%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:35:19 AM UTC 2026
% Result : Unsatisfiable 11.46s 1.82s
% Output : CNFRefutation 11.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 18 unt; 0 def)
% Number of atoms : 110 ( 52 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 86 ( 25 ~; 61 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_c_equals_d,axiom,
cs != ds,
file('theBenchmark.p',prove_c_equals_d) ).
cnf(c_9,plain,
cs != ds,
inference(clausify,[status(thm)],[prove_c_equals_d]) ).
cnf(c_10,plain,
ds != cs,
inference(copy,[status(thm)],[c_9]) ).
fof(b_union_a_is_d,axiom,
union(bs,as) = ds,
file('theBenchmark.p',b_union_a_is_d) ).
cnf(c_11,plain,
union(bs,as) = ds,
inference(clausify,[status(thm)],[b_union_a_is_d]) ).
cnf(c_12,plain,
ds = union(bs,as),
inference(copy,[status(thm)],[c_11]) ).
fof(a_union_b_is_c,axiom,
union(as,bs) = cs,
file('theBenchmark.p',a_union_b_is_c) ).
cnf(c_13,plain,
union(as,bs) = cs,
inference(clausify,[status(thm)],[a_union_b_is_c]) ).
cnf(c_14,plain,
cs = union(as,bs),
inference(copy,[status(thm)],[c_13]) ).
fof(union,axiom,
! [VAR_0,VAR_1] : union(VAR_0,VAR_1) = complement(intersection(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',union) ).
cnf(c_16,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(clausify,[status(thm)],[union]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1)
| member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection3) ).
cnf(c_18,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection3]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_19,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_20,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(extensionality3,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ member(f1(VAR_0,VAR_1),VAR_1)
| ~ member(f1(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',extensionality3) ).
cnf(c_21,plain,
( A = B
| ~ member(f1(A,B),B)
| ~ member(f1(A,B),A) ),
inference(clausify,[status(thm)],[extensionality3]) ).
fof(extensionality2,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| member(f1(VAR_0,VAR_1),VAR_1)
| member(f1(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',extensionality2) ).
cnf(c_22,plain,
( A = B
| member(f1(A,B),B)
| member(f1(A,B),A) ),
inference(clausify,[status(thm)],[extensionality2]) ).
cnf(c_4057,plain,
union(bs,as) != cs,
inference(paramod,[status(thm)],[c_12,c_10]) ).
cnf(c_4058,plain,
complement(intersection(complement(bs),complement(as))) != cs,
inference(paramod,[status(thm)],[c_16,c_4057]) ).
cnf(c_4059,plain,
complement(intersection(complement(bs),complement(as))) != union(as,bs),
inference(paramod,[status(thm)],[c_14,c_4058]) ).
cnf(c_23,plain,
complement(intersection(complement(bs),complement(as))) != complement(intersection(complement(as),complement(bs))),
inference(paramod,[status(thm)],[c_16,c_4059]) ).
cnf(c_45,plain,
( member(f1(intersection(A,B),C),A)
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_46,plain,
( member(f1(intersection(A,B),C),B)
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_4060,plain,
( member(f1(A,intersection(B,C)),B)
| A = intersection(B,C)
| member(f1(A,intersection(B,C)),A) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_51,plain,
( member(f1(A,intersection(B,C)),B)
| intersection(B,C) = A
| member(f1(A,intersection(B,C)),A) ),
inference(copy,[status(thm)],[c_4060]) ).
cnf(c_4061,plain,
( member(f1(A,intersection(B,C)),C)
| A = intersection(B,C)
| member(f1(A,intersection(B,C)),A) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_52,plain,
( member(f1(A,intersection(B,C)),C)
| intersection(B,C) = A
| member(f1(A,intersection(B,C)),A) ),
inference(copy,[status(thm)],[c_4061]) ).
cnf(c_4062,plain,
( intersection(A,B) = C
| member(f1(intersection(A,B),C),C)
| ~ member(f1(intersection(A,B),C),D)
| member(f1(intersection(A,B),C),intersection(B,D)) ),
inference(resolve,[status(thm)],[c_18,c_46]) ).
cnf(c_4063,plain,
( intersection(A,B) = C
| member(f1(intersection(A,B),C),C)
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C)
| member(f1(intersection(A,B),C),intersection(B,A)) ),
inference(resolve,[status(thm)],[c_4062,c_45]) ).
cnf(c_4064,plain,
( intersection(A,B) = C
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C)
| member(f1(intersection(A,B),C),intersection(B,A)) ),
inference(copy,[status(thm)],[c_4063]) ).
