%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP024+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 : n008.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 09:52:58 AM UTC 2026
% Result : Theorem 0.25s 0.56s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 19 unt; 0 def)
% Number of atoms : 143 ( 33 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 144 ( 54 ~; 45 |; 23 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tops_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tops_1(B,A)
<=> k6_pre_topc(A,B) = u1_struct_0(A) ) ) ),
file('theBenchmark.p',d2_tops_3) ).
fof(d5_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)
<=> ( k3_tex_4(A,B) = u1_struct_0(A)
& v1_tsp_1(B,A) ) ) ) ),
file('theBenchmark.p',d5_tsp_2) ).
fof(dt_k2_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ),
file('theBenchmark.p',dt_k2_pre_topc) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_pre_topc) ).
fof(fc8_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ( v4_pre_topc(k2_pre_topc(A),A)
& v3_pre_topc(k2_pre_topc(A),A) ) ),
file('theBenchmark.p',fc8_tops_1) ).
fof(t12_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> k2_pre_topc(A) = u1_struct_0(A) ),
file('theBenchmark.p',t12_pre_topc) ).
fof(t52_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( ( k6_pre_topc(A,B) = B
& v2_pre_topc(A) )
=> v4_pre_topc(B,A) )
& ( v4_pre_topc(B,A)
=> k6_pre_topc(A,B) = B ) ) ) ),
file('theBenchmark.p',t52_pre_topc) ).
fof(t64_tex_4,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)))
=> k6_pre_topc(A,k3_tex_4(A,B)) = k6_pre_topc(A,B) ) ),
file('theBenchmark.p',t64_tex_4) ).
fof(t2_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)
=> v1_tops_1(B,A) ) ) ),
file('theBenchmark.p',t2_tsp_2) ).
fof(t2_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)
=> v1_tops_1(B,A) ) ) ),
inference(assume_negation,[status(cth)],[t2_tsp_2]) ).
fof(nnf_69,plain,
? [A] :
( ? [B] :
( ~ v1_tops_1(B,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)],[t2_tsp_2_neg]) ).
fof(sk_t2_tsp_2_neg,plain,
( ~ v1_tops_1(sK1,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]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_69]) ).
cnf(c_70,negated_conjecture,
v2_pre_topc(sK0),
inference(split_conjunct,[status(thm)],[sk_t2_tsp_2_neg]) ).
cnf(c_71,plain,
( k6_pre_topc(A,k3_tex_4(A,B)) = k6_pre_topc(A,B)
| ~ 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)],[t64_tex_4]) ).
cnf(c_98,plain,
( v4_pre_topc(k2_pre_topc(A),A)
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(clausify,[status(thm)],[fc8_tops_1]) ).
cnf(c_103,plain,
( k3_tex_4(A,B) = 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)],[d5_tsp_2]) ).
cnf(c_118,plain,
( l1_struct_0(A)
| ~ l1_pre_topc(A) ),
inference(clausify,[status(thm)],[dt_l1_pre_topc]) ).
cnf(c_119,plain,
( m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k2_pre_topc]) ).
cnf(c_126,plain,
( k2_pre_topc(A) = u1_struct_0(A)
| ~ l1_struct_0(A) ),
inference(clausify,[status(thm)],[t12_pre_topc]) ).
cnf(c_158,plain,
( k6_pre_topc(A,B) != u1_struct_0(A)
| v1_tops_1(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A) ),
inference(clausify,[status(thm)],[d2_tops_3]) ).
cnf(c_193,plain,
( k6_pre_topc(A,B) = B
| ~ v4_pre_topc(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A) ),
inference(clausify,[status(thm)],[t52_pre_topc]) ).
cnf(c_198,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t2_tsp_2_neg]) ).
cnf(c_199,negated_conjecture,
l1_pre_topc(sK0),
inference(split_conjunct,[status(thm)],[sk_t2_tsp_2_neg]) ).
cnf(c_200,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t2_tsp_2_neg]) ).
cnf(c_201,negated_conjecture,
v1_tsp_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t2_tsp_2_neg]) ).
cnf(c_202,negated_conjecture,
~ v1_tops_1(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t2_tsp_2_neg]) ).
cnf(c_203,negated_conjecture,
( k6_pre_topc(sK0,k3_tex_4(sK0,A)) = k6_pre_topc(sK0,A)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_70,c_71]) ).
cnf(c_632,negated_conjecture,
( k6_pre_topc(sK0,k3_tex_4(sK0,A)) = k6_pre_topc(sK0,A)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_198,c_203]) ).
cnf(c_204,negated_conjecture,
( k6_pre_topc(sK0,k3_tex_4(sK0,A)) = k6_pre_topc(sK0,A)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_199,c_632]) ).
