%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX199+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 05:34:42 PM UTC 2026
% Result : Theorem 1.48s 1.79s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 31 unt; 0 def)
% Number of atoms : 117 ( 64 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 99 ( 48 ~; 42 |; 1 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 144 ( 10 sgn 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_013,conjecture,
? [X6,X8,X9] :
~ ( merge(X6,X8) = merge(X8,X6)
=> ( merge(X6,X9) = merge(X9,X6)
=> merge(X8,X9) = merge(X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_013) ).
fof(axiom_010,axiom,
! [X4,X6] : merge(cons(X4,X6),nil) = cons(X4,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(axiom_009,axiom,
! [X3] : merge(nil,X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(axiom_012,axiom,
! [X4,X6,X7,X8] :
( ~ leqNat(X4,X7)
=> merge(cons(X4,X6),cons(X7,X8)) = cons(X7,merge(cons(X4,X6),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(axiom_011,axiom,
! [X4,X6,X7,X8] :
( leqNat(X4,X7)
=> merge(cons(X4,X6),cons(X7,X8)) = cons(X4,merge(X6,cons(X7,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
fof(axiom_006,axiom,
! [X3] : leqNat(z,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
fof(axiom_001,axiom,
! [X1,X2] : head(cons(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(axiom_002,axiom,
! [X1,X2] : tail(cons(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
fof(axiom_008,axiom,
! [X4,X5] :
( leqNat(s(X4),s(X5))
<=> leqNat(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_007,axiom,
! [X4] : ~ leqNat(s(X4),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(axiom_005,axiom,
! [X1] : z != s(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(c_0_11,negated_conjecture,
~ ? [X6,X8,X9] :
~ ( merge(X6,X8) = merge(X8,X6)
=> ( merge(X6,X9) = merge(X9,X6)
=> merge(X8,X9) = merge(X9,X8) ) ),
inference(assume_negation,[status(cth)],[goal_013]) ).
fof(c_0_12,negated_conjecture,
! [X59,X60,X61] :
( merge(X59,X60) != merge(X60,X59)
| merge(X59,X61) != merge(X61,X59)
| merge(X60,X61) = merge(X61,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_13,plain,
! [X49,X50] : merge(cons(X49,X50),nil) = cons(X49,X50),
inference(variable_rename,[status(thm)],[axiom_010]) ).
fof(c_0_14,plain,
! [X48] : merge(nil,X48) = X48,
inference(variable_rename,[status(thm)],[axiom_009]) ).
fof(c_0_15,plain,
! [X4,X6,X7,X8] :
( ~ leqNat(X4,X7)
=> merge(cons(X4,X6),cons(X7,X8)) = cons(X7,merge(cons(X4,X6),X8)) ),
inference(fof_simplification,[status(thm)],[axiom_012]) ).
fof(c_0_16,plain,
! [X51,X52,X53,X54] :
( ~ leqNat(X51,X53)
| merge(cons(X51,X52),cons(X53,X54)) = cons(X51,merge(X52,cons(X53,X54))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_011])]) ).
cnf(c_0_17,negated_conjecture,
( merge(X2,X3) = merge(X3,X2)
| merge(X1,X2) != merge(X2,X1)
| merge(X1,X3) != merge(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
merge(cons(X1,X2),nil) = cons(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
merge(nil,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X55,X56,X57,X58] :
( leqNat(X55,X57)
| merge(cons(X55,X56),cons(X57,X58)) = cons(X57,merge(cons(X55,X56),X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_21,plain,
( merge(cons(X1,X3),cons(X2,X4)) = cons(X1,merge(X3,cons(X2,X4)))
| ~ leqNat(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( merge(X1,cons(X2,X3)) = merge(cons(X2,X3),X1)
| merge(X1,nil) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_19])]) ).
cnf(c_0_23,plain,
( leqNat(X1,X2)
| merge(cons(X1,X3),cons(X2,X4)) = cons(X2,merge(cons(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( merge(cons(X1,X2),cons(X3,X4)) = cons(X3,merge(X4,cons(X1,X2)))
| ~ leqNat(X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18])]) ).
fof(c_0_25,plain,
! [X44] : leqNat(z,X44),
inference(variable_rename,[status(thm)],[axiom_006]) ).
fof(c_0_26,plain,
! [X36,X37] : head(cons(X36,X37)) = X36,
inference(variable_rename,[status(thm)],[axiom_001]) ).
fof(c_0_27,plain,
! [X38,X39] : tail(cons(X38,X39)) = X39,
inference(variable_rename,[status(thm)],[axiom_002]) ).
