%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN066+2 : TPTP v9.2.1. Released v7.3.0.
% 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 : n005.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 05:00:49 PM UTC 2026
% Result : Theorem 1.60s 1.83s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 7 unt; 0 def)
% Number of atoms : 136 ( 56 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 158 ( 66 ~; 69 |; 23 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 79 ( 3 sgn 39 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_3a,axiom,
! [X26,X27] :
( ! [X28] :
( ! [X29] :
( ~ r2(X26,X29)
| X29 != X28 )
| ~ r2(X27,X28) )
| X26 = X27 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(axiom_7a,axiom,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(nonzerononetwoexist,conjecture,
? [X39] :
( ! [X22] :
( ! [X23] :
( ! [X16] :
( ~ r1(X16)
| ~ r2(X16,X23) )
| ~ r2(X23,X22) )
| X39 != X22 )
& ! [X17] :
( ~ r1(X17)
| X39 != X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerononetwoexist) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(c_0_5,plain,
! [X26,X27] :
( ! [X28] :
( ! [X29] :
( ~ r2(X26,X29)
| X29 != X28 )
| ~ r2(X27,X28) )
| X26 = X27 ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
fof(c_0_6,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_7,plain,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_8,plain,
! [X117,X118,X119,X120] :
( ~ r2(X117,X120)
| X120 != X119
| ~ r2(X118,X119)
| X117 = X118 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
fof(c_0_9,plain,
! [X94,X96] :
( ( r2(X94,X96)
| ~ r2(X94,X96) )
& ( X96 = esk2_1(X94)
| ~ r2(X94,X96) )
& ( r2(X94,X96)
| X96 != esk2_1(X94) )
& ( X96 = esk2_1(X94)
| X96 != esk2_1(X94) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,negated_conjecture,
~ ? [X39] :
( ! [X22] :
( ! [X23] :
( ! [X16] :
( ~ r1(X16)
| ~ r2(X16,X23) )
| ~ r2(X23,X22) )
| X39 != X22 )
& ! [X17] :
( ~ r1(X17)
| X39 != X17 ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[nonzerononetwoexist])]) ).
fof(c_0_11,plain,
! [X132,X133,X134] :
( ~ r1(X134)
| X134 != X133
| ~ r2(X132,X133) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,plain,
( X1 = X4
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,negated_conjecture,
! [X135] :
( ( r1(esk24_1(X135))
| r1(esk23_1(X135)) )
& ( X135 = esk24_1(X135)
| r1(esk23_1(X135)) )
& ( r1(esk24_1(X135))
| r2(esk23_1(X135),esk22_1(X135)) )
& ( X135 = esk24_1(X135)
| r2(esk23_1(X135),esk22_1(X135)) )
& ( r1(esk24_1(X135))
| r2(esk22_1(X135),esk21_1(X135)) )
& ( X135 = esk24_1(X135)
| r2(esk22_1(X135),esk21_1(X135)) )
& ( r1(esk24_1(X135))
| X135 = esk21_1(X135) )
& ( X135 = esk24_1(X135)
| X135 = esk21_1(X135) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
cnf(c_0_15,plain,
( ~ r1(X1)
| X1 != X2
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X1 = X2
| ~ r2(X2,X3)
| ~ r2(X1,X3) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( r1(esk24_1(X1))
| r2(esk22_1(X1),esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( r1(esk24_1(X1))
| X1 = esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
cnf(c_0_21,plain,
( ~ r2(X1,X2)
| ~ r1(X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( r1(esk24_1(X1))
| r2(esk23_1(X1),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ r2(X1,esk2_1(X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( r2(esk22_1(X1),X1)
| r1(esk24_1(X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_25,plain,
! [X93] :
( ( r1(X93)
| ~ r1(X93) )
& ( X93 = esk1_0
| ~ r1(X93) )
& ( r1(X93)
| X93 != esk1_0 )
& ( X93 = esk1_0
| X93 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_20])])]) ).
cnf(c_0_26,negated_conjecture,
( X1 = esk24_1(X1)
| r2(esk22_1(X1),esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
( X1 = esk24_1(X1)
| X1 = esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,negated_conjecture,
( r1(esk24_1(X1))
| ~ r1(esk22_1(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( esk22_1(esk2_1(X1)) = X1
| r1(esk24_1(esk2_1(X1))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( X1 = esk24_1(X1)
| r2(esk23_1(X1),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,negated_conjecture,
( esk24_1(X1) = X1
| r2(esk22_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( r1(esk24_1(esk2_1(X1)))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( esk24_1(X1) = X1
| ~ r1(esk22_1(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( esk24_1(esk2_1(X1)) = esk2_1(X1)
| esk22_1(esk2_1(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_37,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,negated_conjecture,
r1(esk24_1(esk2_1(esk1_0))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( esk24_1(esk2_1(X1)) = esk2_1(X1)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
esk24_1(esk2_1(esk1_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
~ r1(esk2_1(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_42,negated_conjecture,
esk2_1(esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_34]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN066+2 : TPTP v9.2.1. Released v7.3.0.
% 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 : n005.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 01:22:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.60/1.83 % Version : CSE_E---1.7
% 1.60/1.83 % Problem : theBenchmark.p
% 1.60/1.83 % SZS status Theorem for theBenchmark.p
% 1.60/1.83 % SZS output start CNFRefutation
% See solution above
% 1.60/1.83 % Total time : 1.371s
%------------------------------------------------------------------------------