%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 09:09:04 AM UTC 2026
% Result : Theorem 0.44s 0.77s
% Output : Proof 0.55s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
! [X,X2] : head(cons(X,X2)) = X,
file('theBenchmark.p',axiom_001) ).
fof(axiom_002,axiom,
! [X,X2] : tail(cons(X,X2)) = X2,
file('theBenchmark.p',axiom_002) ).
fof(axiom_003,axiom,
! [X,X2] : nil != cons(X,X2),
file('theBenchmark.p',axiom_003) ).
fof(axiom_004,axiom,
! [X] : proj1S(s(X)) = X,
file('theBenchmark.p',axiom_004) ).
fof(axiom_005,axiom,
! [X] : z != s(X),
file('theBenchmark.p',axiom_005) ).
fof(axiom_006,axiom,
! [Y] : leqNat(z,Y),
file('theBenchmark.p',axiom_006) ).
fof(axiom_007,axiom,
! [Z] : ~ leqNat(s(Z),z),
file('theBenchmark.p',axiom_007) ).
fof(axiom_008,axiom,
! [Z,M] :
( leqNat(s(Z),s(M))
<=> leqNat(Z,M) ),
file('theBenchmark.p',axiom_008) ).
fof(axiom_009,axiom,
! [Y] : merge(nil,Y) = Y,
file('theBenchmark.p',axiom_009) ).
fof(axiom_010,axiom,
! [Z,Xs] : merge(cons(Z,Xs),nil) = cons(Z,Xs),
file('theBenchmark.p',axiom_010) ).
fof(axiom_011,axiom,
! [Z,Xs,Y2,Ys] :
( leqNat(Z,Y2)
=> merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys))) ),
file('theBenchmark.p',axiom_011) ).
fof(axiom_012,axiom,
! [Z,Xs,Y2,Ys] :
( ~ leqNat(Z,Y2)
=> merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys)) ),
file('theBenchmark.p',axiom_012) ).
fof(axiom_013,axiom,
ord(nil),
file('theBenchmark.p',axiom_013) ).
fof(axiom_014,axiom,
! [Y] : ord(cons(Y,nil)),
file('theBenchmark.p',axiom_014) ).
fof(axiom_015,axiom,
! [Y,Y2,Xs] :
( ord(cons(Y,cons(Y2,Xs)))
<=> ( ord(cons(Y2,Xs))
& leqNat(Y,Y2) ) ),
file('theBenchmark.p',axiom_015) ).
fof(goal_016,conjecture,
? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
file('theBenchmark.p',goal_016) ).
fof(f_1_1,plain,
! [X,X2] : head(cons(X,X2)) = X,
inference(fof_nnf,[status(thm)],[axiom_001]) ).
fof(f_1_2,plain,
! [U_1,U_0] : head(cons(U_1,U_0)) = U_1,
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
head(cons(U_1,U_0)) = U_1,
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [X,X2] : tail(cons(X,X2)) = X2,
inference(fof_nnf,[status(thm)],[axiom_002]) ).
fof(f_2_2,plain,
! [U_3,U_2] : tail(cons(U_3,U_2)) = U_2,
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
tail(cons(U_3,U_2)) = U_2,
inference(clausify,[status(thm)],[f_2_2]) ).
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_4_1,plain,
! [X] : proj1S(s(X)) = X,
inference(fof_nnf,[status(thm)],[axiom_004]) ).
fof(f_4_2,plain,
! [U_6] : proj1S(s(U_6)) = U_6,
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
proj1S(s(U_6)) = U_6,
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [X] : z != s(X),
inference(fof_nnf,[status(thm)],[axiom_005]) ).
fof(f_5_2,plain,
! [U_7] : z != s(U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
z != s(U_7),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [Y] : leqNat(z,Y),
inference(fof_nnf,[status(thm)],[axiom_006]) ).
fof(f_6_2,plain,
! [U_8] : leqNat(z,U_8),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
leqNat(z,U_8),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [Z] : ~ leqNat(s(Z),z),
inference(fof_nnf,[status(thm)],[axiom_007]) ).
fof(f_7_2,plain,
! [U_9] : ~ leqNat(s(U_9),z),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
~ leqNat(s(U_9),z),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [Z,M] :
( ( leqNat(s(Z),s(M))
| ~ leqNat(Z,M) )
& ( leqNat(Z,M)
| ~ leqNat(s(Z),s(M)) ) ),
inference(fof_nnf,[status(thm)],[axiom_008]) ).
fof(f_8_2,plain,
! [U_11,U_10] :
( ( leqNat(s(U_11),s(U_10))
| ~ leqNat(U_11,U_10) )
& ( leqNat(U_11,U_10)
| ~ leqNat(s(U_11),s(U_10)) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_15,U_13] :
( leqNat(s(U_15),s(U_13))
| ~ leqNat(U_15,U_13) )
& ! [U_14,U_12] :
( leqNat(U_14,U_12)
| ~ leqNat(s(U_14),s(U_12)) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( leqNat(U_14,U_12)
| ~ leqNat(s(U_14),s(U_12)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( leqNat(s(U_15),s(U_13))
| ~ leqNat(U_15,U_13) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [Y] : merge(nil,Y) = Y,
inference(fof_nnf,[status(thm)],[axiom_009]) ).
fof(f_9_2,plain,
! [U_16] : merge(nil,U_16) = U_16,
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
merge(nil,U_16) = U_16,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [Z,Xs] : merge(cons(Z,Xs),nil) = cons(Z,Xs),
inference(fof_nnf,[status(thm)],[axiom_010]) ).
