%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU328+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 : n002.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 02:51:44 PM UTC 2026
% Result : Theorem 244.02s 32.36s
% Output : Proof 244.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 20
% Syntax : Number of formulae : 139 ( 88 unt; 0 def)
% Number of atoms : 222 ( 109 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 156 ( 73 ~; 44 |; 25 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-4 aty)
% Number of variables : 165 ( 7 sgn 87 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
fof(f47_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B)) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f47_nnf,plain,
? [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) != subset_complement(A,meet_of_subsets(A,B))
& B != empty_set
& element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f47_neg]) ).
fof(f47_sk,plain,
( union_of_subsets(sk4,complements_of_subsets(sk4,sk5)) != subset_complement(sk4,meet_of_subsets(sk4,sk5))
& sk5 != empty_set
& element(sk5,powerset(powerset(sk4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f47_nnf]) ).
cnf(c95,plain,
union_of_subsets(sk4,complements_of_subsets(sk4,sk5)) != subset_complement(sk4,meet_of_subsets(sk4,sk5)),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(t197,plain,
eq(union_of_subsets(sk4,complements_of_subsets(sk4,sk5)),subset_complement(sk4,meet_of_subsets(sk4,sk5))) = false,
inference(equality_encoding,[status(esa)],[c95]) ).
cnf(t1970,plain,
eq(union_of_subsets(sk4,complements_of_subsets(sk4,sk5)),subset_complement(sk4,meet_of_subsets(sk4,sk5))) = false,
inference(orient,[status(thm)],[t197]) ).
fof(f44,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f44_nnf,plain,
! [A,B] :
( meet_of_subsets(A,B) = set_meet(B)
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [B,A] :
( meet_of_subsets(A,B) = set_meet(B)
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c90,plain,
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi81,axiom,
ifeq(element(X0,powerset(powerset(X1))),true,meet_of_subsets(X1,X0),set_meet(X0)) = set_meet(X0),
inference(equality_encoding,[status(esa)],[c90]) ).
cnf(c93,plain,
element(sk5,powerset(powerset(sk4))),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(hi84,negated_conjecture,
element(sk5,powerset(powerset(sk4))) = true,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(t50,plain,
meet_of_subsets(sk4,sk5) = set_meet(sk5),
inference(hyper_resolution,[status(thm)],[hi81,hi84]) ).
cnf(t1988,plain,
meet_of_subsets(sk4,sk5) = set_meet(sk5),
inference(orient,[status(thm)],[t50]) ).
cnf(t112662,plain,
eq(union_of_subsets(sk4,complements_of_subsets(sk4,sk5)),subset_complement(sk4,set_meet(sk5))) = false,
inference(step,[status(thm)],[t1970,t1988]) ).
cnf(t1993,plain,
eq(union_of_subsets(sk4,complements_of_subsets(sk4,sk5)),subset_complement(sk4,set_meet(sk5))) = false,
inference(rw,[status(thm)],[t112662]) ).
fof(f28,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f28_nnf,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [B,A] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c52,plain,
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi46,axiom,
ifeq(element(X0,powerset(powerset(X1))),true,element(complements_of_subsets(X1,X0),powerset(powerset(X1))),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(h115,plain,
element(complements_of_subsets(sk4,sk5),powerset(powerset(sk4))) = true,
inference(hyper_resolution,[status(thm)],[hi46,hi84]) ).
fof(f43,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f43_nnf,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [B,A] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c89,plain,
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi80,axiom,
ifeq(element(X0,powerset(powerset(X1))),true,union_of_subsets(X1,X0),union(X0)) = union(X0),
inference(equality_encoding,[status(esa)],[c89]) ).
cnf(t162,plain,
union_of_subsets(sk4,complements_of_subsets(sk4,sk5)) = union(complements_of_subsets(sk4,sk5)),
inference(hyper_resolution,[status(thm)],[hi80,h115]) ).
