%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:36:41 AM UTC 2026
% Result : Theorem 12.27s 2.00s
% Output : CNFRefutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 9 unt; 0 def)
% Number of atoms : 166 ( 33 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 173 ( 61 ~; 82 |; 22 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 5 sgn 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_th118,conjecture,
! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ),
file('theBenchmark.p',prove_th118) ).
fof(prove_th118_neg,negated_conjecture,
~ ! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ),
inference(assume_negation,[status(cth)],[prove_th118]) ).
fof(nnf_10,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [X0] : ~ member(X0,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(sk_empty_defn_sk,plain,
! [B] :
( ( member(sK0(B),B)
| empty(B) )
& ( ! [X0] : ~ member(X0,B)
| ~ empty(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(B))],[nnf_10]) ).
fof(sk_empty_defn,plain,
( ! [VAR_0] :
( member(sK0(VAR_0),VAR_0)
| empty(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ member(VAR_1,VAR_0)
| ~ empty(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_empty_defn_sk]) ).
cnf(c_13,plain,
( member(sK0(A),A)
| empty(A) ),
inference(split_conjunct,[status(thm)],[sk_empty_defn]) ).
cnf(c_14,plain,
( ~ member(B,A)
| ~ empty(A) ),
inference(split_conjunct,[status(thm)],[sk_empty_defn]) ).
cnf(c_15,plain,
( ~ member(B,A)
| member(sK0(A),A) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
fof(nnf_12,plain,
? [B,C] :
( ( intersection(B,C) != empty_set
| ~ disjoint(B,C) )
& ( intersection(B,C) = empty_set
| disjoint(B,C) ) ),
inference(fof_nnf,[status(thm)],[prove_th118_neg]) ).
fof(sk_prove_th118_neg,plain,
( ( intersection(sK1,sK2) != empty_set
| ~ disjoint(sK1,sK2) )
& ( intersection(sK1,sK2) = empty_set
| disjoint(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1),skolemize(C,sK2)],[nnf_12]) ).
cnf(c_16,negated_conjecture,
( intersection(sK1,sK2) != empty_set
| ~ disjoint(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_prove_th118_neg]) ).
cnf(c_17,negated_conjecture,
( intersection(sK1,sK2) = empty_set
| disjoint(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_prove_th118_neg]) ).
fof(nnf_11,plain,
! [B,C] :
( ( ? [D] :
( ( ~ member(D,C)
| ~ member(D,B) )
& ( member(D,C)
| member(D,B) ) )
| C = B )
& ( ! [X0] :
( ( ~ member(X0,C)
| member(X0,B) )
& ( member(X0,C)
| ~ member(X0,B) ) )
| C != B ) ),
inference(fof_nnf,[status(thm)],[equal_member_defn]) ).
fof(sk_equal_member_defn_sk,plain,
! [B,C] :
( ( ( ( ~ member(sK3(B,C),C)
| ~ member(sK3(B,C),B) )
& ( member(sK3(B,C),C)
| member(sK3(B,C),B) ) )
| C = B )
& ( ! [X0] :
( ( ~ member(X0,C)
| member(X0,B) )
& ( member(X0,C)
| ~ member(X0,B) ) )
| C != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(D,sK3(B,C))],[nnf_11]) ).
fof(sk_equal_member_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_1,VAR_0),VAR_0)
| ~ member(sK3(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( member(sK3(VAR_1,VAR_0),VAR_0)
| member(sK3(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_0)
| member(VAR_2,VAR_1)
| VAR_0 != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_0)
| ~ member(VAR_2,VAR_1)
| VAR_0 != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_equal_member_defn_sk]) ).
cnf(c_19,plain,
( member(sK3(B,A),A)
| member(sK3(B,A),B)
| A = B ),
inference(split_conjunct,[status(thm)],[sk_equal_member_defn]) ).
cnf(c_31,plain,
( intersect(A,B)
| disjoint(A,B) ),
inference(clausify,[status(thm)],[disjoint_defn]) ).
cnf(c_32,plain,
( ~ intersect(A,B)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[disjoint_defn]) ).
cnf(c_33,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
fof(nnf_2,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [X0] :
( member(X0,C)
& member(X0,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(sk_intersect_defn_sk,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ( member(sK4(B,C),C)
& member(sK4(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4(B,C))],[nnf_2]) ).
fof(sk_intersect_defn,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK4(VAR_0,VAR_1),VAR_1)
| ~ intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK4(VAR_0,VAR_1),VAR_0)
| ~ intersect(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_intersect_defn_sk]) ).
