%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM531+2 : 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 04:57:43 PM UTC 2026
% Result : Theorem 0.12s 1.52s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 13)
% Comments :
%------------------------------------------------------------------------------
fof(mCountNFin,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(m__,conjecture,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ ( ~ ? [X2] : aElementOf0(X2,X1)
& X1 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
fof(i_0_5,plain,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(i_0_6,negated_conjecture,
~ ! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ ( ~ ? [X2] : aElementOf0(X2,X1)
& X1 = slcrc0 ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(i_0_7,plain,
! [X14,X15] :
( ~ aSet0(X14)
| ~ aElementOf0(X15,X14)
| aElement0(X15) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(i_0_8,plain,
! [X16,X17,X18] :
( ( aSet0(X16)
| X16 != slcrc0 )
& ( ~ aElementOf0(X17,X16)
| X16 != slcrc0 )
& ( ~ aSet0(X18)
| aElementOf0(esk1_1(X18),X18)
| X18 = slcrc0 ) ),
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)],[mDefEmp])])])])])]) ).
fof(i_0_9,plain,
! [X20] :
( ~ aSet0(X20)
| ~ isCountable0(X20)
| ~ isFinite0(X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5])]) ).
fof(i_0_10,negated_conjecture,
! [X22] :
( aSet0(esk2_0)
& isCountable0(esk2_0)
& ~ aElementOf0(X22,esk2_0)
& esk2_0 = slcrc0 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6])])])]) ).
cnf(i_0_11,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_12,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_13,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_14,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| ~ isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_15,negated_conjecture,
~ aElementOf0(X1,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_16,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_17,negated_conjecture,
isCountable0(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_18,plain,
isFinite0(slcrc0),
inference(split_conjunct,[status(thm)],[mEmpFin]),
[final] ).
cnf(i_0_19,negated_conjecture,
aSet0(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_20,negated_conjecture,
esk2_0 = slcrc0,
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_21,axiom,
X1 = X1 ).
cnf(i_0_22,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_23,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_24,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_25,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_26,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_27,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_28,axiom,
( X1 != X2
| ~ isCountable0(X1)
| isCountable0(X2) ) ).
cnf(i_0_29,axiom,
( X1 != X2
| ~ isFinite0(X1)
| isFinite0(X2) ) ).
cnf(i_0_21_001,axiom,
X1 = X1 ).
cnf(i_0_22_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_23_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_24_004,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_25_005,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_26_006,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_27_007,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_28_008,axiom,
( X1 != X2
| ~ isCountable0(X1)
| isCountable0(X2) ) ).
cnf(i_0_29_009,axiom,
( X1 != X2
| ~ isFinite0(X1)
| isFinite0(X2) ) ).
cnf(i_0_30,plain,
~ aElementOf0(X1,slcrc0),
inference(equality_inference,[],[13]) ).
cnf(i_0_31,plain,
aSet0(slcrc0),
inference(equality_inference,[],[16]) ).
cnf(i_0_32,plain,
slcrc0 = esk2_0,
inference(scs_inference,[],[i_0_20,i_0_22]) ).
cnf(i_0_33,plain,
~ isFinite0(esk2_0),
inference(scs_inference,[],[i_0_17,i_0_19,i_0_20,i_0_22,i_0_14]) ).
cnf(i_0_34,plain,
( ~ isCountable0(X1)
| ~ isFinite0(X1)
| ~ aSet0(X1) ),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_35,plain,
isCountable0(slcrc0),
inference(scs_inference,[],[i_0_17,i_0_19,i_0_20,i_0_22,i_0_14,i_0_28]) ).
cnf(i_0_36,plain,
$false,
inference(scs_inference,[],[i_0_17,i_0_19,i_0_20,i_0_18,i_0_22,i_0_14,i_0_28,i_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM531+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 5 00:43:00 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 0.12/1.52 % Version : CSE_E---1.7
% 0.12/1.52 % Problem : theBenchmark.p
% 0.12/1.52 % SZS status Theorem for theBenchmark.p
% 0.12/1.52 % SZS output start CNFRefutation
% See solution above
% 0.12/1.53 % Total time : 1.263s
%------------------------------------------------------------------------------