%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.63s 0.56s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 20 unt; 0 def)
% Number of atoms : 182 ( 21 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 209 ( 87 ~; 86 |; 26 &)
% ( 0 <=>; 10 =>; 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 86 ( 0 sgn 22 !; 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(d6_xboole_0,axiom,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
file('theBenchmark.p',d6_xboole_0) ).
fof(dt_k1_finsub_1,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> element(prebool_union2(A,B,C),A) ),
file('theBenchmark.p',dt_k1_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_k1_finsub_1,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> prebool_union2(A,B,C) = set_union2(B,C) ),
file('theBenchmark.p',redefinition_k1_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(t14_finsub_1,conjecture,
! [A,B,C] :
( ( preboolean(C)
& ~ empty(C) )
=> ( ( element(B,C)
& element(A,C) )
=> element(symmetric_difference(A,B),C) ) ),
file('theBenchmark.p',t14_finsub_1) ).
fof(t14_finsub_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( preboolean(C)
& ~ empty(C) )
=> ( ( element(B,C)
& element(A,C) )
=> element(symmetric_difference(A,B),C) ) ),
inference(assume_negation,[status(cth)],[t14_finsub_1]) ).
cnf(c_46,plain,
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(clausify,[status(thm)],[cc2_finsub_1]) ).
cnf(c_47,plain,
( diff_closed(A)
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[cc1_finsub_1]) ).
cnf(c_48,plain,
( cup_closed(A)
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[cc1_finsub_1]) ).
cnf(c_50,plain,
( element(prebool_union2(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(clausify,[status(thm)],[dt_k1_finsub_1]) ).
cnf(c_51,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_54,plain,
( set_union2(B,C) = prebool_union2(A,B,C)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(clausify,[status(thm)],[redefinition_k1_finsub_1]) ).
cnf(c_55,plain,
( prebool_difference(A,B,C) = set_difference(B,C)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(clausify,[status(thm)],[redefinition_k2_finsub_1]) ).
fof(nnf_45,plain,
? [A,B,C] :
( ~ element(symmetric_difference(A,B),C)
& element(B,C)
& element(A,C)
& preboolean(C)
& ~ empty(C) ),
inference(fof_nnf,[status(thm)],[t14_finsub_1_neg]) ).
fof(sk_t14_finsub_1_neg,plain,
( ~ element(symmetric_difference(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_45]) ).
cnf(c_56,negated_conjecture,
preboolean(sK0),
inference(split_conjunct,[status(thm)],[sk_t14_finsub_1_neg]) ).
cnf(c_57,plain,
( ~ diff_closed(A)
| ~ cup_closed(A)
| prebool_difference(A,B,C) = set_difference(B,C)
| ~ element(C,A)
| ~ element(B,A)
| empty(A) ),
inference(resolve,[status(thm)],[c_55,c_46]) ).
cnf(c_58,negated_conjecture,
cup_closed(sK0),
inference(resolve,[status(thm)],[c_56,c_48]) ).
cnf(c_59,plain,
( ~ diff_closed(A)
| ~ cup_closed(A)
| set_union2(B,C) = prebool_union2(A,B,C)
| ~ element(C,A)
| ~ element(B,A)
| empty(A) ),
inference(resolve,[status(thm)],[c_54,c_46]) ).
cnf(c_62,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_51,c_46]) ).
cnf(c_63,plain,
( ~ diff_closed(A)
| ~ cup_closed(A)
| element(prebool_union2(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| empty(A) ),
inference(resolve,[status(thm)],[c_50,c_46]) ).
cnf(c_70,negated_conjecture,
diff_closed(sK0),
inference(resolve,[status(thm)],[c_56,c_47]) ).
cnf(c_86,negated_conjecture,
~ element(symmetric_difference(sK1,sK2),sK0),
inference(split_conjunct,[status(thm)],[sk_t14_finsub_1_neg]) ).
cnf(c_87,negated_conjecture,
element(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t14_finsub_1_neg]) ).
cnf(c_88,negated_conjecture,
element(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t14_finsub_1_neg]) ).
cnf(c_89,negated_conjecture,
~ empty(sK0),
inference(split_conjunct,[status(thm)],[sk_t14_finsub_1_neg]) ).
cnf(c_128,plain,
symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
inference(clausify,[status(thm)],[d6_xboole_0]) ).
cnf(c_135,negated_conjecture,
( ~ diff_closed(sK0)
| prebool_difference(sK0,A,B) = set_difference(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_57,c_58]) ).
cnf(c_677,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_89,c_135]) ).
cnf(c_136,negated_conjecture,
( prebool_difference(sK0,A,B) = set_difference(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_70,c_677]) ).
