TSTP Solution File: HEN004-6 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : HEN004-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 : Tue May 7 10:34:37 EDT 2024
% Result : Unsatisfiable 100.48s 14.90s
% Output : Refutation 100.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 33 unt; 4 typ; 0 def)
% Number of atoms : 113 ( 50 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 436 ( 56 ~; 38 |; 0 &; 342 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 0 ^ 95 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(divide_type,type,
divide: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(zero_type,type,
zero: $i ).
thf(less_equal_type,type,
less_equal: $i > $i > $o ).
thf(6,axiom,
! [A: $i] : ( less_equal @ zero @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(22,plain,
! [A: $i] : ( less_equal @ zero @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,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(23,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( less_equal @ C @ B )
| ( ( less_equal @ zero @ A )
!= ( less_equal @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,25]) ).
thf(51,plain,
! [A: $i] :
( ( zero = A )
| ~ ( less_equal @ A @ zero ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( less_equal @ A @ B ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(1,negated_conjecture,
( ( divide @ a @ zero )
!= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
thf(11,plain,
( ( divide @ a @ zero )
!= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( divide @ a @ zero )
!= a ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( divide @ a @ zero )
!= a ),
inference(lifteq,[status(thm)],[12]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ~ ( less_equal @ B @ A )
| ( B != a )
| ( A
!= ( divide @ a @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(35,plain,
! [A: $i] :
( ~ ( less_equal @ ( divide @ a @ zero ) @ A )
| ~ ( less_equal @ A @ ( divide @ a @ zero ) )
| ( A != a ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( divide @ a @ zero )),bind(B,$thf( B ))]]) ).
thf(81,plain,
( ~ ( less_equal @ ( divide @ a @ zero ) @ a )
| ~ ( less_equal @ a @ ( divide @ a @ zero ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(20,plain,
! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2659,plain,
( ~ $true
| ~ ( less_equal @ a @ ( divide @ a @ zero ) ) ),
inference(rewrite,[status(thm)],[81,20]) ).
thf(2660,plain,
~ ( less_equal @ a @ ( divide @ a @ zero ) ),
inference(simp,[status(thm)],[2659]) ).
thf(2707,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( ( less_equal @ A @ B )
!= ( less_equal @ a @ ( divide @ a @ zero ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,2660]) ).
thf(2708,plain,
( ( divide @ a @ ( divide @ a @ zero ) )
!= zero ),
inference(pattern_uni,[status(thm)],[2707:[bind(A,$thf( a )),bind(B,$thf( divide @ a @ zero ))]]) ).
thf(2908,plain,
! [A: $i] :
( ~ ( less_equal @ A @ zero )
| ( A
!= ( divide @ a @ ( divide @ a @ zero ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,2708]) ).
thf(2909,plain,
~ ( less_equal @ ( divide @ a @ ( divide @ a @ zero ) ) @ zero ),
inference(pattern_uni,[status(thm)],[2908:[bind(A,$thf( divide @ a @ ( divide @ a @ zero ) ))]]) ).
thf(3617,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
!= zero )
| ( ( less_equal @ A @ B )
!= ( less_equal @ ( divide @ a @ ( divide @ a @ zero ) ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[19,2909]) ).
thf(3618,plain,
( ( divide @ ( divide @ a @ ( divide @ a @ zero ) ) @ zero )
!= zero ),
inference(pattern_uni,[status(thm)],[3617:[bind(A,$thf( divide @ a @ ( divide @ a @ zero ) )),bind(B,$thf( zero ))]]) ).
thf(3887,plain,
! [A: $i] :
( ~ ( less_equal @ A @ zero )
| ( A
!= ( divide @ ( divide @ a @ ( divide @ a @ zero ) ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[51,3618]) ).
thf(3888,plain,
~ ( less_equal @ ( divide @ ( divide @ a @ ( divide @ a @ zero ) ) @ zero ) @ zero ),
inference(pattern_uni,[status(thm)],[3887:[bind(A,$thf( divide @ ( divide @ a @ ( divide @ a @ zero ) ) @ zero ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(29,plain,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,plain,
! [A: $i] :
( ( divide @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[29]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( ( divide @ A @ B )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( ( divide @ A @ B )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( less_equal @ A @ B )
| ( ( divide @ A @ B )
= zero ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( divide @ A @ B )
= zero )
| ~ ( less_equal @ A @ B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( divide @ C @ D )
= zero )
| ( ( less_equal @ ( divide @ A @ B ) @ A )
!= ( less_equal @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,16]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( divide @ ( divide @ A @ B ) @ A )
= zero ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( divide @ E @ F )),bind(D,$thf( E ))]]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( divide @ ( divide @ A @ B ) @ A )
= zero ),
inference(simp,[status(thm)],[176]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( less_equal @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) @ ( divide @ ( divide @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] : ( less_equal @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) @ ( divide @ ( divide @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(374,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( less_equal @ ( divide @ ( divide @ C @ D ) @ ( divide @ E @ D ) ) @ zero )
| ( ( divide @ ( divide @ A @ B ) @ A )
!= ( divide @ ( divide @ C @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[184,21]) ).
