%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET013-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:35:17 AM UTC 2026
% Result : Unsatisfiable 2.56s 1.28s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 93 ( 35 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 73 ( 24 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 2 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_c_equals_d,axiom,
cs != ds,
file('theBenchmark.p',prove_c_equals_d) ).
cnf(c_6,plain,
cs != ds,
inference(clausify,[status(thm)],[prove_c_equals_d]) ).
cnf(c_7,plain,
ds != cs,
inference(copy,[status(thm)],[c_6]) ).
fof(intersection_of_b_and_a_is_d,axiom,
intersection(bs,as) = ds,
file('theBenchmark.p',intersection_of_b_and_a_is_d) ).
cnf(c_8,plain,
intersection(bs,as) = ds,
inference(clausify,[status(thm)],[intersection_of_b_and_a_is_d]) ).
cnf(c_9,plain,
ds = intersection(bs,as),
inference(copy,[status(thm)],[c_8]) ).
fof(intersection_of_a_and_b_is_c,axiom,
intersection(as,bs) = cs,
file('theBenchmark.p',intersection_of_a_and_b_is_c) ).
cnf(c_10,plain,
intersection(as,bs) = cs,
inference(clausify,[status(thm)],[intersection_of_a_and_b_is_c]) ).
cnf(c_11,plain,
cs = intersection(as,bs),
inference(copy,[status(thm)],[c_10]) ).
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_13,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_14,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_15,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_16,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_17,plain,
( A = B
| member(f1(A,B),B)
| member(f1(A,B),A) ),
inference(clausify,[status(thm)],[extensionality2]) ).
cnf(c_1430,plain,
intersection(bs,as) != cs,
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_18,plain,
intersection(bs,as) != intersection(as,bs),
inference(paramod,[status(thm)],[c_11,c_1430]) ).
cnf(c_26,plain,
( member(f1(intersection(A,B),C),A)
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_27,plain,
( member(f1(intersection(A,B),C),B)
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_1431,plain,
( member(f1(A,intersection(B,C)),B)
| A = intersection(B,C)
| member(f1(A,intersection(B,C)),A) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_31,plain,
( member(f1(A,intersection(B,C)),B)
| intersection(B,C) = A
| member(f1(A,intersection(B,C)),A) ),
inference(copy,[status(thm)],[c_1431]) ).
cnf(c_1432,plain,
( member(f1(A,intersection(B,C)),C)
| A = intersection(B,C)
| member(f1(A,intersection(B,C)),A) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_32,plain,
( member(f1(A,intersection(B,C)),C)
| intersection(B,C) = A
| member(f1(A,intersection(B,C)),A) ),
inference(copy,[status(thm)],[c_1432]) ).
cnf(c_111,plain,
( ~ member(f1(intersection(A,B),C),D)
| member(f1(intersection(A,B),C),intersection(D,A))
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C) ),
inference(resolve,[status(thm)],[c_26,c_13]) ).
cnf(c_1433,plain,
( intersection(A,B) = C
| member(f1(intersection(A,B),C),C)
| member(f1(intersection(A,B),C),intersection(B,A))
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C) ),
inference(resolve,[status(thm)],[c_111,c_27]) ).
cnf(c_1434,plain,
( intersection(A,B) = C
| member(f1(intersection(A,B),C),intersection(B,A))
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C) ),
inference(copy,[status(thm)],[c_1433]) ).
cnf(c_892,plain,
( member(f1(intersection(A,B),C),intersection(B,A))
| intersection(A,B) = C
| member(f1(intersection(A,B),C),C) ),
inference(copy,[status(thm)],[c_1434]) ).
cnf(c_896,plain,
( intersection(A,B) = intersection(B,A)
| member(f1(intersection(A,B),intersection(B,A)),intersection(B,A)) ),
inference(factor,[status(thm)],[c_892]) ).
cnf(c_1435,plain,
( intersection(A,B) = intersection(B,A)
| ~ member(f1(intersection(A,B),intersection(B,A)),intersection(A,B))
| intersection(A,B) = intersection(B,A) ),
inference(resolve,[status(thm)],[c_896,c_16]) ).
cnf(c_1088,plain,
( ~ member(f1(intersection(A,B),intersection(B,A)),intersection(A,B))
| intersection(A,B) = intersection(B,A) ),
inference(copy,[status(thm)],[c_1435]) ).
cnf(c_1359,plain,
~ member(f1(intersection(bs,as),intersection(as,bs)),intersection(bs,as)),
inference(resolve,[status(thm)],[c_1088,c_18]) ).
cnf(c_1436,plain,
( member(f1(intersection(bs,as),intersection(as,bs)),bs)
| intersection(as,bs) = intersection(bs,as) ),
inference(resolve,[status(thm)],[c_1359,c_32]) ).
cnf(c_1437,plain,
( member(f1(intersection(bs,as),intersection(as,bs)),bs)
| intersection(bs,as) = intersection(as,bs) ),
inference(copy,[status(thm)],[c_1436]) ).
cnf(c_1411,plain,
member(f1(intersection(bs,as),intersection(as,bs)),bs),
inference(resolve,[status(thm)],[c_18,c_1437]) ).
cnf(c_1438,plain,
( member(f1(intersection(bs,as),intersection(as,bs)),as)
| intersection(as,bs) = intersection(bs,as) ),
inference(resolve,[status(thm)],[c_1359,c_31]) ).
cnf(c_1439,plain,
( member(f1(intersection(bs,as),intersection(as,bs)),as)
| intersection(bs,as) = intersection(as,bs) ),
inference(copy,[status(thm)],[c_1438]) ).
cnf(c_1412,plain,
member(f1(intersection(bs,as),intersection(as,bs)),as),
inference(resolve,[status(thm)],[c_18,c_1439]) ).
cnf(c_1440,plain,
( ~ member(f1(intersection(bs,as),intersection(as,bs)),as)
| ~ member(f1(intersection(bs,as),intersection(as,bs)),bs) ),
inference(resolve,[status(thm)],[c_13,c_1359]) ).
cnf(c_1441,plain,
~ member(f1(intersection(bs,as),intersection(as,bs)),as),
inference(resolve,[status(thm)],[c_1440,c_1411]) ).
cnf(c_1429,plain,
$false,
inference(resolve,[status(thm)],[c_1412,c_1441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET013-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 % Computer : n009.cluster.edu
% 0.10/0.46 % Model : x86_64 x86_64
% 0.10/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.46 % Memory : 8046.5625MB
% 0.10/0.46 % OS : Linux 6.8.0-71-generic
% 0.10/0.46 % CPULimit : 300
% 0.10/0.46 % WCLimit : 300
% 0.10/0.46 % DateTime : Sat Sep 26 06:49:29 UTC 2026
% 0.10/0.47 % CPUTime :
% 0.10/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.47 % Process 3593455 was started by sandbox on n009,
% 0.10/0.47 % Sat Sep 26 06:49:29 2026
% 0.10/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.48
% 0.10/0.48 % From the command line: assign(max_seconds, 300).
% 2.56/1.28
% 2.56/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.56/1.28
% 2.56/1.28 % Proof 1 at 0.28 (+ 0.09) seconds.
% 2.56/1.28 % Length of proof is 24.
% 2.56/1.28 % Level of proof is 8.
% 2.56/1.28 % Maximum clause weight is 28.000.
% 2.56/1.28 % Given clauses 197.
% 2.56/1.28
% 2.56/1.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------