%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV390+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n026.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 09:03:34 AM UTC 2026
% Result : Theorem 76.04s 76.35s
% Output : Proof 76.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 23 unt; 0 def)
% Number of atoms : 111 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 48 ~; 37 |; 18 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 121 ( 5 sgn 77 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bottom_smallest,axiom,
! [U] : less_than(bottom,U),
file('SWV007+0.ax',bottom_smallest) ).
fof(ax37,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
file('SWV007+3.ax',ax37) ).
fof(ax42,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
file('SWV007+3.ax',ax42) ).
fof(l26_li4142,lemma,
! [U,V,W] :
( check_cpq(triple(U,V,W))
<=> ! [X,Y] :
( pair_in_list(V,X,Y)
=> less_than(Y,X) ) ),
file('theBenchmark.p',l26_li4142) ).
fof(l26_co,conjecture,
! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ! [X] : ~ check_cpq(insert_cpq(triple(U,V,W),X)) ),
file('theBenchmark.p',l26_co) ).
fof(f_5_1,plain,
! [U] : less_than(bottom,U),
inference(fof_nnf,[status(thm)],[bottom_smallest]) ).
fof(f_5_2,plain,
! [U_12] : less_than(bottom,U_12),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
less_than(bottom,U_12),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_25_1,plain,
! [U,V,W,X,Y] :
( ( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
| ~ check_cpq(triple(U,V,W)) )
& ( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(fof_nnf,[status(thm)],[ax37]) ).
fof(f_25_2,plain,
! [U_86,U_85,U_84,U_83,U_82] :
( ( ( check_cpq(triple(U_86,insert_slb(U_85,pair(U_83,U_82)),U_84))
| ~ check_cpq(triple(U_86,U_85,U_84)) )
& ( check_cpq(triple(U_86,U_85,U_84))
| ~ check_cpq(triple(U_86,insert_slb(U_85,pair(U_83,U_82)),U_84)) ) )
| ~ less_than(U_82,U_83) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( check_cpq(triple(U_86,U_85,U_84))
| ~ check_cpq(triple(U_86,insert_slb(U_85,pair(U_83,U_82)),U_84))
| ~ less_than(U_82,U_83) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_30_1,plain,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
inference(fof_nnf,[status(thm)],[ax42]) ).
fof(f_30_2,plain,
! [U_116,U_115,U_114,U_113] : insert_cpq(triple(U_116,U_115,U_114),U_113) = triple(insert_pqp(U_116,U_113),insert_slb(U_115,pair(U_113,bottom)),U_114),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
insert_cpq(triple(U_116,U_115,U_114),U_113) = triple(insert_pqp(U_116,U_113),insert_slb(U_115,pair(U_113,bottom)),U_114),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_42_1,plain,
! [U,V,W] :
( ( check_cpq(triple(U,V,W))
| ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(V,X,Y) ) )
& ( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) )
| ~ check_cpq(triple(U,V,W)) ) ),
inference(fof_nnf,[status(thm)],[l26_li4142]) ).
fof(f_42_2,plain,
! [U_157,U_156,U_155] :
( ( check_cpq(triple(U_157,U_156,U_155))
| ? [U_154,U_153] :
( ~ less_than(U_153,U_154)
& pair_in_list(U_156,U_154,U_153) ) )
& ( ! [U_152,U_151] :
( less_than(U_151,U_152)
| ~ pair_in_list(U_156,U_152,U_151) )
| ~ check_cpq(triple(U_157,U_156,U_155)) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_163,U_161] :
( ! [U_159] : check_cpq(triple(U_163,U_161,U_159))
| ? [U_154,U_153] :
( ~ less_than(U_153,U_154)
& pair_in_list(U_161,U_154,U_153) ) )
& ! [U_162,U_160] :
( ! [U_158] : ~ check_cpq(triple(U_162,U_160,U_158))
| ! [U_152,U_151] :
( less_than(U_151,U_152)
| ~ pair_in_list(U_160,U_152,U_151) ) ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
( ! [U_163,U_161] :
( ! [U_159] : check_cpq(triple(U_163,U_161,U_159))
| ? [U_153] :
( ~ less_than(U_153,sK1(U_163,U_161))
& pair_in_list(U_161,sK1(U_163,U_161),U_153) ) )
& ! [U_162,U_160] :
( ! [U_158] : ~ check_cpq(triple(U_162,U_160,U_158))
| ! [U_152,U_151] :
( less_than(U_151,U_152)
| ~ pair_in_list(U_160,U_152,U_151) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_154,sK1(U_163,U_161))],[f_42_3]) ).
fof(f_42_5,plain,
( ! [U_163,U_161] :
( ! [U_159] : check_cpq(triple(U_163,U_161,U_159))
| ( ~ less_than(sK2(U_163,U_161),sK1(U_163,U_161))
& pair_in_list(U_161,sK1(U_163,U_161),sK2(U_163,U_161)) ) )
& ! [U_162,U_160] :
( ! [U_158] : ~ check_cpq(triple(U_162,U_160,U_158))
| ! [U_152,U_151] :
( less_than(U_151,U_152)
| ~ pair_in_list(U_160,U_152,U_151) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_153,sK2(U_163,U_161))],[f_42_4]) ).
