%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU304+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:51:39 PM UTC 2026
% Result : Theorem 34.95s 4.92s
% Output : Proof 34.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 15
% Syntax : Number of formulae : 136 ( 89 unt; 0 def)
% Number of atoms : 308 ( 99 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 288 ( 116 ~; 95 |; 58 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 142 ( 5 sgn 78 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A] :
( ( join_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( below(A,B,C)
<=> join(A,B,C) = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
fof(f6_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( join(A,B,C) != C
| below(A,B,C) )
& ( join(A,B,C) = C
| ~ below(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ( ( join(A,B,C) != C
| below(A,B,C) )
& ( join(A,B,C) = C
| ~ below(A,B,C) ) )
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c8,plain,
( join(X0,X1,X2) != X2
| below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t246,plain,
ifeq(join_semilatt_str(X1),true,ifeq(element(X2,the_carrier(X1)),true,ifeq(element(X3,the_carrier(X1)),true,ifeq(join(X1,X2,X3),X3,or(empty_carrier(X1),below(X1,X2,X3)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t568,plain,
ifeq(join_semilatt_str(X1),true,ifeq(element(X2,the_carrier(X1)),true,ifeq(element(X3,the_carrier(X1)),true,ifeq(join(X1,X2,X3),X3,or(empty_carrier(X1),below(X1,X2,X3)),true),true),true),true) = true,
inference(orient,[status(thm)],[t246]) ).
cnf(t52,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)],[t52]) ).
fof(f7,axiom,
! [A] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> ( meet_absorbing(A)
<=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> join(A,meet(A,B,C),C) = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattices) ).
fof(f7_nnf,plain,
! [A] :
( ( ( ? [B] :
( ? [C] :
( join(A,meet(A,B,C),C) != C
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
| meet_absorbing(A) )
& ( ! [B] :
( ! [C] :
( join(A,meet(A,B,C),C) = C
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ meet_absorbing(A) ) )
| ~ latt_str(A)
| empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( ( ( ( join(A,meet(A,sk0(A),sk1(A)),sk1(A)) != sk1(A)
& element(sk1(A),the_carrier(A))
& element(sk0(A),the_carrier(A)) )
| meet_absorbing(A) )
& ( join(A,meet(A,B,C),C) = C
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_absorbing(A) ) )
| ~ latt_str(A)
| empty_carrier(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f7_nnf]) ).
cnf(c9,plain,
( join(X0,meet(X0,X1,X2),X2) = X2
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_absorbing(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi8,axiom,
ifeq(latt_str(X0),true,ifeq(meet_absorbing(X0),true,ifeq(element(X1,the_carrier(X0)),true,ifeq(element(X2,the_carrier(X0)),true,or(empty_carrier(X0),eq(join(X0,meet(X0,X1,X2),X2),X2)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f42,conjecture,
! [A] :
( ( latt_str(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> below(A,meet_commut(A,B,C),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
fof(f42_neg,negated_conjecture,
~ ! [A] :
( ( latt_str(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> below(A,meet_commut(A,B,C),B) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ below(A,meet_commut(A,B,C),B)
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& latt_str(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
( ~ below(sk11,meet_commut(sk11,sk12,sk13),sk12)
& element(sk13,the_carrier(sk11))
& element(sk12,the_carrier(sk11))
& latt_str(sk11)
& meet_absorbing(sk11)
& meet_commutative(sk11)
& ~ empty_carrier(sk11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13])],[f42_nnf]) ).
cnf(c61,plain,
latt_str(sk11),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi49,negated_conjecture,
latt_str(sk11) = true,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(c60,plain,
meet_absorbing(sk11),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi48,negated_conjecture,
meet_absorbing(sk11) = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(c63,plain,
element(sk13,the_carrier(sk11)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi51,negated_conjecture,
element(sk13,the_carrier(sk11)) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(c62,plain,
element(sk12,the_carrier(sk11)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi50,negated_conjecture,
element(sk12,the_carrier(sk11)) = true,
inference(equality_encoding,[status(esa)],[c62]) ).
cnf(t147,plain,
or(empty_carrier(sk11),eq(join(sk11,meet(sk11,sk13,sk12),sk12),sk12)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi49,hi48,hi51,hi50]) ).
cnf(t335,plain,
or(empty_carrier(sk11),eq(join(sk11,meet(sk11,sk13,sk12),sk12),sk12)) = true,
inference(orient,[status(thm)],[t147]) ).
