%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:35:16 AM UTC 2026
% Result : Unsatisfiable 120.96s 16.08s
% Output : CNFRefutation 120.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 18 unt; 0 def)
% Number of atoms : 180 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 176 ( 70 ~; 106 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 93 ( 5 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_axiom1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(g(VAR_0,VAR_1,VAR_2),VAR_2)
| member(g(VAR_0,VAR_1,VAR_2),VAR_1)
| member(g(VAR_0,VAR_1,VAR_2),VAR_0)
| union(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',union_axiom1) ).
cnf(c_7,plain,
( member(g(A,B,C),C)
| member(g(A,B,C),B)
| member(g(A,B,C),A)
| union(A,B,C) ),
inference(clausify,[status(thm)],[union_axiom1]) ).
fof(member_of_set2_is_member_of_union,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_2)
| ~ member(VAR_3,VAR_1)
| ~ union(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_set2_is_member_of_union) ).
cnf(c_8,plain,
( member(D,C)
| ~ member(D,B)
| ~ union(A,B,C) ),
inference(clausify,[status(thm)],[member_of_set2_is_member_of_union]) ).
fof(union_axiom2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( union(VAR_0,VAR_1,VAR_2)
| ~ member(g(VAR_0,VAR_1,VAR_2),VAR_2)
| ~ member(g(VAR_0,VAR_1,VAR_2),VAR_0) ),
file('theBenchmark.p',union_axiom2) ).
cnf(c_11,plain,
( union(A,B,C)
| ~ member(g(A,B,C),C)
| ~ member(g(A,B,C),A) ),
inference(clausify,[status(thm)],[union_axiom2]) ).
fof(union_axiom3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( union(VAR_0,VAR_1,VAR_2)
| ~ member(g(VAR_0,VAR_1,VAR_2),VAR_2)
| ~ member(g(VAR_0,VAR_1,VAR_2),VAR_1) ),
file('theBenchmark.p',union_axiom3) ).
cnf(c_12,plain,
( union(A,B,C)
| ~ member(g(A,B,C),C)
| ~ member(g(A,B,C),B) ),
inference(clausify,[status(thm)],[union_axiom3]) ).
fof(prove_cDa_union_cDb_is_cD_aIb,axiom,
~ union(cDa,cDb,cD_aIb),
file('theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
cnf(c_13,plain,
~ union(cDa,cDb,cD_aIb),
inference(clausify,[status(thm)],[prove_cDa_union_cDb_is_cD_aIb]) ).
fof(member_of_both_is_member_of_intersection,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_2)
| ~ member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_1)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_both_is_member_of_intersection) ).
cnf(c_14,plain,
( member(D,C)
| ~ member(D,A)
| ~ member(D,B)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_both_is_member_of_intersection]) ).
fof(a_intersection_b,axiom,
intersection(a,b,aIb),
file('theBenchmark.p',a_intersection_b) ).
cnf(c_18,plain,
intersection(a,b,aIb),
inference(clausify,[status(thm)],[a_intersection_b]) ).
fof(member_of_intersection_is_member_of_set2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_1)
| ~ member(VAR_3,VAR_2)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_intersection_is_member_of_set2) ).
cnf(c_19,plain,
( member(D,B)
| ~ member(D,C)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_intersection_is_member_of_set2]) ).
fof(member_of_intersection_is_member_of_set1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_intersection_is_member_of_set1) ).
cnf(c_20,plain,
( member(D,A)
| ~ member(D,C)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_intersection_is_member_of_set1]) ).
fof(member_of_difference_or_set2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,VAR_2)
| member(VAR_0,VAR_3)
| ~ difference(VAR_1,VAR_2,VAR_3)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',member_of_difference_or_set2) ).
cnf(c_22,plain,
( member(A,C)
| member(A,D)
| ~ difference(B,C,D)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[member_of_difference_or_set2]) ).
fof(not_member_of_difference,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ difference(VAR_3,VAR_1,VAR_2)
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',not_member_of_difference) ).
cnf(c_23,plain,
( ~ difference(D,B,C)
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[not_member_of_difference]) ).
fof(member_of_difference,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ difference(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_difference) ).