cnf(f_42_6,plain,
( ~ check_cpq(triple(U_162,U_160,U_158))
| less_than(U_151,U_152)
| ~ pair_in_list(U_160,U_152,U_151) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_7,plain,
( pair_in_list(U_161,sK1(U_163,U_161),sK2(U_163,U_161))
| check_cpq(triple(U_163,U_161,U_159)) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_8,plain,
( ~ less_than(sK2(U_163,U_161),sK1(U_163,U_161))
| check_cpq(triple(U_163,U_161,U_159)) ),
inference(clausify,[status(thm)],[f_42_5]) ).
fof(f_43_1,negated_conjecture,
~ ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ! [X] : ~ check_cpq(insert_cpq(triple(U,V,W),X)) ),
inference(negate,[status(cth)],[l26_co]) ).
fof(f_43_2,negated_conjecture,
? [U,V,W] :
( ? [X] : check_cpq(insert_cpq(triple(U,V,W),X))
& ~ check_cpq(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[f_43_1]) ).
fof(f_43_3,negated_conjecture,
? [U_167,U_166,U_165] :
( ? [U_164] : check_cpq(insert_cpq(triple(U_167,U_166,U_165),U_164))
& ~ check_cpq(triple(U_167,U_166,U_165)) ),
inference(variable_rename,[status(thm)],[f_43_2]) ).
fof(f_43_4,negated_conjecture,
? [U_166,U_165] :
( ? [U_164] : check_cpq(insert_cpq(triple(sK3,U_166,U_165),U_164))
& ~ check_cpq(triple(sK3,U_166,U_165)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_167,sK3)],[f_43_3]) ).
fof(f_43_5,negated_conjecture,
? [U_165] :
( ? [U_164] : check_cpq(insert_cpq(triple(sK3,sK4,U_165),U_164))
& ~ check_cpq(triple(sK3,sK4,U_165)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_166,sK4)],[f_43_4]) ).
fof(f_43_6,negated_conjecture,
( ? [U_164] : check_cpq(insert_cpq(triple(sK3,sK4,sK5),U_164))
& ~ check_cpq(triple(sK3,sK4,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_165,sK5)],[f_43_5]) ).
fof(f_43_7,negated_conjecture,
( check_cpq(insert_cpq(triple(sK3,sK4,sK5),sK6))
& ~ check_cpq(triple(sK3,sK4,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_164,sK6)],[f_43_6]) ).
cnf(f_43_8,negated_conjecture,
~ check_cpq(triple(sK3,sK4,sK5)),
inference(clausify,[status(thm)],[f_43_7]) ).
cnf(f_43_9,negated_conjecture,
check_cpq(insert_cpq(triple(sK3,sK4,sK5),sK6)),
inference(clausify,[status(thm)],[f_43_7]) ).
cnf(equality_27,axiom,
( check_cpq(Eq_y_0)
| ~ check_cpq(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ check_cpq(triple(sK3,sK4,sK5)),
inference(start,[status(thm),parent(0:0)],[f_43_8]) ).
cnf(t2,plain,
( ~ less_than(sK2(sK3,sK4),sK1(sK3,sK4))
| check_cpq(triple(sK3,sK4,sK5)) ),
inference(extension,[status(thm),parent(t1:1)],[f_42_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ check_cpq(triple(insert_pqp(sK3,sK6),sK4,sK5))
| ~ pair_in_list(sK4,sK1(sK3,sK4),sK2(sK3,sK4))
| less_than(sK2(sK3,sK4),sK1(sK3,sK4)) ),
inference(extension,[status(thm),parent(t2:2)],[f_42_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( check_cpq(triple(sK3,sK4,sK5))
| pair_in_list(sK4,sK1(sK3,sK4),sK2(sK3,sK4)) ),
inference(extension,[status(thm),parent(t4:2)],[f_42_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
$false,
inference(reduction,[status(thm),parent(t6:2)],[t6:2,t1:1]) ).
cnf(t9,plain,
( ~ check_cpq(triple(insert_pqp(sK3,sK6),insert_slb(sK4,pair(sK6,bottom)),sK5))
| ~ less_than(bottom,sK6)
| check_cpq(triple(insert_pqp(sK3,sK6),sK4,sK5)) ),
inference(extension,[status(thm),parent(t4:3)],[f_25_3]) ).
cnf(t10,plain,
$false,
inference(connection,[status(thm),parent(t9:1)],[t9:1,t4:3]) ).
cnf(t11,plain,
less_than(bottom,sK6),
inference(extension,[status(thm),parent(t9:2)],[f_5_3]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t9:2]) ).
cnf(t13,plain,
( ~ check_cpq(insert_cpq(triple(sK3,sK4,sK5),sK6))
| insert_cpq(triple(sK3,sK4,sK5),sK6) != triple(insert_pqp(sK3,sK6),insert_slb(sK4,pair(sK6,bottom)),sK5)
| check_cpq(triple(insert_pqp(sK3,sK6),insert_slb(sK4,pair(sK6,bottom)),sK5)) ),
inference(extension,[status(thm),parent(t9:3)],[equality_27]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t9:3]) ).
cnf(t15,plain,
insert_cpq(triple(sK3,sK4,sK5),sK6) = triple(insert_pqp(sK3,sK6),insert_slb(sK4,pair(sK6,bottom)),sK5),
inference(extension,[status(thm),parent(t13:2)],[f_30_3]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
check_cpq(insert_cpq(triple(sK3,sK4,sK5),sK6)),
inference(extension,[status(thm),parent(t13:3)],[f_43_9]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t13:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV390+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 03:32:39 UTC 2026
% 0.08/0.37 % CPUTime :
% 76.04/76.35 % SZS status Theorem for theBenchmark
% 76.04/76.35 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------