cnf(c58,plain,
~ empty_carrier(sk11),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(t0,plain,
empty_carrier(sk11) = false,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(t977,plain,
empty_carrier(sk11) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t1701,plain,
or(false,eq(join(sk11,meet(sk11,sk13,sk12),sk12),sk12)) = true,
inference(step,[status(thm)],[t335,t977]) ).
cnf(t32,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t32]) ).
cnf(t1702,plain,
eq(join(sk11,meet(sk11,sk13,sk12),sk12),sk12) = true,
inference(step,[status(thm)],[t1701,t257]) ).
cnf(t1012,plain,
eq(join(sk11,meet(sk11,sk13,sk12),sk12),sk12) = true,
inference(rw,[status(thm)],[t1702]) ).
fof(f19,axiom,
! [A] :
( latt_str(A)
=> ( join_semilatt_str(A)
& meet_semilatt_str(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f19_nnf,plain,
! [A] :
( ( join_semilatt_str(A)
& meet_semilatt_str(A) )
| ~ latt_str(A) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A] :
( ( join_semilatt_str(A)
& meet_semilatt_str(A) )
| ~ latt_str(A) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c24,plain,
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi18,axiom,
ifeq(latt_str(X0),true,meet_semilatt_str(X0),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h15,plain,
meet_semilatt_str(sk11) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi49]) ).
fof(f38,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> meet_commut(A,B,C) = meet(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(f38_nnf,plain,
! [A,B,C] :
( meet_commut(A,B,C) = meet(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,C] :
( meet_commut(A,B,C) = meet(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c53,plain,
( meet_commut(X0,X1,X2) = meet(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi42,axiom,
ifeq(meet_commutative(X0),true,ifeq(meet_semilatt_str(X0),true,ifeq(element(X1,the_carrier(X0)),true,ifeq(element(X2,the_carrier(X0)),true,or(empty_carrier(X0),eq(meet_commut(X0,X1,X2),meet(X0,X1,X2))),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(c59,plain,
meet_commutative(sk11),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi47,negated_conjecture,
meet_commutative(sk11) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
cnf(t153,plain,
or(empty_carrier(sk11),eq(meet_commut(sk11,sk13,sk12),meet(sk11,sk13,sk12))) = true,
inference(hyper_resolution,[status(thm)],[hi42,hi47,h15,hi51,hi50]) ).
cnf(t316,plain,
or(empty_carrier(sk11),eq(meet_commut(sk11,sk13,sk12),meet(sk11,sk13,sk12))) = true,
inference(orient,[status(thm)],[t153]) ).
cnf(t1667,plain,
or(false,eq(meet_commut(sk11,sk13,sk12),meet(sk11,sk13,sk12))) = true,
inference(step,[status(thm)],[t316,t977]) ).
cnf(t1668,plain,
eq(meet_commut(sk11,sk13,sk12),meet(sk11,sk13,sk12)) = true,
inference(step,[status(thm)],[t1667,t257]) ).
cnf(t995,plain,
eq(meet_commut(sk11,sk13,sk12),meet(sk11,sk13,sk12)) = true,
inference(rw,[status(thm)],[t1668]) ).
cnf(t1603,plain,
eq(meet_commut(sk11,sk13,sk12),meet(sk11,sk13,sk12)) = true,
inference(orient,[status(thm)],[t995]) ).
cnf(t1604,plain,
meet(sk11,sk13,sk12) = ifeq(true,true,meet_commut(sk11,sk13,sk12),meet(sk11,sk13,sk12)),
inference(cp,[status(thm)],[t261,t1603]) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t40]) ).
cnf(t1857,plain,
meet(sk11,sk13,sk12) = meet_commut(sk11,sk13,sk12),
inference(step,[status(thm)],[t1604,t258]) ).
cnf(t1605,plain,
meet(sk11,sk13,sk12) = meet_commut(sk11,sk13,sk12),
inference(orient,[status(thm)],[t1857]) ).
cnf(t1872,plain,
eq(join(sk11,meet_commut(sk11,sk13,sk12),sk12),sk12) = true,
inference(step,[status(thm)],[t1012,t1605]) ).
cnf(t1626,plain,
eq(join(sk11,meet_commut(sk11,sk13,sk12),sk12),sk12) = true,
inference(orient,[status(thm)],[t1872]) ).
cnf(t1627,plain,
sk12 = ifeq(true,true,join(sk11,meet_commut(sk11,sk13,sk12),sk12),sk12),
inference(cp,[status(thm)],[t261,t1626]) ).
cnf(t1873,plain,
sk12 = join(sk11,meet_commut(sk11,sk13,sk12),sk12),
inference(step,[status(thm)],[t1627,t258]) ).
