%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU107+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 : n010.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 08:45:02 AM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 15 unt; 0 def)
% Number of atoms : 84 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 80 ( 32 ~; 30 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 45 ( 1 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t18_finsub_1,conjecture,
! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
file('theBenchmark.p',t18_finsub_1) ).
fof(t18_finsub_1_neg,negated_conjecture,
~ ! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
inference(assume_negation,[status(cth)],[t18_finsub_1]) ).
cnf(c_36,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_38,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_32,plain,
? [A] :
( ~ in(empty_set,A)
& preboolean(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t18_finsub_1_neg]) ).
fof(sk_t18_finsub_1_neg,plain,
( ~ in(empty_set,sK0)
& preboolean(sK0)
& ~ empty(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_32]) ).
cnf(c_39,negated_conjecture,
preboolean(sK0),
inference(split_conjunct,[status(thm)],[sk_t18_finsub_1_neg]) ).
cnf(c_45,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(clausify,[status(thm)],[t37_xboole_1]) ).
cnf(c_47,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_53,plain,
set_difference(A,A) = empty_set,
inference(resolve,[status(thm)],[c_45,c_47]) ).
cnf(c_55,negated_conjecture,
( element(prebool_difference(sK0,A,B),sK0)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_39,c_36]) ).
cnf(c_56,negated_conjecture,
( set_difference(A,B) = prebool_difference(sK0,A,B)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_39,c_38]) ).
cnf(c_57,negated_conjecture,
( prebool_difference(sK0,A,B) = set_difference(A,B)
| ~ element(B,sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_62,negated_conjecture,
~ in(empty_set,sK0),
inference(split_conjunct,[status(thm)],[sk_t18_finsub_1_neg]) ).
cnf(c_63,negated_conjecture,
~ empty(sK0),
inference(split_conjunct,[status(thm)],[sk_t18_finsub_1_neg]) ).
cnf(c_71,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
fof(nnf_7,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(sk_existence_m1_subset_1,plain,
! [A] : element(sK1(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(B,sK1(A))],[nnf_7]) ).
cnf(c_94,plain,
element(sK1(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
cnf(c_160,plain,
( element(prebool_difference(sK0,A,A),sK0)
| ~ element(A,sK0)
| empty(sK0) ),
inference(factor,[status(thm)],[c_55]) ).
cnf(c_106,negated_conjecture,
( element(prebool_difference(sK0,A,A),sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_63,c_160]) ).
cnf(c_161,plain,
( prebool_difference(sK0,A,A) = set_difference(A,A)
| ~ element(A,sK0)
| empty(sK0) ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_162,plain,
( prebool_difference(sK0,A,A) = empty_set
| ~ element(A,sK0)
| empty(sK0) ),
inference(paramod,[status(thm)],[c_53,c_161]) ).
cnf(c_107,negated_conjecture,
( prebool_difference(sK0,A,A) = empty_set
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_63,c_162]) ).
cnf(c_163,negated_conjecture,
( in(A,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_71,c_63]) ).
cnf(c_114,negated_conjecture,
~ element(empty_set,sK0),
inference(resolve,[status(thm)],[c_163,c_62]) ).
cnf(c_157,plain,
element(prebool_difference(sK0,sK1(sK0),sK1(sK0)),sK0),
inference(resolve,[status(thm)],[c_106,c_94]) ).
cnf(c_158,plain,
prebool_difference(sK0,sK1(sK0),sK1(sK0)) = empty_set,
inference(resolve,[status(thm)],[c_107,c_94]) ).
cnf(c_164,plain,
element(empty_set,sK0),
inference(paramod,[status(thm)],[c_158,c_157]) ).
cnf(c_159,plain,
$false,
inference(resolve,[status(thm)],[c_114,c_164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n010.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 26 08:36:44 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 2925056 was started by sandbox on n010,
% 0.07/0.34 % Sat Sep 26 08:36:44 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.07/0.36
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36
% 0.07/0.36 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/0.36 % Length of proof is 26.
% 0.07/0.36 % Level of proof is 6.
% 0.07/0.36 % Maximum clause weight is 16.000.
% 0.07/0.36 % Given clauses 46.
% 0.07/0.36
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------