%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU308+1 : TPTP v9.3.1. Released v3.3.0.
% 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 08:45:46 AM UTC 2026
% Result : Theorem 0.16s 0.43s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 45 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 13 ~; 6 |; 5 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 27 ( 1 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(d3_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',d3_pre_topc) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(t17_pre_topc,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
file('theBenchmark.p',t17_pre_topc) ).
fof(t17_pre_topc_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
inference(assume_negation,[status(cth)],[t17_pre_topc]) ).
cnf(c_55,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_56,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_59,plain,
( the_carrier(A) = cast_as_carrier_subset(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d3_pre_topc]) ).
fof(nnf_53,plain,
? [A] :
( ? [B] :
( subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) != subset_complement(the_carrier(A),B)
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t17_pre_topc_neg]) ).
fof(sk_t17_pre_topc_neg,plain,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1) != subset_complement(the_carrier(sK0),sK1)
& element(sK1,powerset(the_carrier(sK0)))
& one_sorted_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_53]) ).
cnf(c_60,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t17_pre_topc_neg]) ).
cnf(c_62,negated_conjecture,
the_carrier(sK0) = cast_as_carrier_subset(sK0),
inference(resolve,[status(thm)],[c_60,c_59]) ).
cnf(c_63,negated_conjecture,
cast_as_carrier_subset(sK0) = the_carrier(sK0),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_68,negated_conjecture,
subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1) != subset_complement(the_carrier(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_t17_pre_topc_neg]) ).
cnf(c_69,negated_conjecture,
subset_difference(the_carrier(sK0),the_carrier(sK0),sK1) != subset_complement(the_carrier(sK0),sK1),
inference(paramod,[status(thm)],[c_63,c_68]) ).
cnf(c_70,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(split_conjunct,[status(thm)],[sk_t17_pre_topc_neg]) ).
cnf(c_71,plain,
( subset_complement(B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[d5_subset_1]) ).
cnf(c_75,plain,
( subset_difference(B,A,C) = set_difference(A,C)
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[redefinition_k6_subset_1]) ).
cnf(c_143,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_56,c_55]) ).
cnf(c_147,plain,
subset_complement(the_carrier(sK0),sK1) = set_difference(the_carrier(sK0),sK1),
inference(resolve,[status(thm)],[c_71,c_70]) ).
cnf(c_148,negated_conjecture,
subset_difference(the_carrier(sK0),the_carrier(sK0),sK1) != set_difference(the_carrier(sK0),sK1),
inference(paramod,[status(thm)],[c_147,c_69]) ).
cnf(c_283,negated_conjecture,
( subset_difference(the_carrier(sK0),A,sK1) = set_difference(A,sK1)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_75,c_70]) ).
cnf(c_284,negated_conjecture,
~ element(the_carrier(sK0),powerset(the_carrier(sK0))),
inference(resolve,[status(thm)],[c_283,c_148]) ).
cnf(c_282,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_143,c_284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU308+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.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 09:10:09 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 3274345 was started by sandbox2 on n008,
% 0.10/0.37 % Sat Sep 26 09:10:09 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 0.16/0.43
% 0.16/0.43 % SZS status Theorem for theBenchmark
% 0.16/0.43
% 0.16/0.43 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.16/0.43 % Length of proof is 21.
% 0.16/0.43 % Level of proof is 6.
% 0.16/0.43 % Maximum clause weight is 26.000.
% 0.16/0.43 % Given clauses 91.
% 0.16/0.43
% 0.16/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------