thf(375,plain,
! [B: $i,A: $i] : ( less_equal @ ( divide @ ( divide @ A @ A ) @ ( divide @ B @ A ) ) @ zero ),
inference(pattern_uni,[status(thm)],[374:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] :
( ( less_equal @ ( divide @ ( divide @ B @ B ) @ zero ) @ zero )
| ( ( divide @ zero @ A )
!= ( divide @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,375]) ).
thf(641,plain,
! [A: $i] : ( less_equal @ ( divide @ ( divide @ A @ A ) @ zero ) @ zero ),
inference(pattern_uni,[status(thm)],[640:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(1031,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( less_equal @ ( divide @ ( divide @ A @ A ) @ zero ) @ zero )
!= ( less_equal @ B @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[641,51]) ).
thf(1032,plain,
! [A: $i] :
( ( divide @ ( divide @ A @ A ) @ zero )
= zero ),
inference(pattern_uni,[status(thm)],[1031:[bind(A,$thf( F )),bind(B,$thf( divide @ ( divide @ F @ F ) @ zero ))]]) ).
thf(1086,plain,
! [A: $i] :
( ( divide @ ( divide @ A @ A ) @ zero )
= zero ),
inference(simp,[status(thm)],[1032]) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ( less_equal @ B @ C )
| ( ( divide @ ( divide @ A @ A ) @ zero )
!= ( divide @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1086,19]) ).
thf(1391,plain,
! [A: $i] : ( less_equal @ ( divide @ A @ A ) @ zero ),
inference(pattern_uni,[status(thm)],[1390:[bind(A,$thf( E )),bind(B,$thf( divide @ E @ E )),bind(C,$thf( zero ))]]) ).
thf(1422,plain,
! [A: $i] : ( less_equal @ ( divide @ A @ A ) @ zero ),
inference(simp,[status(thm)],[1391]) ).
thf(2123,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( less_equal @ ( divide @ A @ A ) @ zero )
!= ( less_equal @ B @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[1422,51]) ).
thf(2124,plain,
! [A: $i] :
( ( divide @ A @ A )
= zero ),
inference(pattern_uni,[status(thm)],[2123:[bind(A,$thf( D )),bind(B,$thf( divide @ D @ D ))]]) ).
thf(2145,plain,
! [A: $i] :
( ( divide @ A @ A )
= zero ),
inference(simp,[status(thm)],[2124]) ).
thf(401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( less_equal @ ( divide @ ( divide @ B @ C ) @ zero ) @ ( divide @ ( divide @ B @ D ) @ C ) )
| ( ( divide @ zero @ A )
!= ( divide @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[30,21]) ).
thf(402,plain,
! [B: $i,A: $i] : ( less_equal @ ( divide @ ( divide @ B @ A ) @ zero ) @ ( divide @ ( divide @ B @ zero ) @ A ) ),
inference(pattern_uni,[status(thm)],[401:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( zero ))]]) ).
thf(26412,plain,
! [C: $i,B: $i,A: $i] :
( ( less_equal @ ( divide @ ( divide @ C @ B ) @ zero ) @ zero )
| ( ( divide @ A @ A )
!= ( divide @ ( divide @ C @ zero ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2145,402]) ).
thf(26413,plain,
! [A: $i] : ( less_equal @ ( divide @ ( divide @ A @ ( divide @ A @ zero ) ) @ zero ) @ zero ),
inference(pattern_uni,[status(thm)],[26412:[bind(A,$thf( divide @ F @ zero )),bind(B,$thf( divide @ F @ zero )),bind(C,$thf( F ))]]) ).
thf(26568,plain,
! [A: $i] : ( less_equal @ ( divide @ ( divide @ A @ ( divide @ A @ zero ) ) @ zero ) @ zero ),
inference(simp,[status(thm)],[26413]) ).
thf(32464,plain,
~ $true,
inference(rewrite,[status(thm)],[3888,26568]) ).
thf(32465,plain,
$false,
inference(simp,[status(thm)],[32464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN004-6 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n020.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 18:37:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.88/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.92 % [INFO] Parsing done (109ms).
% 1.23/0.93 % [INFO] Running in sequential loop mode.
% 1.49/1.14 % [INFO] nitpick registered as external prover.
% 1.49/1.14 % [INFO] Scanning for conjecture ...
% 1.73/1.19 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.80/1.21 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.80/1.22 % [INFO] Problem is propositional (TPTP CNF).
% 1.80/1.22 % [INFO] Type checking passed.
% 1.80/1.22 % [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 ...
% 100.48/14.89 % [INFO] Killing All external provers ...
% 100.48/14.89 % Time passed: 14358ms (effective reasoning time: 13954ms)
% 100.48/14.89 % 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)>
% 100.48/14.89 % Axioms used in derivation (7): zero_divide_anything_is_zero, quotient_less_equal2, less_equal_and_equal, zero_is_smallest, quotient_less_equal1, quotient_smaller_than_numerator, quotient_property
% 100.48/14.89 % No. of inferences in proof: 63
% 100.48/14.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14358 ms resp. 13954 ms w/o parsing
% 100.48/14.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 100.48/14.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------