cnf(c_24,plain,
( member(D,A)
| ~ member(D,C)
| ~ difference(A,B,C) ),
inference(clausify,[status(thm)],[member_of_difference]) ).
fof(c_minus_a,axiom,
difference(c,a,cDa),
file('theBenchmark.p',c_minus_a) ).
cnf(c_27,plain,
difference(c,a,cDa),
inference(clausify,[status(thm)],[c_minus_a]) ).
fof(c_minus_b,axiom,
difference(c,b,cDb),
file('theBenchmark.p',c_minus_b) ).
cnf(c_28,plain,
difference(c,b,cDb),
inference(clausify,[status(thm)],[c_minus_b]) ).
fof(c_minus_aIb,axiom,
difference(c,aIb,cD_aIb),
file('theBenchmark.p',c_minus_aIb) ).
cnf(c_29,plain,
difference(c,aIb,cD_aIb),
inference(clausify,[status(thm)],[c_minus_aIb]) ).
cnf(c_30,plain,
( member(A,c)
| ~ member(A,cD_aIb) ),
inference(resolve,[status(thm)],[c_29,c_24]) ).
cnf(c_31,plain,
( ~ member(A,cD_aIb)
| ~ member(A,aIb) ),
inference(resolve,[status(thm)],[c_29,c_23]) ).
cnf(c_32,plain,
( member(A,aIb)
| member(A,cD_aIb)
| ~ member(A,c) ),
inference(resolve,[status(thm)],[c_29,c_22]) ).
cnf(c_33,plain,
( member(A,c)
| ~ member(A,cDb) ),
inference(resolve,[status(thm)],[c_28,c_24]) ).
cnf(c_34,plain,
( ~ member(A,cDb)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_35,plain,
( member(A,b)
| member(A,cDb)
| ~ member(A,c) ),
inference(resolve,[status(thm)],[c_28,c_22]) ).
cnf(c_36,plain,
( member(A,c)
| ~ member(A,cDa) ),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_37,plain,
( ~ member(A,cDa)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_38,plain,
( member(A,a)
| member(A,cDa)
| ~ member(A,c) ),
inference(resolve,[status(thm)],[c_27,c_22]) ).
cnf(c_48,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolve,[status(thm)],[c_13,c_7]) ).
cnf(c_49,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_50,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDb) ),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_59,plain,
( member(D,C)
| ~ member(D,B)
| member(g(A,B,C),C)
| member(g(A,B,C),B)
| member(g(A,B,C),A) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_65,plain,
( member(A,aIb)
| ~ member(A,a)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_14,c_18]) ).
cnf(c_69,plain,
( member(A,b)
| ~ member(A,aIb) ),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_73,plain,
( member(A,a)
| ~ member(A,aIb) ),
inference(resolve,[status(thm)],[c_20,c_18]) ).
cnf(c_105,plain,
( member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolve,[status(thm)],[c_48,c_33]) ).
cnf(c_191,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),B)
| member(g(A,cDb,B),B)
| member(g(A,cDb,B),cDb)
| member(g(A,cDb,B),A) ),
inference(resolve,[status(thm)],[c_59,c_48]) ).
cnf(c_194,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(A,cDb,cD_aIb),cD_aIb)
| member(g(A,cDb,cD_aIb),cDb)
| member(g(A,cDb,cD_aIb),A) ),
inference(factor,[status(thm)],[c_191]) ).
cnf(c_41999,plain,
( member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolve,[status(thm)],[c_105,c_36]) ).
cnf(c_4849,plain,
( member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(copy,[status(thm)],[c_41999]) ).
cnf(c_42000,plain,
( member(g(cDa,cDb,cD_aIb),c)
| member(g(cDa,cDb,cD_aIb),c) ),
inference(resolve,[status(thm)],[c_4849,c_30]) ).
cnf(c_4906,plain,
member(g(cDa,cDb,cD_aIb),c),
inference(copy,[status(thm)],[c_42000]) ).
cnf(c_4965,plain,
( member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolve,[status(thm)],[c_4906,c_38]) ).
cnf(c_4966,plain,
( member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(resolve,[status(thm)],[c_4906,c_35]) ).
cnf(c_4967,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolve,[status(thm)],[c_4906,c_32]) ).
