%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWC422-1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n006.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 09:02:19 AM UTC 2026
% Result : Unsatisfiable 86.16s 86.43s
% Output : Proof 86.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 16
% Syntax : Number of clauses : 79 ( 53 unt; 5 nHn; 78 RR)
% Number of literals : 132 ( 51 equ; 50 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause8,axiom,
ssList(nil),
file('SWC001-0.ax',clause8) ).
cnf(clause177,axiom,
( nil = U
| U = V
| nil = V
| ~ ssList(V)
| ~ ssList(U)
| hd(U) != hd(V)
| tl(U) != tl(V) ),
file('SWC001-0.ax',clause177) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(co1_10,negated_conjecture,
( neq(sk2,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(co1_15,negated_conjecture,
( ~ neq(sk4,nil)
| app(app(C,cons(A,nil)),B) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('theBenchmark.p',co1_15) ).
cnf(co1_16,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_16) ).
cnf(co1_17,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('theBenchmark.p',co1_17) ).
cnf(co1_18,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('theBenchmark.p',co1_18) ).
cnf(co1_19,negated_conjecture,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
file('theBenchmark.p',co1_19) ).
cnf(co1_20,negated_conjecture,
( ~ neq(sk4,nil)
| app(app(sk7,cons(sk5,nil)),sk6) = sk3 ),
file('theBenchmark.p',co1_20) ).
cnf(co1_7_simplified,negated_conjecture,
neq(sk2,nil),
inference(simplify_clause,[status(thm)],[co1_7]) ).
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_67,axiom,
( neq(Eq_y_0,Eq_y_1)
| ~ neq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( ~ ssList(sk6)
| ~ ssList(sk7)
| app(app(sk6,cons(sk5,nil)),sk7) != sk2
| app(app(sk7,cons(sk5,nil)),sk6) != sk1
| ~ neq(sk4,nil)
| ~ ssItem(sk5) ),
inference(start,[status(thm),parent(0:0)],[co1_15]) ).
cnf(t2,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(extension,[status(thm),parent(t1:1)],[co1_16]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( nil != nil
| ~ neq(sk2,nil)
| sk2 != sk4
| neq(sk4,nil) ),
inference(extension,[status(thm),parent(t2:2)],[equality_67]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sk2 = sk4,
inference(extension,[status(thm),parent(t4:2)],[co1_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ssItem(sk5)
| neq(sk2,nil) ),
inference(extension,[status(thm),parent(t4:3)],[co1_10]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t1:1]) ).
cnf(t11,plain,
nil = nil,
inference(extension,[status(thm),parent(t4:4)],[equality_1]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t4:4]) ).
cnf(t13,plain,
( nil != nil
| ~ neq(sk2,nil)
| sk2 != sk4
| neq(sk4,nil) ),
inference(extension,[status(thm),parent(t1:2)],[equality_67]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t1:2]) ).
cnf(t15,plain,
sk2 = sk4,
inference(extension,[status(thm),parent(t13:2)],[co1_5]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
neq(sk2,nil),
inference(extension,[status(thm),parent(t13:3)],[co1_7_simplified]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t13:3]) ).
cnf(t19,plain,
( hd(nil) != hd(nil)
| ~ ssList(nil)
| ~ ssList(nil)
| nil = nil
| nil = nil
| tl(nil) != tl(nil)
| nil = nil ),
inference(extension,[status(thm),parent(t13:4)],[clause177]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t13:4]) ).
cnf(t21,plain,
tl(nil) = tl(nil),
inference(extension,[status(thm),parent(t19:2)],[equality_1]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
$false,
inference(reduction,[status(thm),parent(t19:3)],[t19:3,t13:4]) ).
cnf(l12,lemma,
nil != nil,
inference(lemma,[status(cth),parent(t19:3),below(t13:4)],[t19:3]) ).
cnf(t24,plain,
nil != nil,
inference(lemma_extension,[status(thm),parent(t19:4)],[l12:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t19:4]) ).
cnf(t26,plain,
ssList(nil),
inference(extension,[status(thm),parent(t19:5)],[clause8]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t19:5]) ).
cnf(l13,lemma,
ssList(nil),
inference(lemma,[status(cth),parent(t19:5),below(t13:4)],[t19:5]) ).
cnf(t28,plain,
ssList(nil),
inference(lemma_extension,[status(thm),parent(t19:6)],[l13:1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t19:6]) ).
cnf(t30,plain,
hd(nil) = hd(nil),
inference(extension,[status(thm),parent(t19:7)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t19:7]) ).
cnf(l7,lemma,
neq(sk4,nil),
inference(lemma,[status(cth),parent(t1:2),below(0:0)],[t1:2]) ).
cnf(t32,plain,
( sk3 != sk1
| app(app(sk7,cons(sk5,nil)),sk6) != sk3
| app(app(sk7,cons(sk5,nil)),sk6) = sk1 ),
inference(extension,[status(thm),parent(t1:3)],[equality_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t1:3]) ).
cnf(t34,plain,
( ~ neq(sk4,nil)
| app(app(sk7,cons(sk5,nil)),sk6) = sk3 ),
inference(extension,[status(thm),parent(t32:2)],[co1_20]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
neq(sk4,nil),
inference(lemma_extension,[status(thm),parent(t34:2)],[l7:1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( sk1 != sk3
| sk3 = sk1 ),
inference(extension,[status(thm),parent(t32:3)],[equality_2]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t32:3]) ).
cnf(t40,plain,
sk1 = sk3,
inference(extension,[status(thm),parent(t38:2)],[co1_6]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
( sk4 != sk2
| app(app(sk6,cons(sk5,nil)),sk7) != sk4
| app(app(sk6,cons(sk5,nil)),sk7) = sk2 ),
inference(extension,[status(thm),parent(t1:4)],[equality_3]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t1:4]) ).
cnf(t44,plain,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
inference(extension,[status(thm),parent(t42:2)],[co1_19]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
neq(sk4,nil),
inference(lemma_extension,[status(thm),parent(t44:2)],[l7:1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
( sk2 != sk4
| sk4 = sk2 ),
inference(extension,[status(thm),parent(t42:3)],[equality_2]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t42:3]) ).
cnf(t50,plain,
sk2 = sk4,
inference(extension,[status(thm),parent(t48:2)],[co1_5]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(extension,[status(thm),parent(t1:5)],[co1_18]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t1:5]) ).
cnf(t54,plain,
neq(sk4,nil),
inference(lemma_extension,[status(thm),parent(t52:2)],[l7:1]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(extension,[status(thm),parent(t1:6)],[co1_17]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t1:6]) ).
cnf(t58,plain,
neq(sk4,nil),
inference(lemma_extension,[status(thm),parent(t56:2)],[l7:1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC422-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 02:55:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 86.16/86.43 % SZS status Unsatisfiable for theBenchmark
% 86.16/86.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------