%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 : Sun Sep 27 08:46:14 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 120 ( 41 ~; 34 |; 27 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d9_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ),
file('theBenchmark.p',d9_orders_2) ).
fof(dt_k1_latsum_1,axiom,
! [A,B] :
( ( l1_orders_2(B)
& l1_orders_2(A) )
=> ( l1_orders_2(k1_latsum_1(A,B))
& v1_orders_2(k1_latsum_1(A,B)) ) ),
file('theBenchmark.p',dt_k1_latsum_1) ).
fof(t21_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C,D] :
( ( r2_hidden(D,u1_struct_0(A))
& r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ),
file('theBenchmark.p',t21_latsum_1) ).
fof(t23_latsum_1,conjecture,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ) ) ),
file('theBenchmark.p',t23_latsum_1) ).
fof(t23_latsum_1_neg,negated_conjecture,
~ ! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t23_latsum_1]) ).
cnf(c_43,plain,
( r2_hidden(k4_tarski(B,C),u1_orders_2(A))
| ~ r1_orders_2(A,B,C)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_orders_2(A) ),
inference(clausify,[status(thm)],[d9_orders_2]) ).
fof(nnf_41,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ r2_hidden(C,u1_struct_0(A))
& r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B))) )
& m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) )
& l1_orders_2(B) )
& l1_orders_2(A) ),
inference(fof_nnf,[status(thm)],[t23_latsum_1_neg]) ).
fof(sk_t23_latsum_1_neg,plain,
( ~ r2_hidden(sK2,u1_struct_0(sK0))
& r2_hidden(sK3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
& m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
& l1_orders_2(sK1)
& l1_orders_2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_41]) ).
cnf(c_44,negated_conjecture,
r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_62,plain,
( l1_orders_2(k1_latsum_1(A,B))
| ~ l1_orders_2(B)
| ~ l1_orders_2(A) ),
inference(clausify,[status(thm)],[dt_k1_latsum_1]) ).
cnf(c_73,plain,
( r2_hidden(C,u1_struct_0(A))
| ~ r2_hidden(D,u1_struct_0(A))
| ~ r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
| ~ l1_orders_2(B)
| ~ l1_orders_2(A) ),
inference(clausify,[status(thm)],[t21_latsum_1]) ).
cnf(c_81,negated_conjecture,
l1_orders_2(sK0),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_82,negated_conjecture,
l1_orders_2(sK1),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_83,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_84,negated_conjecture,
m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_85,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_86,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_87,negated_conjecture,
r2_hidden(sK3,u1_struct_0(sK0)),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_88,negated_conjecture,
~ r2_hidden(sK2,u1_struct_0(sK0)),
inference(split_conjunct,[status(thm)],[sk_t23_latsum_1_neg]) ).
cnf(c_89,negated_conjecture,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_44,c_43]) ).
cnf(c_172,negated_conjecture,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_83,c_89]) ).
cnf(c_90,negated_conjecture,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_84,c_172]) ).
cnf(c_173,negated_conjecture,
( r2_hidden(B,u1_struct_0(sK0))
| ~ r2_hidden(C,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(B,C),u1_orders_2(k1_latsum_1(sK0,A)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(A)),k1_zfmisc_1(u1_struct_0(A)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(A)),A)
| ~ l1_orders_2(A) ),
inference(resolve,[status(thm)],[c_73,c_81]) ).
cnf(c_174,negated_conjecture,
( r2_hidden(A,u1_struct_0(sK0))
| ~ r2_hidden(B,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(A,B),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1) ),
inference(resolve,[status(thm)],[c_173,c_82]) ).
cnf(c_175,negated_conjecture,
( r2_hidden(A,u1_struct_0(sK0))
| ~ r2_hidden(B,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(A,B),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(resolve,[status(thm)],[c_174,c_85]) ).
cnf(c_176,negated_conjecture,
( r2_hidden(A,u1_struct_0(sK0))
| ~ r2_hidden(B,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(A,B),u1_orders_2(k1_latsum_1(sK0,sK1))) ),
inference(resolve,[status(thm)],[c_175,c_86]) ).
cnf(c_177,negated_conjecture,
( r2_hidden(A,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(A,sK3),u1_orders_2(k1_latsum_1(sK0,sK1))) ),
inference(resolve,[status(thm)],[c_176,c_87]) ).
cnf(c_129,negated_conjecture,
~ r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1))),
inference(resolve,[status(thm)],[c_177,c_88]) ).
cnf(c_130,negated_conjecture,
~ l1_orders_2(k1_latsum_1(sK0,sK1)),
inference(resolve,[status(thm)],[c_129,c_90]) ).
cnf(c_178,negated_conjecture,
( l1_orders_2(k1_latsum_1(A,sK1))
| ~ l1_orders_2(A) ),
inference(resolve,[status(thm)],[c_62,c_82]) ).
cnf(c_179,negated_conjecture,
~ l1_orders_2(sK0),
inference(resolve,[status(thm)],[c_178,c_130]) ).
cnf(c_171,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_81,c_179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.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 : Sat Sep 26 09:31:29 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3018139 was started by sandbox2 on n010,
% 0.13/0.36 % Sat Sep 26 09:31:29 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 21.
% 0.13/0.39 % Level of proof is 5.
% 0.13/0.39 % Maximum clause weight is 36.000.
% 0.13/0.39 % Given clauses 53.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------