%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX187+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 : 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 05:34:39 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 38 unt; 0 def)
% Number of atoms : 95 ( 67 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 77 ( 34 ~; 31 |; 1 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 123 ( 6 sgn 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_017,conjecture,
? [X8,X9,X10,X4] :
~ ( x2(X8,length(X4))
=> ( x2(X9,length(X10))
=> ( X4 = X10
=> ( rotate(s(z),X4) != X4
=> ( rotate(X8,X4) = rotate(X9,X10)
=> X8 = X9 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_017) ).
fof(axiom_016,axiom,
! [X3] : rotate(z,X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
fof(axiom_015,axiom,
! [X5,X2,X7] : rotate(s(X5),cons(X2,X7)) = rotate(X5,x(X7,cons(X2,nil))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(axiom_013,axiom,
! [X3,X5,X4] : x(cons(X5,X4),X3) = cons(X5,x(X4,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(axiom_007,axiom,
! [X3,X4] : length(cons(X3,X4)) = s(length(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(axiom_010,axiom,
! [X2] : x2(z,s(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(axiom_012,axiom,
! [X3] : x(nil,X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(axiom_008,axiom,
! [X5,X6] :
( x2(s(X5),s(X6))
<=> x2(X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_005,axiom,
! [X1] : s(X1) != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(axiom_006,axiom,
length(nil) = z,
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(c_0_11,negated_conjecture,
~ ? [X8,X9,X10,X4] :
~ ( x2(X8,length(X4))
=> ( x2(X9,length(X10))
=> ( X4 = X10
=> ( rotate(s(z),X4) != X4
=> ( rotate(X8,X4) = rotate(X9,X10)
=> X8 = X9 ) ) ) ) ),
inference(assume_negation,[status(cth)],[goal_017]) ).
fof(c_0_12,plain,
! [X60] : rotate(z,X60) = X60,
inference(variable_rename,[status(thm)],[axiom_016]) ).
fof(c_0_13,plain,
! [X57,X58,X59] : rotate(s(X57),cons(X58,X59)) = rotate(X57,x(X59,cons(X58,nil))),
inference(variable_rename,[status(thm)],[axiom_015]) ).
fof(c_0_14,negated_conjecture,
! [X61,X62,X63,X64] :
( ~ x2(X61,length(X64))
| ~ x2(X62,length(X63))
| X64 != X63
| rotate(s(z),X64) = X64
| rotate(X61,X64) != rotate(X62,X63)
| X61 = X62 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_15,plain,
rotate(z,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
rotate(s(X1),cons(X2,X3)) = rotate(X1,x(X3,cons(X2,nil))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X53,X54,X55] : x(cons(X54,X55),X53) = cons(X54,x(X55,X53)),
inference(variable_rename,[status(thm)],[axiom_013]) ).
cnf(c_0_18,negated_conjecture,
( rotate(s(z),X2) = X2
| X1 = X3
| ~ x2(X1,length(X2))
| ~ x2(X3,length(X4))
| X2 != X4
| rotate(X1,X2) != rotate(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X46,X47] : length(cons(X46,X47)) = s(length(X47)),
inference(variable_rename,[status(thm)],[axiom_007]) ).
cnf(c_0_20,plain,
x(X1,cons(X2,nil)) = rotate(s(z),cons(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
x(cons(X1,X2),X3) = cons(X1,x(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( rotate(s(z),X1) = X1
| X2 = X3
| rotate(X2,X1) != rotate(X3,X1)
| ~ x2(X3,length(X1))
| ~ x2(X2,length(X1)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
length(cons(X1,X2)) = s(length(X2)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X51] : x2(z,s(X51)),
inference(variable_rename,[status(thm)],[axiom_010]) ).
cnf(c_0_25,plain,
rotate(X1,rotate(s(z),cons(X2,X3))) = rotate(s(X1),cons(X2,X3)),
inference(rw,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_26,plain,
rotate(s(z),cons(X1,cons(X2,X3))) = cons(X2,rotate(s(z),cons(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_20]) ).
fof(c_0_27,plain,
! [X52] : x(nil,X52) = X52,
inference(variable_rename,[status(thm)],[axiom_012]) ).
