%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 : Fri Sep 25 02:51:40 PM UTC 2026
% Result : Theorem 28.51s 4.17s
% Output : Proof 28.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 12 unt; 0 def)
% Number of atoms : 74 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 64 ( 27 ~; 21 |; 7 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 43 ( 0 sgn 31 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f58,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f58_nnf,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c117,plain,
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
fof(f56,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f56_nnf,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c113,plain,
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
fof(f57,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
fof(f57_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(negated_conjecture,[status(cth)],[f57]) ).
fof(f57_nnf,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(nnf_transformation,[status(thm)],[f57_neg]) ).
fof(f57_sk,plain,
( subset_intersection2(the_carrier(sk5),sk6,cast_as_carrier_subset(sk5)) != sk6
& element(sk6,powerset(the_carrier(sk5)))
& one_sorted_str(sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6])],[f57_nnf]) ).
cnf(c114,plain,
one_sorted_str(sk5),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(p484,plain,
cast_as_carrier_subset(sk5) = the_carrier(sk5),
inference(resolution,[status(thm)],[c113,c114]) ).
fof(f55,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f55_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c111,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c115,plain,
element(sk6,powerset(the_carrier(sk5))),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(p448,plain,
subset(sk6,the_carrier(sk5)),
inference(resolution,[status(thm)],[c111,c115]) ).
cnf(p520,plain,
subset(sk6,cast_as_carrier_subset(sk5)),
inference(superposition,[status(thm)],[p484,p448]) ).
cnf(p533,plain,
set_intersection2(sk6,cast_as_carrier_subset(sk5)) = sk6,
inference(resolution,[status(thm)],[c117,p520]) ).
fof(f48,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f48_nnf,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c104,plain,
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(p431,plain,
element(cast_as_carrier_subset(sk5),powerset(the_carrier(sk5))),
inference(resolution,[status(thm)],[c104,c114]) ).
fof(f46,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,C) = set_intersection2(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(f46_nnf,plain,
! [A,B,C] :
( subset_intersection2(A,B,C) = set_intersection2(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [B,A,C] :
( subset_intersection2(A,B,C) = set_intersection2(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c102,plain,
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p421,plain,
( subset_intersection2(the_carrier(sk5),sk6,X0) = set_intersection2(sk6,X0)
| ~ element(X0,powerset(the_carrier(sk5))) ),
inference(resolution,[status(thm)],[c102,c115]) ).
cnf(p437,plain,
subset_intersection2(the_carrier(sk5),sk6,cast_as_carrier_subset(sk5)) = set_intersection2(sk6,cast_as_carrier_subset(sk5)),
inference(resolution,[status(thm)],[p431,p421]) ).
cnf(c116,plain,
subset_intersection2(the_carrier(sk5),sk6,cast_as_carrier_subset(sk5)) != sk6,
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(p438,plain,
set_intersection2(sk6,cast_as_carrier_subset(sk5)) != sk6,
inference(demodulation,[status(thm)],[p437,c116]) ).
cnf(p535,plain,
sk6 != sk6,
inference(demodulation,[status(thm)],[p533,p438]) ).
cnf(p553,plain,
$false,
inference(equality_resolution,[status(thm)],[p535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 13:37:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 28.51/4.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.51/4.17 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------