%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP027+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:52:59 AM UTC 2026
% Result : Theorem 0.86s 0.52s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 118 ( 21 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 133 ( 52 ~; 43 |; 22 &)
% ( 0 <=>; 16 =>; 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 : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_k5_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> k5_subset_1(A,B,C) = k3_xboole_0(B,C) ),
file('theBenchmark.p',redefinition_k5_subset_1) ).
fof(dt_k1_tops_1,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_pre_topc(A) )
=> m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ),
file('theBenchmark.p',dt_k1_tops_1) ).
fof(fc6_tops_1,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_pre_topc(A)
& v2_pre_topc(A) )
=> v3_pre_topc(k1_tops_1(A,B),A) ),
file('theBenchmark.p',fc6_tops_1) ).
fof(t6_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)))
=> ( v3_pre_topc(C,A)
=> C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ),
file('theBenchmark.p',t6_tsp_2) ).
fof(t8_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)))
=> k1_tops_1(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,C))) ) ) ) ),
file('theBenchmark.p',t8_tsp_2) ).
fof(t8_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)))
=> k1_tops_1(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,C))) ) ) ) ),
inference(assume_negation,[status(cth)],[t8_tsp_2]) ).
fof(nnf_79,plain,
? [A] :
( ? [B] :
( ? [C] :
( k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,C))) != k1_tops_1(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)],[t8_tsp_2_neg]) ).
fof(sk_t8_tsp_2_neg,plain,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k1_tops_1(sK0,sK2))) != k1_tops_1(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_79]) ).
cnf(c_80,negated_conjecture,
v2_pre_topc(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_tsp_2_neg]) ).
cnf(c_81,plain,
( k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = C
| ~ v3_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)],[t6_tsp_2]) ).
cnf(c_84,plain,
( v3_pre_topc(k1_tops_1(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)],[fc6_tops_1]) ).
cnf(c_241,plain,
( k3_xboole_0(A,C) = k5_subset_1(B,A,C)
| ~ m1_subset_1(C,k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(clausify,[status(thm)],[redefinition_k5_subset_1]) ).
cnf(c_242,plain,
( k5_subset_1(B,A,C) = k3_xboole_0(A,C)
| ~ m1_subset_1(C,k1_zfmisc_1(B))
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ),
inference(copy,[status(thm)],[c_241]) ).
cnf(c_243,plain,
( m1_subset_1(k1_tops_1(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_k1_tops_1]) ).
cnf(c_247,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_tsp_2_neg]) ).
cnf(c_248,negated_conjecture,
l1_pre_topc(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_tsp_2_neg]) ).
cnf(c_249,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t8_tsp_2_neg]) ).
cnf(c_250,negated_conjecture,
v1_tsp_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t8_tsp_2_neg]) ).
cnf(c_251,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t8_tsp_2_neg]) ).
cnf(c_252,negated_conjecture,
k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k1_tops_1(sK0,sK2))) != k1_tops_1(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_tsp_2_neg]) ).
cnf(c_253,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),A,B)) = B
| ~ v3_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_80,c_81]) ).
cnf(c_1880,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),A,B)) = B
| ~ v3_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_247,c_253]) ).
cnf(c_254,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),A,B)) = B
| ~ v3_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_248,c_1880]) ).
cnf(c_259,negated_conjecture,
( v3_pre_topc(k1_tops_1(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_80,c_84]) ).
cnf(c_260,negated_conjecture,
( v3_pre_topc(k1_tops_1(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_248,c_259]) ).
cnf(c_558,plain,
( k5_subset_1(u1_struct_0(sK0),sK1,A) = k3_xboole_0(sK1,A)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_249,c_242]) ).
cnf(c_1881,negated_conjecture,
( m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_251,c_243]) ).
cnf(c_588,negated_conjecture,
m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_248,c_1881]) ).
cnf(c_1882,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,A)) = A
| ~ v3_pre_topc(A,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_tsp_2(sK1,sK0) ),
inference(resolve,[status(thm)],[c_254,c_249]) ).
cnf(c_618,negated_conjecture,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,A)) = A
| ~ v3_pre_topc(A,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_250,c_1882]) ).
cnf(c_660,plain,
v3_pre_topc(k1_tops_1(sK0,sK2),sK0),
inference(resolve,[status(thm)],[c_260,c_251]) ).
cnf(c_1772,plain,
k5_subset_1(u1_struct_0(sK0),sK1,k1_tops_1(sK0,sK2)) = k3_xboole_0(sK1,k1_tops_1(sK0,sK2)),
inference(resolve,[status(thm)],[c_588,c_558]) ).
cnf(c_1823,negated_conjecture,
k3_tex_4(sK0,k3_xboole_0(sK1,k1_tops_1(sK0,sK2))) != k1_tops_1(sK0,sK2),
inference(paramod,[status(thm)],[c_1772,c_252]) ).
cnf(c_1883,plain,
( k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k1_tops_1(sK0,sK2))) = k1_tops_1(sK0,sK2)
| ~ v3_pre_topc(k1_tops_1(sK0,sK2),sK0) ),
inference(resolve,[status(thm)],[c_618,c_588]) ).
cnf(c_1884,plain,
( k3_tex_4(sK0,k3_xboole_0(sK1,k1_tops_1(sK0,sK2))) = k1_tops_1(sK0,sK2)
| ~ v3_pre_topc(k1_tops_1(sK0,sK2),sK0) ),
inference(paramod,[status(thm)],[c_1772,c_1883]) ).
cnf(c_1885,plain,
k3_tex_4(sK0,k3_xboole_0(sK1,k1_tops_1(sK0,sK2))) = k1_tops_1(sK0,sK2),
inference(resolve,[status(thm)],[c_660,c_1884]) ).
cnf(c_1879,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1823,c_1885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP027+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 20:34:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 4160957 was started by sandbox on n010,
% 0.09/0.36 % Sat Sep 26 20:34:00 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.86/0.52
% 0.86/0.52 % given #500 (W,wt=17): 567 -v2_tops_1(c6,c5) | v2_membered(k1_tops_1(c5,c6)). [resolve(249,a,161,c),unit_del(a,248)].
% 0.86/0.52
% 0.86/0.52 % SZS status Theorem for theBenchmark
% 0.86/0.52
% 0.86/0.52 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.86/0.52 % Length of proof is 28.
% 0.86/0.52 % Level of proof is 6.
% 0.86/0.52 % Maximum clause weight is 45.000.
% 0.86/0.52 % Given clauses 632.
% 0.86/0.52
% 0.86/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------