%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU308+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 : n011.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 35.93s 5.75s
% Output : Proof 35.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 73 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 25 ~; 18 |; 7 &)
% ( 1 <=>; 7 =>; 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 : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 47 ( 2 sgn 33 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f39_nnf,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [B,A,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c85,plain,
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f49,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f49_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c96,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
fof(f28,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f28_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c68,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p227,plain,
element(X0,powerset(X0)),
inference(resolution,[status(thm)],[c96,c68]) ).
cnf(p325,plain,
( subset_difference(X1,X1,X0) = set_difference(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[c85,p227]) ).
fof(f50,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(f50_nnf,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c97,plain,
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
fof(f51,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f51_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(negated_conjecture,[status(cth)],[f51]) ).
fof(f51_nnf,plain,
? [A] :
( ? [B] :
( subset_complement(the_carrier(A),B) != subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f51_neg]) ).
fof(f51_sk,plain,
( subset_complement(the_carrier(sk5),sk6) != subset_difference(the_carrier(sk5),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])],[f51_nnf]) ).
cnf(c98,plain,
one_sorted_str(sk5),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p229,plain,
cast_as_carrier_subset(sk5) = the_carrier(sk5),
inference(resolution,[status(thm)],[c97,c98]) ).
cnf(c99,plain,
element(sk6,powerset(the_carrier(sk5))),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p234,plain,
element(sk6,powerset(cast_as_carrier_subset(sk5))),
inference(superposition,[status(thm)],[p229,c99]) ).
cnf(p1050,plain,
subset_difference(cast_as_carrier_subset(sk5),cast_as_carrier_subset(sk5),sk6) = set_difference(cast_as_carrier_subset(sk5),sk6),
inference(resolution,[status(thm)],[p325,p234]) ).
fof(f52,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f52_nnf,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [B,A] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c101,plain,
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p408,plain,
subset_complement(the_carrier(sk5),sk6) = set_difference(the_carrier(sk5),sk6),
inference(resolution,[status(thm)],[c101,c99]) ).
cnf(c100,plain,
subset_complement(the_carrier(sk5),sk6) != subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),sk6),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p392,plain,
subset_complement(the_carrier(sk5),sk6) != subset_difference(cast_as_carrier_subset(sk5),cast_as_carrier_subset(sk5),sk6),
inference(superposition,[status(thm)],[p229,c100]) ).
cnf(p412,plain,
set_difference(the_carrier(sk5),sk6) != subset_difference(cast_as_carrier_subset(sk5),cast_as_carrier_subset(sk5),sk6),
inference(demodulation,[status(thm)],[p408,p392]) ).
cnf(p1051,plain,
set_difference(the_carrier(sk5),sk6) != set_difference(cast_as_carrier_subset(sk5),sk6),
inference(demodulation,[status(thm)],[p1050,p412]) ).
cnf(p715,plain,
subset_complement(cast_as_carrier_subset(sk5),sk6) = set_difference(the_carrier(sk5),sk6),
inference(superposition,[status(thm)],[p229,p408]) ).
cnf(p425,plain,
subset_complement(cast_as_carrier_subset(sk5),sk6) = set_difference(cast_as_carrier_subset(sk5),sk6),
inference(resolution,[status(thm)],[c101,p234]) ).
cnf(p716,plain,
set_difference(the_carrier(sk5),sk6) = set_difference(cast_as_carrier_subset(sk5),sk6),
inference(demodulation,[status(thm)],[p715,p425]) ).
cnf(p1062,plain,
$false,
inference(resolution,[status(thm)],[p1051,p716]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU308+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:37:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 35.93/5.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.93/5.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------