cnf(c_0_28,negated_conjecture,
( rotate(s(z),cons(X1,X2)) = cons(X1,X2)
| X3 = X4
| rotate(X3,cons(X1,X2)) != rotate(X4,cons(X1,X2))
| ~ x2(X4,s(length(X2)))
| ~ x2(X3,s(length(X2))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
x2(z,s(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X48,X49] :
( ( ~ x2(s(X48),s(X49))
| x2(X48,X49) )
& ( ~ x2(X48,X49)
| x2(s(X48),s(X49)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_008])]) ).
fof(c_0_31,plain,
! [X45] : s(X45) != z,
inference(variable_rename,[status(thm)],[axiom_005]) ).
cnf(c_0_32,plain,
rotate(X1,cons(X2,rotate(s(z),cons(X3,X4)))) = rotate(s(X1),cons(X3,cons(X2,X4))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
x(nil,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( rotate(s(z),cons(X1,X2)) = cons(X1,X2)
| X3 = z
| rotate(X3,cons(X1,X2)) != cons(X1,X2)
| ~ x2(X3,s(length(X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_15]) ).
cnf(c_0_35,plain,
( x2(s(X1),s(X2))
| ~ x2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
s(X1) != z,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
rotate(X1,cons(X2,cons(X3,rotate(s(z),cons(X4,X5))))) = rotate(s(X1),cons(X4,cons(X2,cons(X3,X5)))),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_38,plain,
rotate(s(X1),cons(X2,nil)) = rotate(X1,cons(X2,nil)),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( rotate(s(z),cons(X1,X2)) = cons(X1,X2)
| rotate(s(X3),cons(X1,X2)) != cons(X1,X2)
| ~ x2(X3,length(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_40,plain,
rotate(s(s(z)),cons(X1,cons(X2,cons(X3,X4)))) = cons(X3,rotate(s(s(z)),cons(X1,cons(X2,X4)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_32]) ).
cnf(c_0_41,plain,
rotate(s(X1),cons(X2,cons(X3,nil))) = rotate(X1,cons(X3,cons(X2,nil))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_38]),c_0_15]) ).
cnf(c_0_42,negated_conjecture,
( cons(X1,cons(X2,rotate(s(z),cons(X3,X4)))) = cons(X3,cons(X1,cons(X2,X4)))
| cons(X2,rotate(s(s(z)),cons(X3,cons(X1,X4)))) != cons(X3,cons(X1,cons(X2,X4)))
| ~ x2(s(z),s(s(length(X4)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_26]),c_0_26]),c_0_23]),c_0_23]) ).
cnf(c_0_43,plain,
rotate(s(X1),cons(X2,cons(X3,cons(X4,nil)))) = rotate(X1,cons(X3,cons(X4,cons(X2,nil)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_15]) ).
cnf(c_0_44,plain,
length(nil) = z,
inference(split_conjunct,[status(thm)],[axiom_006]) ).
cnf(c_0_45,negated_conjecture,
( cons(X1,cons(X2,cons(X3,cons(X4,nil)))) = cons(X4,cons(X1,cons(X2,cons(X3,nil))))
| cons(X2,cons(X3,cons(X4,cons(X1,nil)))) != cons(X4,cons(X1,cons(X2,cons(X3,nil))))
| ~ x2(s(z),s(s(s(z)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_26]),c_0_38]),c_0_15]),c_0_26]),c_0_26]),c_0_38]),c_0_15]),c_0_23]),c_0_44]) ).
fof(c_0_46,plain,
! [X38,X39] : head(cons(X38,X39)) = X38,
inference(variable_rename,[status(thm)],[axiom_001]) ).
cnf(c_0_47,negated_conjecture,
( cons(X1,cons(X2,cons(X3,cons(X4,nil)))) = cons(X4,cons(X1,cons(X2,cons(X3,nil))))
| cons(X2,cons(X3,cons(X4,cons(X1,nil)))) != cons(X4,cons(X1,cons(X2,cons(X3,nil)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_29])]) ).
cnf(c_0_48,plain,
head(cons(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_49,negated_conjecture,
cons(X1,cons(X2,cons(X1,cons(X2,nil)))) = cons(X2,cons(X1,cons(X2,cons(X1,nil)))),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
X1 = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_48]) ).
cnf(c_0_51,plain,
$false,
inference(sr,[status(thm)],[c_0_36,c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX187+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 07:54:15 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------