fof(f_10_2,plain,
! [U_18,U_17] : merge(cons(U_18,U_17),nil) = cons(U_18,U_17),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
merge(cons(U_18,U_17),nil) = cons(U_18,U_17),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [Z,Xs,Y2,Ys] :
( merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys)))
| ~ leqNat(Z,Y2) ),
inference(fof_nnf,[status(thm)],[axiom_011]) ).
fof(f_11_2,plain,
! [U_22,U_21,U_20,U_19] :
( merge(cons(U_22,U_21),cons(U_20,U_19)) = cons(U_22,merge(U_21,cons(U_20,U_19)))
| ~ leqNat(U_22,U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_22,U_21,U_20] :
( ! [U_19] : merge(cons(U_22,U_21),cons(U_20,U_19)) = cons(U_22,merge(U_21,cons(U_20,U_19)))
| ~ leqNat(U_22,U_20) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( merge(cons(U_22,U_21),cons(U_20,U_19)) = cons(U_22,merge(U_21,cons(U_20,U_19)))
| ~ leqNat(U_22,U_20) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [Z,Xs,Y2,Ys] :
( merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys))
| leqNat(Z,Y2) ),
inference(fof_nnf,[status(thm)],[axiom_012]) ).
fof(f_12_2,plain,
! [U_26,U_25,U_24,U_23] :
( merge(cons(U_26,U_25),cons(U_24,U_23)) = cons(U_24,merge(cons(U_26,U_25),U_23))
| leqNat(U_26,U_24) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_26,U_25,U_24] :
( ! [U_23] : merge(cons(U_26,U_25),cons(U_24,U_23)) = cons(U_24,merge(cons(U_26,U_25),U_23))
| leqNat(U_26,U_24) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( merge(cons(U_26,U_25),cons(U_24,U_23)) = cons(U_24,merge(cons(U_26,U_25),U_23))
| leqNat(U_26,U_24) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
ord(nil),
inference(fof_nnf,[status(thm)],[axiom_013]) ).
cnf(f_13_2,plain,
ord(nil),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [Y] : ord(cons(Y,nil)),
inference(fof_nnf,[status(thm)],[axiom_014]) ).
fof(f_14_2,plain,
! [U_27] : ord(cons(U_27,nil)),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
ord(cons(U_27,nil)),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [Y,Y2,Xs] :
( ( ord(cons(Y,cons(Y2,Xs)))
| ~ ord(cons(Y2,Xs))
| ~ leqNat(Y,Y2) )
& ( ( ord(cons(Y2,Xs))
& leqNat(Y,Y2) )
| ~ ord(cons(Y,cons(Y2,Xs))) ) ),
inference(fof_nnf,[status(thm)],[axiom_015]) ).
fof(f_15_2,plain,
! [U_30,U_29,U_28] :
( ( ord(cons(U_30,cons(U_29,U_28)))
| ~ ord(cons(U_29,U_28))
| ~ leqNat(U_30,U_29) )
& ( ( ord(cons(U_29,U_28))
& leqNat(U_30,U_29) )
| ~ ord(cons(U_30,cons(U_29,U_28))) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_36,U_34,U_32] :
( ord(cons(U_36,cons(U_34,U_32)))
| ~ ord(cons(U_34,U_32))
| ~ leqNat(U_36,U_34) )
& ! [U_35,U_33,U_31] :
( ( ord(cons(U_33,U_31))
& leqNat(U_35,U_33) )
| ~ ord(cons(U_35,cons(U_33,U_31))) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( leqNat(U_35,U_33)
| ~ ord(cons(U_35,cons(U_33,U_31))) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( ord(cons(U_33,U_31))
| ~ ord(cons(U_35,cons(U_33,U_31))) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( ord(cons(U_36,cons(U_34,U_32)))
| ~ ord(cons(U_34,U_32))
| ~ leqNat(U_36,U_34) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,negated_conjecture,
~ ? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
inference(negate,[status(cth)],[goal_016]) ).
fof(f_16_2,negated_conjecture,
! [Xs,Ys] :
( ord(merge(Xs,Ys))
| ord(Ys)
| ~ ord(Xs) ),
inference(fof_nnf,[status(thm)],[f_16_1]) ).
fof(f_16_3,negated_conjecture,
! [U_38,U_37] :
( ord(merge(U_38,U_37))
| ord(U_37)
| ~ ord(U_38) ),
inference(variable_rename,[status(thm)],[f_16_2]) ).
fof(f_16_4,negated_conjecture,
! [U_38] :
( ! [U_37] :
( ord(merge(U_38,U_37))
| ord(U_37) )
| ~ ord(U_38) ),
inference(miniscope,[status(thm)],[f_16_3]) ).
fof(f_16_5,negated_conjecture,
! [U_38,U_37] :
( ord(merge(U_38,U_37))
| ord(U_37)
| ~ ord(U_38) ),
inference(definitional_conversion,[status(esa)],[f_16_4]) ).
cnf(f_16_6,negated_conjecture,
( ord(merge(U_38,U_37))
| ord(U_37)
| ~ ord(U_38) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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(equality_4,axiom,
( cons(Eq_x_0,Eq_x_1) = cons(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( head(Eq_x_0) = head(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( tail(Eq_x_0) = tail(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( s(Eq_x_0) = s(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( proj1S(Eq_x_0) = proj1S(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( merge(Eq_x_0,Eq_x_1) = merge(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( leqNat(Eq_y_0,Eq_y_1)
| ~ leqNat(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( ord(Eq_y_0)
| ~ ord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 06:17:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.44/0.77 % SZS status Theorem for theBenchmark
% 0.44/0.77 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------