cnf(c_257,negated_conjecture,
( v4_pre_topc(k2_pre_topc(sK0),sK0)
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_70,c_98]) ).
cnf(c_258,negated_conjecture,
v4_pre_topc(k2_pre_topc(sK0),sK0),
inference(resolve,[status(thm)],[c_199,c_257]) ).
cnf(c_265,negated_conjecture,
( k3_tex_4(sK0,A) = 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_70,c_103]) ).
cnf(c_633,negated_conjecture,
( k3_tex_4(sK0,A) = 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_198,c_265]) ).
cnf(c_266,negated_conjecture,
( k3_tex_4(sK0,A) = 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_199,c_633]) ).
cnf(c_295,plain,
( m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A) ),
inference(resolve,[status(thm)],[c_118,c_119]) ).
cnf(c_316,plain,
( ~ l1_pre_topc(A)
| k2_pre_topc(A) = u1_struct_0(A) ),
inference(resolve,[status(thm)],[c_126,c_118]) ).
cnf(c_634,negated_conjecture,
( k6_pre_topc(sK0,sK1) != u1_struct_0(sK0)
| v1_tops_1(sK1,sK0)
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_200,c_158]) ).
cnf(c_635,negated_conjecture,
( k6_pre_topc(sK0,sK1) != u1_struct_0(sK0)
| v1_tops_1(sK1,sK0) ),
inference(resolve,[status(thm)],[c_199,c_634]) ).
cnf(c_421,negated_conjecture,
k6_pre_topc(sK0,sK1) != u1_struct_0(sK0),
inference(resolve,[status(thm)],[c_202,c_635]) ).
cnf(c_438,plain,
k6_pre_topc(sK0,k3_tex_4(sK0,sK1)) = k6_pre_topc(sK0,sK1),
inference(resolve,[status(thm)],[c_204,c_200]) ).
cnf(c_636,negated_conjecture,
( k6_pre_topc(sK0,k2_pre_topc(sK0)) = k2_pre_topc(sK0)
| ~ m1_subset_1(k2_pre_topc(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0) ),
inference(resolve,[status(thm)],[c_258,c_193]) ).
cnf(c_560,negated_conjecture,
( k6_pre_topc(sK0,k2_pre_topc(sK0)) = k2_pre_topc(sK0)
| ~ m1_subset_1(k2_pre_topc(sK0),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_199,c_636]) ).
cnf(c_637,negated_conjecture,
( k3_tex_4(sK0,sK1) = u1_struct_0(sK0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_266,c_201]) ).
cnf(c_566,negated_conjecture,
k3_tex_4(sK0,sK1) = u1_struct_0(sK0),
inference(resolve,[status(thm)],[c_200,c_637]) ).
cnf(c_638,plain,
k6_pre_topc(sK0,u1_struct_0(sK0)) = k6_pre_topc(sK0,sK1),
inference(paramod,[status(thm)],[c_566,c_438]) ).
cnf(c_567,plain,
k6_pre_topc(sK0,sK1) = k6_pre_topc(sK0,u1_struct_0(sK0)),
inference(copy,[status(thm)],[c_638]) ).
cnf(c_569,negated_conjecture,
k6_pre_topc(sK0,u1_struct_0(sK0)) != u1_struct_0(sK0),
inference(paramod,[status(thm)],[c_567,c_421]) ).
cnf(c_586,plain,
m1_subset_1(k2_pre_topc(sK0),k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_295,c_199]) ).
cnf(c_588,negated_conjecture,
k6_pre_topc(sK0,k2_pre_topc(sK0)) = k2_pre_topc(sK0),
inference(resolve,[status(thm)],[c_586,c_560]) ).
cnf(c_629,plain,
k2_pre_topc(sK0) = u1_struct_0(sK0),
inference(resolve,[status(thm)],[c_316,c_199]) ).
cnf(c_639,negated_conjecture,
k6_pre_topc(sK0,u1_struct_0(sK0)) = k2_pre_topc(sK0),
inference(paramod,[status(thm)],[c_629,c_588]) ).
cnf(c_640,negated_conjecture,
k6_pre_topc(sK0,u1_struct_0(sK0)) = u1_struct_0(sK0),
inference(paramod,[status(thm)],[c_629,c_639]) ).
cnf(c_631,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_569,c_640]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : TOP024+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n008.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 20:32:39 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 292903 was started by sandbox2 on n008,
% 0.19/0.45 % Sat Sep 26 20:32:39 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 0.25/0.56
% 0.25/0.56 % SZS status Theorem for theBenchmark
% 0.25/0.56
% 0.25/0.56 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.25/0.56 % Length of proof is 41.
% 0.25/0.56 % Level of proof is 7.
% 0.25/0.56 % Maximum clause weight is 16.000.
% 0.25/0.56 % Given clauses 131.
% 0.25/0.56
% 0.25/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------