cnf(t1628,plain,
join(sk11,meet_commut(sk11,sk13,sk12),sk12) = sk12,
inference(orient,[status(thm)],[t1873]) ).
cnf(t1629,plain,
true = ifeq(join_semilatt_str(sk11),true,ifeq(element(meet_commut(sk11,sk13,sk12),the_carrier(sk11)),true,ifeq(element(sk12,the_carrier(sk11)),true,ifeq(sk12,sk12,or(empty_carrier(sk11),below(sk11,meet_commut(sk11,sk13,sk12),sk12)),true),true),true),true),
inference(cp,[status(thm)],[t568,t1628]) ).
cnf(c25,plain,
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(latt_str(X0),true,join_semilatt_str(X0),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t2,plain,
join_semilatt_str(sk11) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi49]) ).
cnf(t833,plain,
join_semilatt_str(sk11) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t1874,plain,
true = ifeq(true,true,ifeq(element(meet_commut(sk11,sk13,sk12),the_carrier(sk11)),true,ifeq(element(sk12,the_carrier(sk11)),true,ifeq(sk12,sk12,or(empty_carrier(sk11),below(sk11,meet_commut(sk11,sk13,sk12),sk12)),true),true),true),true),
inference(step,[status(thm)],[t1629,t833]) ).
cnf(t1875,plain,
true = ifeq(element(meet_commut(sk11,sk13,sk12),the_carrier(sk11)),true,ifeq(element(sk12,the_carrier(sk11)),true,ifeq(sk12,sk12,or(empty_carrier(sk11),below(sk11,meet_commut(sk11,sk13,sk12),sk12)),true),true),true),
inference(step,[status(thm)],[t1874,t258]) ).
fof(f15,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> element(meet_commut(A,B,C),the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
fof(f15_nnf,plain,
! [A,B,C] :
( element(meet_commut(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C] :
( element(meet_commut(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c20,plain,
( element(meet_commut(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(meet_commutative(X0),true,ifeq(meet_semilatt_str(X0),true,ifeq(element(X1,the_carrier(X0)),true,ifeq(element(X2,the_carrier(X0)),true,or(empty_carrier(X0),element(meet_commut(X0,X1,X2),the_carrier(X0))),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t90,plain,
or(empty_carrier(sk11),element(meet_commut(sk11,sk13,sk12),the_carrier(sk11))) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi47,h15,hi51,hi50]) ).
cnf(t282,plain,
or(empty_carrier(sk11),element(meet_commut(sk11,sk13,sk12),the_carrier(sk11))) = true,
inference(orient,[status(thm)],[t90]) ).
cnf(t1685,plain,
or(false,element(meet_commut(sk11,sk13,sk12),the_carrier(sk11))) = true,
inference(step,[status(thm)],[t282,t977]) ).
cnf(t1686,plain,
element(meet_commut(sk11,sk13,sk12),the_carrier(sk11)) = true,
inference(step,[status(thm)],[t1685,t257]) ).
cnf(t1004,plain,
element(meet_commut(sk11,sk13,sk12),the_carrier(sk11)) = true,
inference(rw,[status(thm)],[t1686]) ).
cnf(t1330,plain,
element(meet_commut(sk11,sk13,sk12),the_carrier(sk11)) = true,
inference(orient,[status(thm)],[t1004]) ).
cnf(t1876,plain,
true = ifeq(true,true,ifeq(element(sk12,the_carrier(sk11)),true,ifeq(sk12,sk12,or(empty_carrier(sk11),below(sk11,meet_commut(sk11,sk13,sk12),sk12)),true),true),true),
inference(step,[status(thm)],[t1875,t1330]) ).
cnf(t1877,plain,
true = ifeq(element(sk12,the_carrier(sk11)),true,ifeq(sk12,sk12,or(empty_carrier(sk11),below(sk11,meet_commut(sk11,sk13,sk12),sk12)),true),true),
inference(step,[status(thm)],[t1876,t258]) ).
cnf(t37,plain,
element(sk12,the_carrier(sk11)) = true,
inference(equality_encoding,[status(esa)],[c62]) ).
cnf(t393,plain,
element(sk12,the_carrier(sk11)) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(t1878,plain,
true = ifeq(true,true,ifeq(sk12,sk12,or(empty_carrier(sk11),below(sk11,meet_commut(sk11,sk13,sk12),sk12)),true),true),
inference(step,[status(thm)],[t1877,t393]) ).
cnf(t1879,plain,
true = ifeq(sk12,sk12,or(empty_carrier(sk11),below(sk11,meet_commut(sk11,sk13,sk12),sk12)),true),
inference(step,[status(thm)],[t1878,t258]) ).
