%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU307+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 : 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 08:45:45 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 49 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 13 ~; 8 |; 5 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 31 ( 1 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(redefinition_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,C) = set_intersection2(B,C) ),
file('theBenchmark.p',redefinition_k5_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(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t15_pre_topc,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ),
file('theBenchmark.p',t15_pre_topc) ).
fof(t15_pre_topc_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ),
inference(assume_negation,[status(cth)],[t15_pre_topc]) ).
cnf(c_60,plain,
( subset(A,B)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_61,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_62,plain,
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t28_xboole_1]) ).
cnf(c_63,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_66,plain,
( the_carrier(A) = cast_as_carrier_subset(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d3_pre_topc]) ).
fof(nnf_59,plain,
? [A] :
( ? [B] :
( subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) != B
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t15_pre_topc_neg]) ).
fof(sk_t15_pre_topc_neg,plain,
( subset_intersection2(the_carrier(sK0),sK1,cast_as_carrier_subset(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_59]) ).
cnf(c_67,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_pre_topc_neg]) ).
cnf(c_69,negated_conjecture,
the_carrier(sK0) = cast_as_carrier_subset(sK0),
inference(resolve,[status(thm)],[c_67,c_66]) ).
cnf(c_70,negated_conjecture,
cast_as_carrier_subset(sK0) = the_carrier(sK0),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_75,negated_conjecture,
subset_intersection2(the_carrier(sK0),sK1,cast_as_carrier_subset(sK0)) != sK1,
inference(split_conjunct,[status(thm)],[sk_t15_pre_topc_neg]) ).
cnf(c_76,negated_conjecture,
subset_intersection2(the_carrier(sK0),sK1,the_carrier(sK0)) != sK1,
inference(paramod,[status(thm)],[c_70,c_75]) ).
cnf(c_77,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(split_conjunct,[status(thm)],[sk_t15_pre_topc_neg]) ).
cnf(c_80,plain,
( subset_intersection2(B,A,C) = set_intersection2(A,C)
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[redefinition_k5_subset_1]) ).
cnf(c_165,plain,
( set_intersection2(A,B) = A
| ~ element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_60,c_62]) ).
cnf(c_166,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_63,c_61]) ).
cnf(c_290,plain,
set_intersection2(sK1,the_carrier(sK0)) = sK1,
inference(resolve,[status(thm)],[c_165,c_77]) ).
cnf(c_310,negated_conjecture,
( subset_intersection2(the_carrier(sK0),sK1,A) = set_intersection2(sK1,A)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_80,c_77]) ).
cnf(c_311,negated_conjecture,
subset_intersection2(the_carrier(sK0),sK1,the_carrier(sK0)) = set_intersection2(sK1,the_carrier(sK0)),
inference(resolve,[status(thm)],[c_310,c_166]) ).
cnf(c_312,negated_conjecture,
subset_intersection2(the_carrier(sK0),sK1,the_carrier(sK0)) = sK1,
inference(paramod,[status(thm)],[c_290,c_311]) ).
cnf(c_309,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_76,c_312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.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 09:10:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2979630 was started by sandbox2 on n010,
% 0.09/0.36 % Sat Sep 26 09:10:00 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.42
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 22.
% 0.13/0.42 % Level of proof is 5.
% 0.13/0.42 % Maximum clause weight is 26.000.
% 0.13/0.42 % Given clauses 91.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------