TSTP Solution File: ALG227+1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ALG227+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 : Mon May 20 18:14:29 EDT 2024
% Result : Theorem 3.44s 1.89s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 38
% Syntax : Number of formulae : 65 ( 11 unt; 13 typ; 0 def)
% Number of atoms : 150 ( 21 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 334 ( 27 ~; 2 |; 49 &; 209 @)
% ( 3 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 86 ( 0 ^ 65 !; 21 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(m1_pboole_type,type,
m1_pboole: $i > $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k1_closure3_type,type,
k1_closure3: $i > $i > $i ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(v1_fraenkel_type,type,
v1_fraenkel: $i > $o ).
thf(a_2_0_closure3_type,type,
a_2_0_closure3: $i > $i > $i ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(9,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(52,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( C
= ( k1_closure3 @ A @ B ) )
<=> ( C
= ( a_2_0_closure3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).
thf(106,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( ( C
= ( k1_closure3 @ A @ B ) )
=> ( C
= ( a_2_0_closure3 @ A @ B ) ) )
& ( ( C
= ( a_2_0_closure3 @ A @ B ) )
=> ( C
= ( k1_closure3 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(38,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_fraenkel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_closure2) ).
thf(41,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_fraenkel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(34,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
=> ( ( k1_funct_1 @ B @ C )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_closure3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
=> ( ( k1_funct_1 @ B @ C )
= k1_xboole_0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
=> ( ( k1_funct_1 @ B @ C )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(66,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(48,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(67,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(43,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(114,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_fraenkel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_closure2) ).
thf(69,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A )
& ( v1_fraenkel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(88,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_pboole @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( ( k1_funct_1 @ C @ D )
!= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
thf(57,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_pboole @ C @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( ( k1_funct_1 @ C @ D )
!= k1_xboole_0 ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( ( k1_funct_1 @ C @ D )
!= k1_xboole_0 ) )
=> ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(117,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(23,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(102,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(54,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(86,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(76,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(98,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(83,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(100,plain,
! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(121,plain,
$false,
inference(e,[status(thm)],[52,106,38,41,34,27,66,80,48,67,43,114,69,88,46,57,78,117,102,54,86,76,98,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ALG227+1 : TPTP v8.2.0. Released v3.4.0.
% 0.05/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat May 18 23:01:24 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.86/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.04/0.92 % [INFO] Parsing done (117ms).
% 1.29/0.93 % [INFO] Running in sequential loop mode.
% 1.64/1.17 % [INFO] eprover registered as external prover.
% 1.64/1.17 % [INFO] cvc4 registered as external prover.
% 1.73/1.18 % [INFO] Scanning for conjecture ...
% 1.84/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 1.89/1.30 % [INFO] Axiom selection finished. Selected 24 axioms (removed 4 axioms).
% 2.13/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.13/1.33 % [INFO] Type checking passed.
% 2.13/1.34 % [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 ...
% 3.44/1.89 % External prover 'e' found a proof!
% 3.44/1.89 % [INFO] Killing All external provers ...
% 3.44/1.89 % Time passed: 1415ms (effective reasoning time: 955ms)
% 3.44/1.89 % 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)>
% 3.44/1.89 % Axioms used in derivation (24): d3_closure3, rc3_funct_1, t6_boole, t2_tarski, cc1_closure2, rc2_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, fraenkel_a_2_0_closure3, rc1_funct_1, t7_boole, cc1_funct_1, dt_m1_pboole, existence_m1_pboole, cc2_funct_1, existence_m1_subset_1, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, t2_subset, rc1_closure2
% 3.44/1.89 % No. of inferences in proof: 52
% 3.44/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1415 ms resp. 955 ms w/o parsing
% 3.70/1.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.70/1.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------