cnf(c_34,plain,
( ~ member(C,B)
| ~ member(C,A)
| intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_35,plain,
( member(sK4(A,B),B)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_36,plain,
( member(sK4(A,B),A)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_37,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_38,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_39,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_42,plain,
( member(sK0(B),B)
| member(sK3(B,A),A)
| A = B ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_61,plain,
( intersection(sK1,sK2) != empty_set
| intersect(sK1,sK2) ),
inference(resolve,[status(thm)],[c_31,c_16]) ).
cnf(c_62,plain,
( intersection(sK1,sK2) = empty_set
| ~ intersect(sK1,sK2) ),
inference(resolve,[status(thm)],[c_32,c_17]) ).
cnf(c_97,plain,
( member(sK3(C,intersection(A,B)),A)
| member(sK0(C),C)
| intersection(A,B) = C ),
inference(resolve,[status(thm)],[c_42,c_39]) ).
cnf(c_98,plain,
( member(sK3(C,intersection(A,B)),B)
| member(sK0(C),C)
| intersection(A,B) = C ),
inference(resolve,[status(thm)],[c_42,c_38]) ).
cnf(c_3007,plain,
( member(sK0(C),C)
| intersection(A,D) = C
| ~ member(sK3(C,intersection(A,D)),B)
| intersect(A,B) ),
inference(resolve,[status(thm)],[c_34,c_97]) ).
cnf(c_3008,plain,
( member(sK0(C),C)
| intersection(A,B) = C
| member(sK0(C),C)
| intersection(A,B) = C
| intersect(A,B) ),
inference(resolve,[status(thm)],[c_3007,c_98]) ).
cnf(c_3009,plain,
( member(sK0(C),C)
| member(sK0(C),C)
| intersection(A,B) = C
| intersect(A,B) ),
inference(copy,[status(thm)],[c_3008]) ).
cnf(c_2948,plain,
( member(sK0(C),C)
| intersection(A,B) = C
| intersect(A,B) ),
inference(copy,[status(thm)],[c_3009]) ).
cnf(c_2959,plain,
( intersection(sK1,sK2) = empty_set
| member(sK0(A),A)
| intersection(sK1,sK2) = A ),
inference(resolve,[status(thm)],[c_2948,c_62]) ).
cnf(c_3010,plain,
( member(sK0(empty_set),empty_set)
| intersection(sK1,sK2) = empty_set ),
inference(factor,[status(thm)],[c_2959]) ).
cnf(c_2962,plain,
intersection(sK1,sK2) = empty_set,
inference(resolve,[status(thm)],[c_33,c_3010]) ).
cnf(c_3011,plain,
( empty_set != empty_set
| intersect(sK1,sK2) ),
inference(paramod,[status(thm)],[c_2962,c_61]) ).
cnf(c_2963,plain,
intersect(sK1,sK2),
inference(copy,[status(thm)],[c_3011]) ).
cnf(c_2965,plain,
member(sK4(sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_2963,c_36]) ).
cnf(c_2966,plain,
member(sK4(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_2963,c_35]) ).
cnf(c_3012,plain,
( ~ member(sK4(sK1,sK2),A)
| member(sK4(sK1,sK2),intersection(sK1,A)) ),
inference(resolve,[status(thm)],[c_37,c_2965]) ).
cnf(c_3013,plain,
member(sK4(sK1,sK2),intersection(sK1,sK2)),
inference(resolve,[status(thm)],[c_3012,c_2966]) ).
cnf(c_3014,plain,
member(sK4(sK1,sK2),empty_set),
inference(paramod,[status(thm)],[c_2962,c_3013]) ).
cnf(c_3006,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_3014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.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
% 0.09/0.35 % DateTime : Sat Sep 26 08:05:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3524218 was started by sandbox on n015,
% 0.09/0.35 % Sat Sep 26 08:05:44 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 12.27/2.00
% 12.27/2.00 % Assigning unary symbol f3 kb_weight 0 and highest precedence (13).
% 12.27/2.00
% 12.27/2.00 % SZS status Theorem for theBenchmark
% 12.27/2.00
% 12.27/2.00 % Proof 1 at 1.22 (+ 0.41) seconds.
% 12.27/2.00 % Length of proof is 34.
% 12.27/2.00 % Level of proof is 10.
% 12.27/2.00 % Maximum clause weight is 31.000.
% 12.27/2.00 % Given clauses 314.
% 12.27/2.00
% 12.27/2.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------