%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU102+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:45:01 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 116 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 51 ~; 46 |; 20 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_finsub_1,axiom,
! [A] :
( preboolean(A)
=> ( diff_closed(A)
& cup_closed(A) ) ),
file('theBenchmark.p',cc1_finsub_1) ).
fof(cc2_finsub_1,axiom,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
=> preboolean(A) ),
file('theBenchmark.p',cc2_finsub_1) ).
fof(dt_k2_finsub_1,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> element(prebool_difference(A,B,C),A) ),
file('theBenchmark.p',dt_k2_finsub_1) ).
fof(redefinition_k2_finsub_1,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> prebool_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k2_finsub_1) ).
fof(t48_xboole_1,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t13_finsub_1,conjecture,
! [A,B,C] :
( ( preboolean(C)
& ~ empty(C) )
=> ( ( element(B,C)
& element(A,C) )
=> element(set_intersection2(A,B),C) ) ),
file('theBenchmark.p',t13_finsub_1) ).
fof(t13_finsub_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( preboolean(C)
& ~ empty(C) )
=> ( ( element(B,C)
& element(A,C) )
=> element(set_intersection2(A,B),C) ) ),
inference(assume_negation,[status(cth)],[t13_finsub_1]) ).
cnf(c_38,plain,
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(clausify,[status(thm)],[cc2_finsub_1]) ).
cnf(c_39,plain,
( diff_closed(A)
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[cc1_finsub_1]) ).
cnf(c_40,plain,
( cup_closed(A)
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[cc1_finsub_1]) ).
cnf(c_41,plain,
( element(prebool_difference(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(clausify,[status(thm)],[dt_k2_finsub_1]) ).
cnf(c_43,plain,
( set_difference(B,C) = prebool_difference(A,B,C)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(clausify,[status(thm)],[redefinition_k2_finsub_1]) ).
fof(nnf_37,plain,
? [A,B,C] :
( ~ element(set_intersection2(A,B),C)
& element(B,C)
& element(A,C)
& preboolean(C)
& ~ empty(C) ),
inference(fof_nnf,[status(thm)],[t13_finsub_1_neg]) ).
fof(sk_t13_finsub_1_neg,plain,
( ~ element(set_intersection2(sK1,sK2),sK0)
& element(sK2,sK0)
& element(sK1,sK0)
& preboolean(sK0)
& ~ empty(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK0)],[nnf_37]) ).
cnf(c_44,negated_conjecture,
preboolean(sK0),
inference(split_conjunct,[status(thm)],[sk_t13_finsub_1_neg]) ).
cnf(c_45,plain,
( ~ diff_closed(A)
| ~ cup_closed(A)
| set_difference(B,C) = prebool_difference(A,B,C)
| ~ element(C,A)
| ~ element(B,A)
| empty(A) ),
inference(resolve,[status(thm)],[c_43,c_38]) ).
cnf(c_46,negated_conjecture,
cup_closed(sK0),
inference(resolve,[status(thm)],[c_44,c_40]) ).
cnf(c_48,plain,
( ~ diff_closed(A)
| ~ cup_closed(A)
| element(prebool_difference(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| empty(A) ),
inference(resolve,[status(thm)],[c_41,c_38]) ).
cnf(c_54,negated_conjecture,
diff_closed(sK0),
inference(resolve,[status(thm)],[c_44,c_39]) ).
cnf(c_62,negated_conjecture,
~ element(set_intersection2(sK1,sK2),sK0),
inference(split_conjunct,[status(thm)],[sk_t13_finsub_1_neg]) ).
cnf(c_63,negated_conjecture,
element(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t13_finsub_1_neg]) ).
cnf(c_64,negated_conjecture,
element(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t13_finsub_1_neg]) ).
cnf(c_65,negated_conjecture,
~ empty(sK0),
inference(split_conjunct,[status(thm)],[sk_t13_finsub_1_neg]) ).
cnf(c_72,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(clausify,[status(thm)],[t48_xboole_1]) ).
cnf(c_73,plain,
set_intersection2(A,B) = set_difference(A,set_difference(A,B)),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_110,negated_conjecture,
( ~ diff_closed(sK0)
| set_difference(A,B) = prebool_difference(sK0,A,B)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_45,c_46]) ).
cnf(c_638,negated_conjecture,
( ~ diff_closed(sK0)
| prebool_difference(sK0,A,B) = set_difference(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(copy,[status(thm)],[c_110]) ).
cnf(c_639,negated_conjecture,
( ~ diff_closed(sK0)
| prebool_difference(sK0,A,B) = set_difference(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_65,c_638]) ).
cnf(c_111,negated_conjecture,
( prebool_difference(sK0,A,B) = set_difference(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_54,c_639]) ).
cnf(c_116,negated_conjecture,
( ~ diff_closed(sK0)
| element(prebool_difference(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_48,c_46]) ).
cnf(c_640,negated_conjecture,
( ~ diff_closed(sK0)
| element(prebool_difference(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_65,c_116]) ).
cnf(c_117,negated_conjecture,
( element(prebool_difference(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_54,c_640]) ).
cnf(c_122,negated_conjecture,
~ element(set_difference(sK1,set_difference(sK1,sK2)),sK0),
inference(paramod,[status(thm)],[c_73,c_62]) ).
cnf(c_175,plain,
( prebool_difference(sK0,sK1,A) = set_difference(sK1,A)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_111,c_64]) ).
cnf(c_185,plain,
( element(prebool_difference(sK0,sK1,A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_117,c_64]) ).
cnf(c_601,plain,
element(prebool_difference(sK0,sK1,sK2),sK0),
inference(resolve,[status(thm)],[c_185,c_63]) ).
cnf(c_619,plain,
prebool_difference(sK0,sK1,sK2) = set_difference(sK1,sK2),
inference(resolve,[status(thm)],[c_175,c_63]) ).
cnf(c_621,plain,
element(set_difference(sK1,sK2),sK0),
inference(paramod,[status(thm)],[c_619,c_601]) ).
cnf(c_626,plain,
element(prebool_difference(sK0,sK1,set_difference(sK1,sK2)),sK0),
inference(resolve,[status(thm)],[c_621,c_185]) ).
cnf(c_629,plain,
prebool_difference(sK0,sK1,set_difference(sK1,sK2)) = set_difference(sK1,set_difference(sK1,sK2)),
inference(resolve,[status(thm)],[c_621,c_175]) ).
cnf(c_641,plain,
element(set_difference(sK1,set_difference(sK1,sK2)),sK0),
inference(paramod,[status(thm)],[c_629,c_626]) ).
cnf(c_637,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_122,c_641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU102+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.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 08:36:16 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2663558 was started by sandbox on n014,
% 0.09/0.36 % Sat Sep 26 08:36:16 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.13/0.44 % Length of proof is 35.
% 0.13/0.44 % Level of proof is 9.
% 0.13/0.44 % Maximum clause weight is 32.000.
% 0.13/0.44 % Given clauses 177.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------