TSTP Solution File: SEU221+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU221+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:57:39 EDT 2023
% Result : Theorem 27.70s 5.08s
% Output : Refutation 27.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 56
% Syntax : Number of formulae : 142 ( 47 unt; 22 typ; 0 def)
% Number of atoms : 331 ( 57 equ; 0 cnn)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 723 ( 70 ~; 20 |; 110 &; 458 @)
% ( 2 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 10 con; 0-2 aty)
% Number of variables : 119 ( 0 ^; 97 !; 22 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(function_inverse_type,type,
function_inverse: $i > $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(relation_rng_type,type,
relation_rng: $i > $i ).
thf(relation_composition_type,type,
relation_composition: $i > $i > $i ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(28,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(109,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(110,plain,
relation_empty_yielding @ empty_set,
inference(cnf,[status(esa)],[109]) ).
thf(13,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(65,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(51,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
~ ( empty @ sk4 ),
inference(cnf,[status(esa)],[52]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,plain,
one_to_one @ sk1,
inference(cnf,[status(esa)],[36]) ).
thf(37,plain,
~ ( one_to_one @ ( function_inverse @ sk1 ) ),
inference(cnf,[status(esa)],[36]) ).
thf(175,plain,
( ( one_to_one @ ( function_inverse @ sk1 ) )
!= ( one_to_one @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[38,37]) ).
thf(176,plain,
( ( function_inverse @ sk1 )
!= sk1 ),
inference(simp,[status(thm)],[175]) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(100,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(103,plain,
relation @ sk7,
inference(cnf,[status(esa)],[100]) ).
thf(32,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(123,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( ( one_to_one @ A )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) )
=> ( one_to_one @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ),
inference(cnf,[status(esa)],[49]) ).
thf(26,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(104,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(69,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(35,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( function_inverse @ A ) )
<=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(138,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( B
= ( function_inverse @ A ) )
=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) )
& ( ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) )
=> ( B
= ( function_inverse @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(101,plain,
function @ sk7,
inference(cnf,[status(esa)],[100]) ).
thf(20,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(88,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(47,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,plain,
empty @ sk3,
inference(cnf,[status(esa)],[47]) ).
thf(106,plain,
~ ( empty @ sk8 ),
inference(cnf,[status(esa)],[104]) ).
thf(169,plain,
( ( empty @ sk8 )
!= ( empty @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[48,106]) ).
thf(170,plain,
sk8 != sk3,
inference(simp,[status(thm)],[169]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(43,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(44,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( B != sk1 )
| ( A
!= ( function_inverse @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46,176]) ).
thf(197,plain,
! [A: $i] :
( ~ ( empty @ ( function_inverse @ sk1 ) )
| ~ ( empty @ A )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( function_inverse @ sk1 )),bind(B,$thf( B ))]]) ).
thf(276,plain,
( ~ ( empty @ ( function_inverse @ sk1 ) )
| ~ ( empty @ sk1 ) ),
inference(simp,[status(thm)],[197]) ).
thf(31,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(120,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(8,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(54,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(172,plain,
( ( empty @ sk4 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[54,53]) ).
thf(174,plain,
sk4 != empty_set,
inference(simp,[status(thm)],[172]) ).
thf(3,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(41,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,plain,
! [A: $i] : ( element @ ( sk2 @ A ) @ A ),
inference(cnf,[status(esa)],[41]) ).
thf(22,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(93,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(55,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(56,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ( empty @ B ) ),
inference(miniscope,[status(thm)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[56]) ).
thf(17,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(78,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(79,plain,
one_to_one @ sk6,
inference(cnf,[status(esa)],[78]) ).
thf(178,plain,
( ( one_to_one @ ( function_inverse @ sk1 ) )
!= ( one_to_one @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[79,37]) ).
thf(179,plain,
( ( function_inverse @ sk1 )
!= sk6 ),
inference(simp,[status(thm)],[178]) ).
thf(102,plain,
empty @ sk7,
inference(cnf,[status(esa)],[100]) ).
