%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN081+1 : 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 : n014.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 05:00:52 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 50 ~; 40 |; 21 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-1 aty)
% Number of variables : 90 ( 8 sgn 32 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_6,axiom,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(axiom_7,axiom,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( id(X55,X54)
& ? [X56] :
( r1(X56)
& r3(X54,X56,X55) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(xplusyidthree,conjecture,
? [X63,X46,X47] :
( r3(X63,X46,X47)
& ? [X40] :
( id(X47,X40)
& ? [X41] :
( r2(X41,X40)
& ? [X49] :
( r2(X49,X41)
& ? [X43] :
( r1(X43)
& r2(X43,X49) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xplusyidthree) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(c_0_6,plain,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_7,plain,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(c_0_8,plain,
! [X156,X157] :
( ~ id(X156,X157)
| id(X157,X156) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X195] :
( id(esk13_1(X195),X195)
& r1(esk14_1(X195))
& r3(X195,esk14_1(X195),esk13_1(X195)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_10,plain,
! [X158,X159,X160] :
( ~ id(X158,X159)
| id(X158,X160)
| ~ id(X159,X160) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( id(X2,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,negated_conjecture,
~ ? [X63,X46,X47] :
( r3(X63,X46,X47)
& ? [X40] :
( id(X47,X40)
& ? [X41] :
( r2(X41,X40)
& ? [X49] :
( r2(X49,X41)
& ? [X43] :
( r1(X43)
& r2(X43,X49) ) ) ) ) ),
inference(assume_negation,[status(cth)],[xplusyidthree]) ).
cnf(c_0_14,plain,
( id(X1,X3)
| ~ id(X1,X2)
| ~ id(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
id(X1,esk13_1(X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,negated_conjecture,
! [X209,X210,X211,X212,X213,X214,X215] :
( ~ r3(X209,X210,X211)
| ~ id(X211,X212)
| ~ r2(X213,X212)
| ~ r2(X214,X213)
| ~ r1(X215)
| ~ r2(X215,X214) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_17,plain,
( id(X1,esk13_1(X2))
| ~ id(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_19,negated_conjecture,
( ~ r3(X1,X2,X3)
| ~ id(X3,X4)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
id(X1,esk13_1(esk13_1(X1))),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
fof(c_0_22,plain,
! [X144,X146] :
( ( ~ r2(X144,X146)
| id(X146,esk2_1(X144)) )
& ( ~ id(X146,esk2_1(X144))
| id(X146,esk2_1(X144)) )
& ( ~ r2(X144,X146)
| r2(X144,X146) )
& ( ~ id(X146,esk2_1(X144))
| r2(X144,X146) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_18])])]) ).
fof(c_0_23,plain,
! [X155] : id(X155,X155),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(c_0_24,negated_conjecture,
( ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r1(X1)
| ~ id(esk13_1(X5),X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
id(esk13_1(esk13_1(X1)),X1),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_26,plain,
( r2(X2,X1)
| ~ id(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( ~ r2(esk2_1(X1),X2)
| ~ r2(X2,X3)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( ~ r2(esk2_1(esk2_1(X1)),X2)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_32,plain,
r2(X1,esk13_1(esk2_1(X1))),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_33,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
$false,
inference(sr,[status(thm)],[c_0_33,c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN081+1 : 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 : n014.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 01:23:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------