TSTP Solution File: ALG203+1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ALG203+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 18:14:15 EDT 2024
% Result : Theorem 4.26s 2.66s
% Output : Refutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 18 ( 1 unt; 6 typ; 0 def)
% Number of atoms : 71 ( 20 equ; 0 cnn)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 204 ( 11 ~; 0 |; 24 &; 134 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 0 ^ 32 !; 8 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(sorti1_type,type,
sorti1: $i > $o ).
thf(sorti2_type,type,
sorti2: $i > $o ).
thf(h_type,type,
h: $i > $i ).
thf(j_type,type,
j: $i > $i ).
thf(op1_type,type,
op1: $i > $i > $i ).
thf(op2_type,type,
op2: $i > $i > $i ).
thf(4,axiom,
! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( sorti2 @ ( op2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(25,plain,
! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( sorti2 @ ( op2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
~ ( ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(34,plain,
~ ( ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
( ? [A: $i] :
( ( sorti1 @ A )
& ( ( op1 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti1 @ A )
& ( ( op1 @ A @ A )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(27,plain,
( ? [A: $i] :
( ( sorti1 @ A )
& ( ( op1 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti1 @ A )
& ( ( op1 @ A @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( sorti1 @ ( op1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(23,plain,
! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( sorti1 @ ( op1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[25,34,27,7,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG203+1 : TPTP v8.2.0. Released v2.7.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 23:38:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.18/1.12 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.31 % [INFO] Parsing done (182ms).
% 1.49/1.32 % [INFO] Running in sequential loop mode.
% 2.13/1.75 % [INFO] eprover registered as external prover.
% 2.27/1.76 % [INFO] cvc4 registered as external prover.
% 2.27/1.77 % [INFO] Scanning for conjecture ...
% 2.42/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.59/1.95 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.59/1.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.59/1.98 % [INFO] Type checking passed.
% 2.59/1.98 % [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 ...
% 4.09/2.66 % External prover 'e' found a proof!
% 4.26/2.66 % [INFO] Killing All external provers ...
% 4.26/2.66 % Time passed: 2123ms (effective reasoning time: 1330ms)
% 4.26/2.66 % 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)>
% 4.26/2.66 % Axioms used in derivation (4): ax2, ax4, ax3, ax1
% 4.26/2.66 % No. of inferences in proof: 12
% 4.26/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2123 ms resp. 1330 ms w/o parsing
% 4.26/2.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.26/2.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------