cnf(t2018,plain,
union_of_subsets(sk4,complements_of_subsets(sk4,sk5)) = union(complements_of_subsets(sk4,sk5)),
inference(orient,[status(thm)],[t162]) ).
fof(f45,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(f45_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)],[f45]) ).
fof(f45_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)],[f45_nnf]) ).
cnf(c91,plain,
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(t254,plain,
ifeq(element(X1,powerset(X2)),true,ifeq(element(X3,powerset(X2)),true,subset_difference(X2,X1,X3),set_difference(X1,X3)),set_difference(X1,X3)) = set_difference(X1,X3),
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(t1700,plain,
ifeq(element(X1,powerset(X2)),true,ifeq(element(X3,powerset(X2)),true,subset_difference(X2,X1,X3),set_difference(X1,X3)),set_difference(X1,X3)) = set_difference(X1,X3),
inference(orient,[status(thm)],[t254]) ).
cnf(t145,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t261,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t145]) ).
fof(f52,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f52_nnf,plain,
! [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [B,A] :
( union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c101,plain,
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| X1 = empty_set
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t255,plain,
ifeq(element(X1,powerset(powerset(X2))),true,or(eq(X1,empty_set),eq(union_of_subsets(X2,complements_of_subsets(X2,X1)),subset_difference(X2,cast_to_subset(X2),meet_of_subsets(X2,X1)))),true) = true,
inference(equality_encoding,[status(esa)],[c101]) ).
fof(f16,axiom,
! [A] : cast_to_subset(A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f16_nnf,plain,
! [A] : cast_to_subset(A) = A,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A] : cast_to_subset(A) = A,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c40,plain,
cast_to_subset(X0) = X0,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t0,plain,
cast_to_subset(X1) = X1,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t268,plain,
cast_to_subset(X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t112623,plain,
ifeq(element(X1,powerset(powerset(X2))),true,or(eq(X1,empty_set),eq(union_of_subsets(X2,complements_of_subsets(X2,X1)),subset_difference(X2,X2,meet_of_subsets(X2,X1)))),true) = true,
inference(step,[status(thm)],[t255,t268]) ).
cnf(t277,plain,
ifeq(element(X1,powerset(powerset(X2))),true,or(eq(X1,empty_set),eq(union_of_subsets(X2,complements_of_subsets(X2,X1)),subset_difference(X2,X2,meet_of_subsets(X2,X1)))),true) = true,
inference(orient,[status(thm)],[t112623]) ).
cnf(t82,plain,
element(sk5,powerset(powerset(sk4))) = true,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(t499,plain,
element(sk5,powerset(powerset(sk4))) = true,
inference(orient,[status(thm)],[t82]) ).
cnf(t545,plain,
true = ifeq(true,true,or(eq(sk5,empty_set),eq(union_of_subsets(sk4,complements_of_subsets(sk4,sk5)),subset_difference(sk4,sk4,meet_of_subsets(sk4,sk5)))),true),
inference(cp,[status(thm)],[t277,t499]) ).
cnf(t83,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t83]) ).
cnf(t113486,plain,
true = or(eq(sk5,empty_set),eq(union_of_subsets(sk4,complements_of_subsets(sk4,sk5)),subset_difference(sk4,sk4,meet_of_subsets(sk4,sk5)))),
inference(step,[status(thm)],[t545,t256]) ).
cnf(c94,plain,
sk5 != empty_set,
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(t19,plain,
eq(sk5,empty_set) = false,
inference(equality_encoding,[status(esa)],[c94]) ).
cnf(t1967,plain,
eq(sk5,empty_set) = false,
inference(orient,[status(thm)],[t19]) ).
cnf(t113487,plain,
true = or(false,eq(union_of_subsets(sk4,complements_of_subsets(sk4,sk5)),subset_difference(sk4,sk4,meet_of_subsets(sk4,sk5)))),
inference(step,[status(thm)],[t113486,t1967]) ).
cnf(t24,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t267,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t24]) ).