cnf(t1880,plain,
true = or(empty_carrier(sk11),below(sk11,meet_commut(sk11,sk13,sk12),sk12)),
inference(step,[status(thm)],[t1879,t258]) ).
cnf(t1881,plain,
true = or(false,below(sk11,meet_commut(sk11,sk13,sk12),sk12)),
inference(step,[status(thm)],[t1880,t977]) ).
cnf(t1882,plain,
true = below(sk11,meet_commut(sk11,sk13,sk12),sk12),
inference(step,[status(thm)],[t1881,t257]) ).
cnf(c64,plain,
~ below(sk11,meet_commut(sk11,sk12,sk13),sk12),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(t50,plain,
below(sk11,meet_commut(sk11,sk12,sk13),sk12) = false,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t1100,plain,
below(sk11,meet_commut(sk11,sk12,sk13),sk12) = false,
inference(orient,[status(thm)],[t50]) ).
fof(f3,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> meet_commut(A,B,C) = meet_commut(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(f3_nnf,plain,
! [A,B,C] :
( meet_commut(A,B,C) = meet_commut(A,C,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( meet_commut(A,B,C) = meet_commut(A,C,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(meet_commutative(X0),true,ifeq(meet_semilatt_str(X0),true,ifeq(element(X1,the_carrier(X0)),true,ifeq(element(X2,the_carrier(X0)),true,or(empty_carrier(X0),eq(meet_commut(X0,X1,X2),meet_commut(X0,X2,X1))),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t154,plain,
or(empty_carrier(sk11),eq(meet_commut(sk11,sk13,sk12),meet_commut(sk11,sk12,sk13))) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi47,h15,hi51,hi50]) ).
cnf(t317,plain,
or(empty_carrier(sk11),eq(meet_commut(sk11,sk13,sk12),meet_commut(sk11,sk12,sk13))) = true,
inference(orient,[status(thm)],[t154]) ).
cnf(t1665,plain,
or(false,eq(meet_commut(sk11,sk13,sk12),meet_commut(sk11,sk12,sk13))) = true,
inference(step,[status(thm)],[t317,t977]) ).
cnf(t1666,plain,
eq(meet_commut(sk11,sk13,sk12),meet_commut(sk11,sk12,sk13)) = true,
inference(step,[status(thm)],[t1665,t257]) ).
cnf(t994,plain,
eq(meet_commut(sk11,sk13,sk12),meet_commut(sk11,sk12,sk13)) = true,
inference(rw,[status(thm)],[t1666]) ).
cnf(t1595,plain,
eq(meet_commut(sk11,sk13,sk12),meet_commut(sk11,sk12,sk13)) = true,
inference(orient,[status(thm)],[t994]) ).
cnf(t1596,plain,
meet_commut(sk11,sk12,sk13) = ifeq(true,true,meet_commut(sk11,sk13,sk12),meet_commut(sk11,sk12,sk13)),
inference(cp,[status(thm)],[t261,t1595]) ).
cnf(t1855,plain,
meet_commut(sk11,sk12,sk13) = meet_commut(sk11,sk13,sk12),
inference(step,[status(thm)],[t1596,t258]) ).
cnf(t1597,plain,
meet_commut(sk11,sk12,sk13) = meet_commut(sk11,sk13,sk12),
inference(orient,[status(thm)],[t1855]) ).
cnf(t1856,plain,
below(sk11,meet_commut(sk11,sk13,sk12),sk12) = false,
inference(step,[status(thm)],[t1100,t1597]) ).
cnf(t1599,plain,
below(sk11,meet_commut(sk11,sk13,sk12),sk12) = false,
inference(rw,[status(thm)],[t1856]) ).
cnf(t1600,plain,
below(sk11,meet_commut(sk11,sk13,sk12),sk12) = false,
inference(orient,[status(thm)],[t1599]) ).
cnf(t1883,plain,
true = false,
inference(step,[status(thm)],[t1882,t1600]) ).
cnf(t1631,plain,
false = true,
inference(orient,[status(thm)],[t1883]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/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(f33,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(f33_nnf,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c43,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f35,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f35_nnf,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
( ~ empty_carrier(sk9)
& one_sorted_str(sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f35_nnf]) ).
cnf(c49,plain,
~ empty_carrier(sk9),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f46,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f46_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c69,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
fof(f48,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f48_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c71,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c43,c49,c58,c64,c69,c71]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1631]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU304+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 13:39:34 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 34.95/4.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.95/4.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------