%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP026+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 : n014.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 09:52:59 AM UTC 2026
% Result : Theorem 1.08s 0.59s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 103 ( 14 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 118 ( 45 ~; 37 |; 21 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k6_pre_topc,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_pre_topc(A) )
=> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ),
file('theBenchmark.p',dt_k6_pre_topc) ).
fof(fc2_tops_1,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_pre_topc(A)
& v2_pre_topc(A) )
=> v4_pre_topc(k6_pre_topc(A,B),A) ),
file('theBenchmark.p',fc2_tops_1) ).
fof(t5_tsp_2,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(C,A)
=> C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ),
file('theBenchmark.p',t5_tsp_2) ).
fof(t7_tsp_2,conjecture,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) ) ) ) ),
file('theBenchmark.p',t7_tsp_2) ).
fof(t7_tsp_2_neg,negated_conjecture,
~ ! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) ) ) ) ),
inference(assume_negation,[status(cth)],[t7_tsp_2]) ).
fof(nnf_78,plain,
? [A] :
( ? [B] :
( ? [C] :
( k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) != k6_pre_topc(A,C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
& v1_tsp_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
& l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t7_tsp_2_neg]) ).
fof(sk_t7_tsp_2_neg,plain,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k6_pre_topc(sK0,sK2))) != k6_pre_topc(sK0,sK2)
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
& v1_tsp_2(sK1,sK0)
& m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
& l1_pre_topc(sK0)
& v2_pre_topc(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_78]) ).
cnf(c_79,negated_conjecture,
v2_pre_topc(sK0),
inference(split_conjunct,[status(thm)],[sk_t7_tsp_2_neg]) ).
cnf(c_80,plain,
( k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = C
| ~ v4_pre_topc(C,A)
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_tsp_2(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t5_tsp_2]) ).
cnf(c_83,plain,
( v4_pre_topc(k6_pre_topc(A,B),A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(clausify,[status(thm)],[fc2_tops_1]) ).
cnf(c_237,plain,
( m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A)))
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A) ),
inference(clausify,[status(thm)],[dt_k6_pre_topc]) ).
cnf(c_239,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t7_tsp_2_neg]) ).
cnf(c_240,negated_conjecture,
l1_pre_topc(sK0),
inference(split_conjunct,[status(thm)],[sk_t7_tsp_2_neg]) ).
cnf(c_241,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t7_tsp_2_neg]) ).
cnf(c_242,negated_conjecture,
v1_tsp_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t7_tsp_2_neg]) ).
cnf(c_243,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t7_tsp_2_neg]) ).
cnf(c_244,negated_conjecture,
k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k6_pre_topc(sK0,sK2))) != k6_pre_topc(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t7_tsp_2_neg]) ).
cnf(c_245,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),A,B)) = B
| ~ v4_pre_topc(B,sK0)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_tsp_2(A,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_79,c_80]) ).
cnf(c_1704,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),A,B)) = B
| ~ v4_pre_topc(B,sK0)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_tsp_2(A,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_239,c_245]) ).
cnf(c_246,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),A,B)) = B
| ~ v4_pre_topc(B,sK0)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_tsp_2(A,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_240,c_1704]) ).
cnf(c_251,negated_conjecture,
( v4_pre_topc(k6_pre_topc(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_79,c_83]) ).
cnf(c_252,negated_conjecture,
( v4_pre_topc(k6_pre_topc(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_240,c_251]) ).
cnf(c_1705,negated_conjecture,
( m1_subset_1(k6_pre_topc(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_243,c_237]) ).
cnf(c_498,negated_conjecture,
m1_subset_1(k6_pre_topc(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_240,c_1705]) ).
cnf(c_1706,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,A)) = A
| ~ v4_pre_topc(A,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_246,c_242]) ).
cnf(c_522,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,A)) = A
| ~ v4_pre_topc(A,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_241,c_1706]) ).
cnf(c_548,plain,
v4_pre_topc(k6_pre_topc(sK0,sK2),sK0),
inference(resolve,[status(thm)],[c_252,c_243]) ).
cnf(c_1707,plain,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k6_pre_topc(sK0,sK2))) = k6_pre_topc(sK0,sK2)
| ~ m1_subset_1(k6_pre_topc(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_522,c_548]) ).
cnf(c_1708,plain,
k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k6_pre_topc(sK0,sK2))) = k6_pre_topc(sK0,sK2),
inference(resolve,[status(thm)],[c_498,c_1707]) ).
cnf(c_1703,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_244,c_1708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : TOP026+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 20:34:03 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.40 % Process 4036430 was started by sandbox2 on n014,
% 0.12/0.40 % Sat Sep 26 20:34:03 2026
% 0.12/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 1.08/0.59
% 1.08/0.59 % SZS status Theorem for theBenchmark
% 1.08/0.59
% 1.08/0.59 % Proof 1 at 0.09 (+ 0.05) seconds.
% 1.08/0.59 % Length of proof is 22.
% 1.08/0.59 % Level of proof is 5.
% 1.08/0.59 % Maximum clause weight is 45.000.
% 1.08/0.59 % Given clauses 475.
% 1.08/0.59
% 1.08/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------