thf(320,plain,
( ( empty @ sk8 )
!= ( empty @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[102,106]) ).
thf(321,plain,
sk8 != sk7,
inference(simp,[status(thm)],[320]) ).
thf(121,plain,
function @ sk9,
inference(cnf,[status(esa)],[120]) ).
thf(33,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(132,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(72,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(74,plain,
relation @ sk5,
inference(cnf,[status(esa)],[72]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(70,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[69]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( A != sk6 )
| ( B
!= ( function_inverse @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46,179]) ).
thf(257,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( function_inverse @ sk1 ) )
| ( A != sk6 ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( A )),bind(B,$thf( function_inverse @ sk1 ))]]) ).
thf(275,plain,
( ~ ( empty @ sk6 )
| ~ ( empty @ ( function_inverse @ sk1 ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(171,plain,
( ( empty @ sk8 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[54,106]) ).
thf(173,plain,
sk8 != empty_set,
inference(simp,[status(thm)],[171]) ).
thf(73,plain,
relation_empty_yielding @ sk5,
inference(cnf,[status(esa)],[72]) ).
thf(105,plain,
relation @ sk8,
inference(cnf,[status(esa)],[104]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(81,plain,
relation @ sk6,
inference(cnf,[status(esa)],[78]) ).
thf(39,plain,
function @ sk1,
inference(cnf,[status(esa)],[36]) ).
thf(24,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(98,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(34,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(135,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(80,plain,
function @ sk6,
inference(cnf,[status(esa)],[78]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(40,plain,
relation @ sk1,
inference(cnf,[status(esa)],[36]) ).
thf(16,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(75,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(167,plain,
( ( empty @ sk4 )
!= ( empty @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[48,53]) ).
thf(168,plain,
sk4 != sk3,
inference(simp,[status(thm)],[167]) ).
thf(27,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(107,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(62,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(90,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(319,plain,
( ( empty @ sk7 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[102,53]) ).
thf(322,plain,
sk7 != sk4,
inference(simp,[status(thm)],[319]) ).
thf(122,plain,
relation @ sk9,
inference(cnf,[status(esa)],[120]) ).
thf(7966,plain,
$false,
inference(e,[status(thm)],[110,65,53,109,176,103,123,50,104,69,138,101,88,170,115,276,120,174,42,37,46,93,57,78,179,321,106,121,132,74,60,85,102,38,70,275,173,41,73,105,54,49,113,81,39,98,135,80,48,95,72,43,40,55,75,58,82,36,168,51,107,79,47,62,90,322,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU221+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 13:12:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.92/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (132ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.70/1.18 % [INFO] eprover registered as external prover.
% 1.70/1.18 % [INFO] cvc4 registered as external prover.
% 1.70/1.18 % [INFO] Scanning for conjecture ...
% 1.88/1.24 % [INFO] Found a conjecture and 38 axioms. Running axiom selection ...
% 1.98/1.29 % [INFO] Axiom selection finished. Selected 33 axioms (removed 5 axioms).
% 1.98/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.26/1.34 % [INFO] Type checking passed.
% 2.26/1.34 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 27.70/5.08 % External prover 'e' found a proof!
% 27.70/5.08 % [INFO] Killing All external provers ...
% 27.70/5.08 % Time passed: 4567ms (effective reasoning time: 4102ms)
% 27.70/5.08 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 27.70/5.08 % Axioms used in derivation (33): d8_funct_1, fc9_relat_1, cc1_relat_1, rc1_funct_1, dt_k2_funct_1, fc5_relat_1, rc2_relat_1, fc6_relat_1, t57_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_funct_1, fc1_funct_1, rc3_relat_1, t6_boole, t7_boole, cc1_funct_1, rc2_funct_1, fc10_relat_1, cc2_funct_1, existence_m1_subset_1, rc1_relat_1, t54_funct_1, dt_k5_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, fc8_relat_1
% 27.70/5.08 % No. of inferences in proof: 120
% 27.70/5.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4567 ms resp. 4102 ms w/o parsing
% 27.70/5.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.70/5.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------