TSTP Solution File: HEN007-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : HEN007-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:16:51 EDT 2023
% Result : Unsatisfiable 2.92s 1.65s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 49 ( 23 unt; 10 typ; 0 def)
% Number of atoms : 73 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 248 ( 36 ~; 34 |; 0 &; 178 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_equal_type,type,
less_equal: $i > $i > $o ).
thf(zQy_type,type,
zQy: $i ).
thf(zQx_type,type,
zQx: $i ).
thf(quotient_type,type,
quotient: $i > $i > $i > $o ).
thf(zero_type,type,
zero: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(z_type,type,
z: $i ).
thf(y_type,type,
y: $i ).
thf(x_type,type,
x: $i ).
thf(14,axiom,
less_equal @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
thf(39,plain,
less_equal @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ C )
| ( less_equal @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ C )
| ( less_equal @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( quotient @ A @ B @ zero )
| ( less_equal @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( quotient @ A @ B @ zero )
| ( less_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ( less_equal @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ( less_equal @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [A: $i] : ( quotient @ A @ identity @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
thf(24,plain,
! [A: $i] : ( quotient @ A @ identity @ zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( quotient @ A @ B @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( quotient @ A @ B @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( quotient @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( quotient @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
~ ( less_equal @ zQy @ zQx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
thf(20,plain,
~ ( less_equal @ zQy @ zQx ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] : ( quotient @ A @ A @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(29,plain,
! [A: $i] : ( quotient @ A @ A @ zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i] : ( quotient @ zero @ A @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(28,plain,
! [A: $i] : ( quotient @ zero @ A @ zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
quotient @ z @ y @ zQy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQy) ).
thf(33,plain,
quotient @ z @ y @ zQy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( less_equal @ C @ D )
| ~ ( quotient @ A @ D @ E )
| ( less_equal @ E @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
thf(45,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( less_equal @ C @ D )
| ~ ( quotient @ A @ D @ E )
| ( less_equal @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(9,axiom,
! [A: $i] : ( less_equal @ zero @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(32,plain,
! [A: $i] : ( less_equal @ zero @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
quotient @ z @ x @ zQx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zQx) ).
thf(34,plain,
quotient @ z @ x @ zQx,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] : ( quotient @ A @ zero @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
thf(22,plain,
! [A: $i] : ( quotient @ A @ zero @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [A: $i] : ( less_equal @ A @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(44,plain,
! [A: $i] : ( less_equal @ A @ identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( quotient @ B @ D @ E )
| ~ ( quotient @ A @ D @ F )
| ~ ( quotient @ F @ E @ G )
| ~ ( quotient @ C @ D @ H )
| ( less_equal @ G @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(40,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( quotient @ A @ B @ C )
| ~ ( quotient @ B @ D @ E )
| ~ ( quotient @ A @ D @ F )
| ~ ( quotient @ F @ E @ G )
| ~ ( quotient @ C @ D @ H )
| ( less_equal @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( quotient @ A @ B @ ( divide @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
thf(23,plain,
! [B: $i,A: $i] : ( quotient @ A @ B @ ( divide @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(52,plain,
$false,
inference(e,[status(thm)],[39,35,30,47,42,24,37,25,20,29,28,33,45,32,34,22,44,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : HEN007-2 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 15:34:21 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.85/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/0.96 % [INFO] Parsing done (125ms).
% 1.15/0.97 % [INFO] Running in sequential loop mode.
% 1.53/1.16 % [INFO] eprover registered as external prover.
% 1.53/1.16 % [INFO] cvc4 registered as external prover.
% 1.53/1.17 % [INFO] Scanning for conjecture ...
% 1.79/1.22 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.85/1.26 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.85/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.85/1.29 % [INFO] Type checking passed.
% 1.85/1.29 % [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 ...
% 2.92/1.64 % External prover 'e' found a proof!
% 2.92/1.65 % [INFO] Killing All external provers ...
% 2.92/1.65 % Time passed: 1140ms (effective reasoning time: 674ms)
% 2.92/1.65 % 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)>
% 2.92/1.65 % Axioms used in derivation (18): zQx, quotient_property, zQy, closure, everything_divide_identity_is_zero, zero_divide_anything_is_zero, zero_is_smallest, xQyLEz_implies_xQzLEy, xLEy, transitivity_of_less_equal, less_equal_quotient, identity_is_largest, x_divide_x_is_zero, quotient_less_equal, divisor_existence, well_defined, x_divde_zero_is_x, less_equal_and_equal
% 2.92/1.65 % No. of inferences in proof: 39
% 2.92/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1140 ms resp. 674 ms w/o parsing
% 3.12/1.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.12/1.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------