cnf(c_137,negated_conjecture,
( ~ diff_closed(sK0)
| set_union2(A,B) = prebool_union2(sK0,A,B)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_59,c_58]) ).
cnf(c_678,negated_conjecture,
( ~ diff_closed(sK0)
| prebool_union2(sK0,A,B) = set_union2(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_679,negated_conjecture,
( ~ diff_closed(sK0)
| prebool_union2(sK0,A,B) = set_union2(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_89,c_678]) ).
cnf(c_138,negated_conjecture,
( prebool_union2(sK0,A,B) = set_union2(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_70,c_679]) ).
cnf(c_149,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_62,c_58]) ).
cnf(c_680,negated_conjecture,
( ~ diff_closed(sK0)
| element(prebool_difference(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_89,c_149]) ).
cnf(c_150,negated_conjecture,
( element(prebool_difference(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_70,c_680]) ).
cnf(c_153,negated_conjecture,
( ~ diff_closed(sK0)
| element(prebool_union2(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_63,c_58]) ).
cnf(c_681,negated_conjecture,
( ~ diff_closed(sK0)
| element(prebool_union2(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_89,c_153]) ).
cnf(c_154,negated_conjecture,
( element(prebool_union2(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_70,c_681]) ).
cnf(c_168,negated_conjecture,
~ element(set_union2(set_difference(sK1,sK2),set_difference(sK2,sK1)),sK0),
inference(paramod,[status(thm)],[c_128,c_86]) ).
cnf(c_682,negated_conjecture,
( prebool_difference(sK0,sK1,A) = set_difference(sK1,A)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_136,c_88]) ).
cnf(c_247,negated_conjecture,
prebool_difference(sK0,sK1,sK2) = set_difference(sK1,sK2),
inference(resolve,[status(thm)],[c_682,c_87]) ).
cnf(c_683,negated_conjecture,
( prebool_difference(sK0,sK2,A) = set_difference(sK2,A)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_136,c_87]) ).
cnf(c_249,negated_conjecture,
prebool_difference(sK0,sK2,sK1) = set_difference(sK2,sK1),
inference(resolve,[status(thm)],[c_683,c_88]) ).
cnf(c_684,negated_conjecture,
( element(prebool_difference(sK0,sK1,A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_150,c_88]) ).
cnf(c_685,negated_conjecture,
element(prebool_difference(sK0,sK1,sK2),sK0),
inference(resolve,[status(thm)],[c_684,c_87]) ).
cnf(c_286,negated_conjecture,
element(set_difference(sK1,sK2),sK0),
inference(paramod,[status(thm)],[c_247,c_685]) ).
cnf(c_686,negated_conjecture,
( element(prebool_difference(sK0,sK2,A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_150,c_87]) ).
cnf(c_687,negated_conjecture,
element(prebool_difference(sK0,sK2,sK1),sK0),
inference(resolve,[status(thm)],[c_686,c_88]) ).
cnf(c_288,negated_conjecture,
element(set_difference(sK2,sK1),sK0),
inference(paramod,[status(thm)],[c_249,c_687]) ).
cnf(c_688,negated_conjecture,
( element(prebool_union2(sK0,set_difference(sK1,sK2),A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_154,c_286]) ).
cnf(c_646,negated_conjecture,
element(prebool_union2(sK0,set_difference(sK1,sK2),set_difference(sK2,sK1)),sK0),
inference(resolve,[status(thm)],[c_688,c_288]) ).
cnf(c_689,negated_conjecture,
( prebool_union2(sK0,set_difference(sK1,sK2),A) = set_union2(set_difference(sK1,sK2),A)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_138,c_286]) ).
cnf(c_661,negated_conjecture,
prebool_union2(sK0,set_difference(sK1,sK2),set_difference(sK2,sK1)) = set_union2(set_difference(sK1,sK2),set_difference(sK2,sK1)),
inference(resolve,[status(thm)],[c_689,c_288]) ).
cnf(c_690,negated_conjecture,
element(set_union2(set_difference(sK1,sK2),set_difference(sK2,sK1)),sK0),
inference(paramod,[status(thm)],[c_661,c_646]) ).
cnf(c_676,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_168,c_690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 08:36:54 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 3227743 was started by sandbox2 on n008,
% 0.12/0.37 % Sat Sep 26 08:36:54 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.63/0.56
% 0.63/0.56 % SZS status Theorem for theBenchmark
% 0.63/0.56
% 0.63/0.56 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.63/0.56 % Length of proof is 43.
% 0.63/0.56 % Level of proof is 8.
% 0.63/0.56 % Maximum clause weight is 31.000.
% 0.63/0.56 % Given clauses 107.
% 0.63/0.56
% 0.63/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------