(i_0_24,plain,
! [X58] :
( vd151 != vplus(vd165,X58)
| X58 = v1
| vsucc(vskolem3) = vplus(v1,vskolem3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 4)'])]) ).
fof(i_0_25,plain,
! [X59] :
( vd151 != vplus(vd165,X59)
| X59 = v1
| X59 = vsucc(vskolem3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 5)'])]) ).
fof(i_0_26,plain,
( vd151 != vd165
| m(vsucc(vd165)) ),
inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 0), 0)']) ).
fof(i_0_27,plain,
! [X75] : vplus(v1,X75) = vsucc(X75),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
fof(i_0_28,plain,
! [X82] : vsucc(X82) != X82,
inference(variable_rename,[status(thm)],['ass(cond(12, 0), 0)']) ).
fof(i_0_29,plain,
! [X81] :
( X81 = v1
| X81 = vsucc(vskolem2(X81)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(20, 0), 0)'])]) ).
fof(i_0_30,negated_conjecture,
~ ( ? [X1] : vd165 = vplus(vd151,X1)
| ? [X2] : vd151 = vplus(vd165,X2)
| vd151 = vd165 ),
inference(assume_negation,[status(cth)],['dis(case_distinction(conseq(110)))']) ).
fof(i_0_31,plain,
! [X63,X64,X67,X68,X69,X70] :
( ( ~ m(X64)
| X63 = X64
| X63 = vplus(X64,esk1_2(X63,X64))
| X64 = vplus(X63,esk2_2(X63,X64)) )
& ( X67 != X68
| m(X68) )
& ( X67 != vplus(X68,X69)
| m(X68) )
& ( X68 != vplus(X67,X70)
| m(X68) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(105), 0), 1)'])])])])])]) ).
cnf(i_0_32,plain,
( vsucc(vplus(vd151,X1)) = vplus(vd151,vsucc(X1))
| vd165 != vplus(vd151,X1) ),
inference(split_conjunct,[status(thm)],[i_0_18]) ).
cnf(i_0_33,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[i_0_19]) ).
fof(i_0_34,plain,
! [X56] :
( vd151 != vplus(vd165,X56)
| X56 = v1
| vplus(vd165,vplus(v1,vskolem3)) = vplus(vplus(vd165,v1),vskolem3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 2)'])]) ).
fof(i_0_35,plain,
! [X76,X77,X78] : vplus(vplus(X76,X77),X78) = vplus(X76,vplus(X77,X78)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(i_0_36,plain,
vplus(vsucc(X1),X2) = vsucc(vplus(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_20]) ).
cnf(i_0_37,plain,
vplus(X1,vsucc(X2)) = vsucc(vplus(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_19]) ).
fof(i_0_38,plain,
! [X57] :
( vd151 != vplus(vd165,X57)
| X57 = v1
| vd151 = vplus(vd165,vplus(v1,vskolem3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 3)'])]) ).
cnf(i_0_39,plain,
( m(vsucc(vd165))
| vd151 != vplus(vd165,X1)
| X1 != v1 ),
inference(split_conjunct,[status(thm)],[i_0_21]) ).
cnf(i_0_40,plain,
( X1 = v1
| m(vsucc(vd165))
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]) ).
cnf(i_0_41,plain,
( m(vsucc(vd165))
| vd165 != vplus(vd151,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]) ).
cnf(i_0_42,plain,
( X1 = v1
| vsucc(vskolem3) = vplus(v1,vskolem3)
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]) ).
cnf(i_0_43,plain,
( X1 = v1
| X1 = vsucc(vskolem3)
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_25]) ).
fof(i_0_44,plain,
! [X71,X72] : vplus(X72,X71) = vplus(X71,X72),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(i_0_45,plain,
( m(vsucc(vd165))
| vd151 != vd165 ),
inference(split_conjunct,[status(thm)],[i_0_26]) ).
cnf(i_0_46,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[i_0_27]) ).
cnf(i_0_47,plain,
vsucc(X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_28]) ).
cnf(i_0_48,plain,
( X1 = v1
| X1 = vsucc(vskolem2(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_29]) ).
fof(i_0_49,negated_conjecture,
! [X49,X50] :
( vd165 != vplus(vd151,X49)
& vd151 != vplus(vd165,X50)
& vd151 != vd165 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_30])])]) ).
cnf(i_0_50,plain,
( X2 = X1
| X2 = vplus(X1,esk1_2(X2,X1))
| X1 = vplus(X2,esk2_2(X2,X1))
| ~ m(X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_51,plain,
( vplus(vplus(vd151,X1),v1) = vplus(vd151,vplus(X1,v1))
| vd165 != vplus(vd151,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_32,c_0_33]),c_0_33]),
[final] ).