cnf(t113488,plain,
true = eq(union_of_subsets(sk4,complements_of_subsets(sk4,sk5)),subset_difference(sk4,sk4,meet_of_subsets(sk4,sk5))),
inference(step,[status(thm)],[t113487,t267]) ).
cnf(t113489,plain,
true = eq(union(complements_of_subsets(sk4,sk5)),subset_difference(sk4,sk4,meet_of_subsets(sk4,sk5))),
inference(step,[status(thm)],[t113488,t2018]) ).
cnf(t113490,plain,
true = eq(union(complements_of_subsets(sk4,sk5)),subset_difference(sk4,sk4,set_meet(sk5))),
inference(step,[status(thm)],[t113489,t1988]) ).
cnf(t27138,plain,
eq(union(complements_of_subsets(sk4,sk5)),subset_difference(sk4,sk4,set_meet(sk5))) = true,
inference(orient,[status(thm)],[t113490]) ).
cnf(t27139,plain,
subset_difference(sk4,sk4,set_meet(sk5)) = ifeq(true,true,union(complements_of_subsets(sk4,sk5)),subset_difference(sk4,sk4,set_meet(sk5))),
inference(cp,[status(thm)],[t261,t27138]) ).
cnf(t113491,plain,
subset_difference(sk4,sk4,set_meet(sk5)) = union(complements_of_subsets(sk4,sk5)),
inference(step,[status(thm)],[t27139,t256]) ).
cnf(t27140,plain,
subset_difference(sk4,sk4,set_meet(sk5)) = union(complements_of_subsets(sk4,sk5)),
inference(orient,[status(thm)],[t113491]) ).
cnf(t27141,plain,
set_difference(sk4,set_meet(sk5)) = ifeq(element(sk4,powerset(sk4)),true,ifeq(element(set_meet(sk5),powerset(sk4)),true,union(complements_of_subsets(sk4,sk5)),set_difference(sk4,set_meet(sk5))),set_difference(sk4,set_meet(sk5))),
inference(cp,[status(thm)],[t1700,t27140]) ).
fof(f17,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(f17_nnf,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [B,A] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c41,plain,
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t226,plain,
ifeq(element(X1,powerset(X2)),true,subset_complement(X2,X1),set_difference(X2,X1)) = set_difference(X2,X1),
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(t1721,plain,
ifeq(element(X1,powerset(X2)),true,subset_complement(X2,X1),set_difference(X2,X1)) = set_difference(X2,X1),
inference(orient,[status(thm)],[t226]) ).
fof(f26,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f26_nnf,plain,
! [A,B] :
( element(meet_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [B,A] :
( element(meet_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c50,plain,
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t227,plain,
ifeq(element(X1,powerset(powerset(X2))),true,element(meet_of_subsets(X2,X1),powerset(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t275,plain,
ifeq(element(X1,powerset(powerset(X2))),true,element(meet_of_subsets(X2,X1),powerset(X2)),true) = true,
inference(orient,[status(thm)],[t227]) ).
cnf(t1989,plain,
true = ifeq(element(sk5,powerset(powerset(sk4))),true,element(set_meet(sk5),powerset(sk4)),true),
inference(cp,[status(thm)],[t275,t1988]) ).
cnf(t112689,plain,
true = ifeq(true,true,element(set_meet(sk5),powerset(sk4)),true),
inference(step,[status(thm)],[t1989,t499]) ).
cnf(t112690,plain,
true = element(set_meet(sk5),powerset(sk4)),
inference(step,[status(thm)],[t112689,t256]) ).
cnf(t2252,plain,
element(set_meet(sk5),powerset(sk4)) = true,
inference(orient,[status(thm)],[t112690]) ).
cnf(t2255,plain,
set_difference(sk4,set_meet(sk5)) = ifeq(true,true,subset_complement(sk4,set_meet(sk5)),set_difference(sk4,set_meet(sk5))),
inference(cp,[status(thm)],[t1721,t2252]) ).