cnf(c_0_28,negated_conjecture,
( cons(X1,merge(X2,cons(X3,X4))) = cons(X1,merge(cons(X3,X4),X2))
| leqNat(X3,X1)
| ~ leqNat(X1,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
leqNat(z,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
head(cons(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( cons(X1,merge(X2,cons(X3,X4))) = cons(X3,merge(X4,cons(X1,X2)))
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
fof(c_0_32,plain,
! [X46,X47] :
( ( ~ leqNat(s(X46),s(X47))
| leqNat(X46,X47) )
& ( ~ leqNat(X46,X47)
| leqNat(s(X46),s(X47)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_008])]) ).
fof(c_0_33,plain,
! [X4] : ~ leqNat(s(X4),z),
inference(fof_simplification,[status(thm)],[axiom_007]) ).
cnf(c_0_34,plain,
tail(cons(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( cons(z,merge(X1,cons(X2,X3))) = cons(z,merge(cons(X2,X3),X1))
| leqNat(X2,z) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( X1 = X2
| ~ leqNat(X2,X1)
| ~ leqNat(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_30]) ).
cnf(c_0_37,plain,
( leqNat(s(X1),s(X2))
| ~ leqNat(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_38,plain,
! [X45] : ~ leqNat(s(X45),z),
inference(variable_rename,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( merge(X1,nil) = X1
| merge(cons(X2,X3),X1) != merge(X1,cons(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_19])]) ).
cnf(c_0_40,negated_conjecture,
( merge(X1,cons(X2,X3)) = merge(cons(X2,X3),X1)
| leqNat(X2,z) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( s(X1) = s(X2)
| ~ leqNat(s(X1),s(X2))
| ~ leqNat(X2,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
~ leqNat(s(X1),z),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( merge(X1,nil) = X1
| leqNat(X2,z) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( s(X1) = s(X2)
| ~ leqNat(X2,X1)
| ~ leqNat(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( merge(X1,X2) = merge(X2,X1)
| merge(X2,nil) != X2
| merge(X1,nil) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_19]) ).
cnf(c_0_46,negated_conjecture,
merge(X1,nil) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( s(X1) = s(z)
| ~ leqNat(X1,z) ),
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_48,negated_conjecture,
merge(X1,X2) = merge(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_46])]) ).
cnf(c_0_49,negated_conjecture,
( leqNat(s(X1),s(X2))
| ~ leqNat(X1,z) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_47]),c_0_29])]) ).
cnf(c_0_50,negated_conjecture,
( cons(X1,merge(X2,cons(X3,nil))) = cons(X3,cons(X1,X2))
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_51,negated_conjecture,
( cons(X1,merge(X2,cons(X3,X4))) = cons(X3,merge(cons(X1,X2),X4))
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( leqNat(s(z),s(X1))
| ~ leqNat(X2,z) ),
inference(spm,[status(thm)],[c_0_49,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( cons(X1,X2) = merge(X2,cons(X3,nil))
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_50]),c_0_34]) ).
cnf(c_0_54,negated_conjecture,
( merge(X1,cons(X2,X3)) = merge(cons(X4,X1),X3)
| ~ leqNat(X2,X4)
| ~ leqNat(X4,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_51]),c_0_34]) ).
cnf(c_0_55,negated_conjecture,
leqNat(s(z),s(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_29]) ).
cnf(c_0_56,negated_conjecture,
( cons(X1,X2) = merge(X2,cons(z,nil))
| ~ leqNat(X1,z) ),
inference(spm,[status(thm)],[c_0_53,c_0_29]) ).
cnf(c_0_57,negated_conjecture,
( merge(cons(s(X1),X2),X3) = merge(X2,cons(s(z),X3))
| ~ leqNat(s(X1),s(z)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
merge(X1,cons(z,nil)) = cons(z,X1),
inference(spm,[status(thm)],[c_0_56,c_0_29]) ).
cnf(c_0_59,negated_conjecture,
merge(cons(s(z),X1),X2) = merge(X1,cons(s(z),X2)),
inference(spm,[status(thm)],[c_0_57,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
merge(cons(z,nil),X1) = cons(z,X1),
inference(spm,[status(thm)],[c_0_48,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
merge(X1,cons(s(z),nil)) = cons(s(z),X1),
inference(spm,[status(thm)],[c_0_46,c_0_59]) ).
fof(c_0_62,plain,
! [X43] : z != s(X43),
inference(variable_rename,[status(thm)],[axiom_005]) ).
cnf(c_0_63,negated_conjecture,
cons(s(z),cons(z,nil)) = cons(z,cons(s(z),nil)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_64,plain,
z != s(X1),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_63]),c_0_30]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX199+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n018.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 07:55:47 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.48/1.79 % Version : CSE_E---1.7
% 1.48/1.79 % Problem : theBenchmark.p
% 1.48/1.79 % SZS status Theorem for theBenchmark.p
% 1.48/1.79 % SZS output start CNFRefutation
% See solution above
% 1.48/1.80 % Total time : 1.371s
%------------------------------------------------------------------------------