%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:09:03 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 21 unt; 0 def)
% Number of atoms : 47 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 20 ~; 12 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 5 sgn 27 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_003,axiom,
! [X,X2] : nil != cons(X,X2),
file('theBenchmark.p',axiom_003) ).
fof(axiom_007,axiom,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
file('theBenchmark.p',axiom_007) ).
fof(axiom_008,axiom,
! [Y] : drop(z,Y) = Y,
file('theBenchmark.p',axiom_008) ).
fof(goal_009,conjecture,
? [N,Xs,Ys] :
~ ( drop(N,Xs) = drop(N,Ys)
=> Xs = Ys ),
file('theBenchmark.p',goal_009) ).
fof(f_3_1,plain,
! [X,X2] : nil != cons(X,X2),
inference(fof_nnf,[status(thm)],[axiom_003]) ).
fof(f_3_2,plain,
! [U_5,U_4] : nil != cons(U_5,U_4),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
nil != cons(U_5,U_4),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_7_1,plain,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
inference(fof_nnf,[status(thm)],[axiom_007]) ).
fof(f_7_2,plain,
! [U_11,U_10,U_9] : drop(s(U_11),cons(U_10,U_9)) = drop(U_11,U_9),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
drop(s(U_11),cons(U_10,U_9)) = drop(U_11,U_9),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [Y] : drop(z,Y) = Y,
inference(fof_nnf,[status(thm)],[axiom_008]) ).
fof(f_8_2,plain,
! [U_12] : drop(z,U_12) = U_12,
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
drop(z,U_12) = U_12,
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,negated_conjecture,
~ ? [N,Xs,Ys] :
~ ( drop(N,Xs) = drop(N,Ys)
=> Xs = Ys ),
inference(negate,[status(cth)],[goal_009]) ).
fof(f_9_2,negated_conjecture,
! [N,Xs,Ys] :
( Xs = Ys
| drop(N,Xs) != drop(N,Ys) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
! [U_15,U_14,U_13] :
( U_14 = U_13
| drop(U_15,U_14) != drop(U_15,U_13) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
! [U_13,U_14,U_15] :
( U_14 = U_13
| drop(U_15,U_14) != drop(U_15,U_13) ),
inference(definitional_conversion,[status(esa)],[f_9_3]) ).
cnf(f_9_5,negated_conjecture,
( U_14 = U_13
| drop(U_15,U_14) != drop(U_15,U_13) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(t1,plain,
nil != cons(U_224,drop(s(z),nil)),
inference(start,[status(thm),parent(0:0)],[f_3_3]) ).
cnf(t2,plain,
( drop(s(z),nil) != drop(s(z),cons(U_224,drop(s(z),nil)))
| nil = cons(U_224,drop(s(z),nil)) ),
inference(extension,[status(thm),parent(t1:1)],[f_9_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( drop(z,drop(s(z),nil)) != drop(z,drop(s(z),cons(U_224,drop(s(z),nil))))
| drop(s(z),nil) = drop(s(z),cons(U_224,drop(s(z),nil))) ),
inference(extension,[status(thm),parent(t2:2)],[f_9_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( drop(z,drop(s(z),cons(U_224,drop(s(z),nil)))) != drop(z,drop(s(z),nil))
| drop(z,drop(s(z),nil)) = drop(z,drop(s(z),cons(U_224,drop(s(z),nil)))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( drop(s(z),cons(U_224,drop(s(z),nil))) != drop(z,drop(s(z),nil))
| drop(z,drop(s(z),cons(U_224,drop(s(z),nil)))) != drop(s(z),cons(U_224,drop(s(z),nil)))
| drop(z,drop(s(z),cons(U_224,drop(s(z),nil)))) = drop(z,drop(s(z),nil)) ),
inference(extension,[status(thm),parent(t6:2)],[equality_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
drop(z,drop(s(z),cons(U_224,drop(s(z),nil)))) = drop(s(z),cons(U_224,drop(s(z),nil))),
inference(extension,[status(thm),parent(t8:2)],[f_8_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
drop(s(z),cons(U_224,drop(s(z),nil))) = drop(z,drop(s(z),nil)),
inference(extension,[status(thm),parent(t8:3)],[f_7_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_PEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 06:12:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------