cnf(t112703,plain,
set_difference(sk4,set_meet(sk5)) = subset_complement(sk4,set_meet(sk5)),
inference(step,[status(thm)],[t2255,t256]) ).
cnf(t2458,plain,
set_difference(sk4,set_meet(sk5)) = subset_complement(sk4,set_meet(sk5)),
inference(orient,[status(thm)],[t112703]) ).
cnf(t113492,plain,
subset_complement(sk4,set_meet(sk5)) = ifeq(element(sk4,powerset(sk4)),true,ifeq(element(set_meet(sk5),powerset(sk4)),true,union(complements_of_subsets(sk4,sk5)),set_difference(sk4,set_meet(sk5))),set_difference(sk4,set_meet(sk5))),
inference(step,[status(thm)],[t27141,t2458]) ).
fof(f51,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f51_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c100,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(hi89,axiom,
ifeq(subset(X0,X1),true,element(X0,powerset(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c100]) ).
fof(f46,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f46_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c92,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(hi83,axiom,
subset(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t48,plain,
element(X1,powerset(X1)) = true,
inference(hyper_resolution,[status(thm)],[hi89,hi83]) ).
cnf(t365,plain,
element(X1,powerset(X1)) = true,
inference(orient,[status(thm)],[t48]) ).
cnf(t113493,plain,
subset_complement(sk4,set_meet(sk5)) = ifeq(true,true,ifeq(element(set_meet(sk5),powerset(sk4)),true,union(complements_of_subsets(sk4,sk5)),set_difference(sk4,set_meet(sk5))),set_difference(sk4,set_meet(sk5))),
inference(step,[status(thm)],[t113492,t365]) ).
cnf(t113494,plain,
subset_complement(sk4,set_meet(sk5)) = ifeq(element(set_meet(sk5),powerset(sk4)),true,union(complements_of_subsets(sk4,sk5)),set_difference(sk4,set_meet(sk5))),
inference(step,[status(thm)],[t113493,t256]) ).
cnf(t113495,plain,
subset_complement(sk4,set_meet(sk5)) = ifeq(true,true,union(complements_of_subsets(sk4,sk5)),set_difference(sk4,set_meet(sk5))),
inference(step,[status(thm)],[t113494,t2252]) ).
cnf(t113496,plain,
subset_complement(sk4,set_meet(sk5)) = union(complements_of_subsets(sk4,sk5)),
inference(step,[status(thm)],[t113495,t256]) ).
cnf(t27142,plain,
union(complements_of_subsets(sk4,sk5)) = subset_complement(sk4,set_meet(sk5)),
inference(orient,[status(thm)],[t113496]) ).
cnf(t113497,plain,
union_of_subsets(sk4,complements_of_subsets(sk4,sk5)) = subset_complement(sk4,set_meet(sk5)),
inference(step,[status(thm)],[t2018,t27142]) ).
cnf(t27143,plain,
union_of_subsets(sk4,complements_of_subsets(sk4,sk5)) = subset_complement(sk4,set_meet(sk5)),
inference(orient,[status(thm)],[t113497]) ).
cnf(t115518,plain,
eq(subset_complement(sk4,set_meet(sk5)),subset_complement(sk4,set_meet(sk5))) = false,
inference(step,[status(thm)],[t1993,t27143]) ).
cnf(t18,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t1510,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t115519,plain,
true = false,
inference(step,[status(thm)],[t115518,t1510]) ).
cnf(t112588,plain,
false = true,
inference(orient,[status(thm)],[t115519]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f31,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f31_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c55,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f40,axiom,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
fof(f40_nnf,plain,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
( v5_membered(sk1)
& v4_membered(sk1)
& v3_membered(sk1)
& v2_membered(sk1)
& v1_membered(sk1)
& ~ empty(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f40_nnf]) ).
cnf(c79,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f55,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f55_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c104,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
fof(f57,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f57_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c106,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c55,c79,c94,c95,c104,c106]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t112588]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n002.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 : Thu Sep 24 13:45:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 244.02/32.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 244.02/32.36 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------