cnf(i_0_52,plain,
( X1 = v1
| vplus(vd165,vplus(v1,vskolem3)) = vplus(vplus(vd165,v1),vskolem3)
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_53,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_54,plain,
vplus(vplus(X1,v1),X2) = vplus(vplus(X1,X2),v1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_36,c_0_33]),c_0_33]),
[final] ).
cnf(i_0_55,plain,
vplus(X1,vplus(X2,v1)) = vplus(vplus(X1,X2),v1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_37,c_0_33]),c_0_33]),
[final] ).
cnf(i_0_56,plain,
( X1 = v1
| vd151 = vplus(vd165,vplus(v1,vskolem3))
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_57,plain,
( m(vplus(vd165,v1))
| X1 != v1
| vd151 != vplus(vd165,X1) ),
inference(rw,[status(thm)],[i_0_39,c_0_33]),
[final] ).
cnf(i_0_58,plain,
( X1 = v1
| m(vplus(vd165,v1))
| vd151 != vplus(vd165,X1) ),
inference(rw,[status(thm)],[i_0_40,c_0_33]),
[final] ).
cnf(i_0_59,plain,
( m(vplus(vd165,v1))
| vd165 != vplus(vd151,X1) ),
inference(rw,[status(thm)],[i_0_41,c_0_33]),
[final] ).
cnf(i_0_60,plain,
( X1 = v1
| vplus(vskolem3,v1) = vplus(v1,vskolem3)
| vd151 != vplus(vd165,X1) ),
inference(rw,[status(thm)],[i_0_42,c_0_33]),
[final] ).
cnf(i_0_61,plain,
( X1 = v1
| X1 = vplus(vskolem3,v1)
| vd151 != vplus(vd165,X1) ),
inference(rw,[status(thm)],[i_0_43,c_0_33]),
[final] ).
cnf(i_0_62,plain,
( m(X1)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_63,plain,
( m(X2)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_64,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_65,plain,
( m(vplus(vd165,v1))
| vd151 != vd165 ),
inference(rw,[status(thm)],[i_0_45,c_0_33]),
[final] ).
cnf(i_0_66,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[i_0_46,c_0_33]),
[final] ).
cnf(i_0_67,plain,
vplus(X1,v1) != X1,
inference(rw,[status(thm)],[i_0_47,c_0_33]),
[final] ).
cnf(i_0_68,plain,
( X1 = v1
| X1 = vplus(vskolem2(X1),v1) ),
inference(rw,[status(thm)],[i_0_48,c_0_33]),
[final] ).
cnf(i_0_69,negated_conjecture,
vd151 != vplus(vd165,X1),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_70,negated_conjecture,
vd165 != vplus(vd151,X1),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_71,plain,
( m(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_72,negated_conjecture,
vd151 != vd165,
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_73,axiom,
X1 = X1 ).
cnf(i_0_74,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_75,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_76,axiom,
( X1 != X2
| vplus(X1,X3) = vplus(X2,X3) ) ).
cnf(i_0_77,axiom,
( X1 != X2
| vplus(X3,X1) = vplus(X3,X2) ) ).
cnf(i_0_78,axiom,
( X1 != X2
| ~ m(X1)
| m(X2) ) ).
cnf(i_0_73_001,axiom,
X1 = X1 ).
cnf(i_0_74_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_75_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_76_004,axiom,
( X1 != X2
| vplus(X1,X3) = vplus(X2,X3) ) ).
cnf(i_0_77_005,axiom,
( X1 != X2
| vplus(X3,X1) = vplus(X3,X2) ) ).
cnf(i_0_78_006,axiom,
( X1 != X2
| ~ m(X1)
| m(X2) ) ).
cnf(i_0_79,plain,
m(vplus(X1,X2)),
inference(equality_inference,[],[62]) ).
cnf(i_0_80,plain,
m(X1),
inference(equality_inference,[],[63]) ).
cnf(i_0_81,plain,
m(X1),
inference(equality_inference,[],[71]) ).
cnf(i_0_82,plain,
vplus(X1,vplus(X2,X3)) = vplus(vplus(X1,X2),X3),
inference(scs_inference,[],[i_0_53,i_0_74]) ).
cnf(i_0_83,plain,
vd151 != vplus(X1,vd165),
inference(scs_inference,[],[i_0_69,i_0_64,i_0_53,i_0_74,i_0_75]) ).
cnf(i_0_84,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_85,plain,
$false,
inference(scs_inference,[],[i_0_69,i_0_72,i_0_70,i_0_80,i_0_64,i_0_53,i_0_74,i_0_75,i_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM835+2 : TPTP v9.2.1. Released v4.1.0.
% 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
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:14:24 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.27/1.62 % Version : CSE_E---1.7
% 0.27/1.62 % Problem : theBenchmark.p
% 0.27/1.62 % SZS status Theorem for theBenchmark.p
% 0.27/1.62 % SZS output start CNFRefutation
% See solution above
% 0.27/1.65 % Total time : 1.274s
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