cnf(c_2860,plain,
( intersection(A,B) = C
| member(f1(intersection(A,B),C),C)
| member(f1(intersection(A,B),C),intersection(B,A)) ),
inference(copy,[status(thm)],[c_4064]) ).
cnf(c_2920,plain,
( intersection(A,B) = intersection(B,A)
| member(f1(intersection(A,B),intersection(B,A)),intersection(B,A)) ),
inference(factor,[status(thm)],[c_2860]) ).
cnf(c_4065,plain,
( intersection(B,C) = A
| member(f1(A,intersection(B,C)),A)
| ~ member(f1(A,intersection(B,C)),D)
| member(f1(A,intersection(B,C)),intersection(C,D)) ),
inference(resolve,[status(thm)],[c_18,c_52]) ).
cnf(c_4066,plain,
( intersection(B,C) = A
| member(f1(A,intersection(B,C)),A)
| intersection(B,C) = A
| member(f1(A,intersection(B,C)),A)
| member(f1(A,intersection(B,C)),intersection(C,B)) ),
inference(resolve,[status(thm)],[c_4065,c_51]) ).
cnf(c_4067,plain,
( intersection(B,C) = A
| intersection(B,C) = A
| member(f1(A,intersection(B,C)),A)
| member(f1(A,intersection(B,C)),intersection(C,B)) ),
inference(copy,[status(thm)],[c_4066]) ).
cnf(c_3271,plain,
( intersection(B,C) = A
| member(f1(A,intersection(B,C)),A)
| member(f1(A,intersection(B,C)),intersection(C,B)) ),
inference(copy,[status(thm)],[c_4067]) ).
cnf(c_3301,plain,
( intersection(B,A) = intersection(A,B)
| member(f1(intersection(A,B),intersection(B,A)),intersection(A,B)) ),
inference(factor,[status(thm)],[c_3271]) ).
cnf(c_4068,plain,
( intersection(B,A) = intersection(A,B)
| intersection(A,B) = intersection(B,A)
| ~ member(f1(intersection(A,B),intersection(B,A)),intersection(B,A)) ),
inference(resolve,[status(thm)],[c_21,c_3301]) ).
cnf(c_4069,plain,
( intersection(A,B) = intersection(B,A)
| intersection(B,A) = intersection(A,B)
| intersection(A,B) = intersection(B,A) ),
inference(resolve,[status(thm)],[c_4068,c_2920]) ).
cnf(c_3963,plain,
( intersection(B,A) = intersection(A,B)
| intersection(A,B) = intersection(B,A) ),
inference(copy,[status(thm)],[c_4069]) ).
cnf(c_4070,plain,
( complement(intersection(complement(as),complement(bs))) != complement(intersection(complement(as),complement(bs)))
| intersection(complement(as),complement(bs)) = intersection(complement(bs),complement(as)) ),
inference(paramod,[status(thm)],[c_3963,c_23]) ).
cnf(c_4071,plain,
( complement(intersection(complement(as),complement(bs))) != complement(intersection(complement(as),complement(bs)))
| intersection(complement(bs),complement(as)) = intersection(complement(as),complement(bs)) ),
inference(copy,[status(thm)],[c_4070]) ).
cnf(c_3970,plain,
intersection(complement(bs),complement(as)) = intersection(complement(as),complement(bs)),
inference(copy,[status(thm)],[c_4071]) ).
cnf(c_4072,plain,
complement(intersection(complement(as),complement(bs))) != complement(intersection(complement(as),complement(bs))),
inference(paramod,[status(thm)],[c_3970,c_23]) ).
cnf(c_4056,plain,
$false,
inference(copy,[status(thm)],[c_4072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 06:51:00 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 3599498 was started by sandbox2 on n009,
% 0.12/0.36 % Sat Sep 26 06:51:00 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 11.46/1.82
% 11.46/1.82 % Assigning unary symbol complement kb_weight 0 and highest precedence (12).
% 11.46/1.82
% 11.46/1.82 % SZS status Unsatisfiable for theBenchmark
% 11.46/1.82
% 11.46/1.82 % Proof 1 at 1.17 (+ 0.26) seconds.
% 11.46/1.82 % Length of proof is 24.
% 11.46/1.82 % Level of proof is 6.
% 11.46/1.82 % Maximum clause weight is 36.000.
% 11.46/1.82 % Given clauses 167.
% 11.46/1.82
% 11.46/1.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------