cnf(c_10031,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(resolve,[status(thm)],[c_4966,c_65]) ).
cnf(c_10699,plain,
( member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolve,[status(thm)],[c_4967,c_73]) ).
cnf(c_10703,plain,
( member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolve,[status(thm)],[c_4967,c_69]) ).
cnf(c_18082,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolve,[status(thm)],[c_10699,c_37]) ).
cnf(c_18911,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolve,[status(thm)],[c_10703,c_34]) ).
cnf(c_42001,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolve,[status(thm)],[c_18911,c_194]) ).
cnf(c_42002,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(copy,[status(thm)],[c_42001]) ).
cnf(c_42003,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(copy,[status(thm)],[c_42002]) ).
cnf(c_34331,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(copy,[status(thm)],[c_42003]) ).
cnf(c_42004,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolve,[status(thm)],[c_34331,c_18082]) ).
cnf(c_41861,plain,
member(g(cDa,cDb,cD_aIb),cD_aIb),
inference(copy,[status(thm)],[c_42004]) ).
cnf(c_41868,plain,
~ member(g(cDa,cDb,cD_aIb),cDb),
inference(resolve,[status(thm)],[c_41861,c_50]) ).
cnf(c_41869,plain,
~ member(g(cDa,cDb,cD_aIb),cDa),
inference(resolve,[status(thm)],[c_41861,c_49]) ).
cnf(c_41910,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ member(g(cDa,cDb,cD_aIb),a) ),
inference(resolve,[status(thm)],[c_41868,c_10031]) ).
cnf(c_41969,plain,
member(g(cDa,cDb,cD_aIb),a),
inference(resolve,[status(thm)],[c_41869,c_4965]) ).
cnf(c_41978,plain,
member(g(cDa,cDb,cD_aIb),aIb),
inference(resolve,[status(thm)],[c_41969,c_41910]) ).
cnf(c_42005,plain,
~ member(g(cDa,cDb,cD_aIb),aIb),
inference(resolve,[status(thm)],[c_31,c_41861]) ).
cnf(c_41998,plain,
$false,
inference(resolve,[status(thm)],[c_41978,c_42005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 06:48:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1041900 was started by sandbox on n004,
% 0.10/0.37 % Sat Sep 26 06:48:51 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 120.96/16.08
% 120.96/16.08 % given #500 (T,wt=11): 15211 member(k(aIb,c,c),c) | member(member_of_1_not_of_2(a,c),a). [factor(15166,a,b)].
% 120.96/16.08
% 120.96/16.08 % given #1000 (T,wt=12): 17491 member(k(cD_aIb,c,c),cDb) | -member(g(cDb,b,cDb),cDb). [factor(17458,a,c)].
% 120.96/16.08
% 120.96/16.08 % given #1500 (T,wt=11): 27561 member(member_of_1_not_of_2(a,b),a) | -member(h(a,cDa,a),cD_aIb). [resolve(25620,b,31,a)].
% 120.96/16.08
% 120.96/16.08 % given #2000 (T,wt=11): 33711 member(member_of_1_not_of_2(cD_aIb,b),c) | -member(h(aIb,cD_aIb,cD_aIb),cDb). [resolve(32814,a,34,a)].
% 120.96/16.08
% 120.96/16.08 % given #2500 (T,wt=12): 22336 member(k(cD_aIb,c,c),cD_aIb) | member(k(aIb,c,aIb),b). [resolve(17349,a,69,a)].
% 120.96/16.08
% 120.96/16.08 % given #3000 (A,wt=18): 5006 -member(g(A,c,B),A) | -member(g(A,c,B),B) | member(k(c,c,c),B). [resolve(4909,a,56,c)].
% 120.96/16.08
% 120.96/16.08 % SZS status Unsatisfiable for theBenchmark
% 120.96/16.08
% 120.96/16.08 % Proof 1 at 11.42 (+ 3.35) seconds.
% 120.96/16.08 % Length of proof is 52.
% 120.96/16.08 % Level of proof is 13.
% 120.96/16.08 % Maximum clause weight is 36.000.
% 120.96/16.08 % Given clauses 3298.
% 120.96/16.08
% 120.96/16.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------