TSTP Solution File: GRP002-10 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:12:58 EDT 2023
% Result : Unsatisfiable 4.99s 2.14s
% Output : Refutation 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 51 ( 37 unt; 14 typ; 0 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 264 ( 2 ~; 0 |; 0 &; 262 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 64 ( 0 ^; 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(true_type,type,
true: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(d_type,type,
d: $i ).
thf(h_type,type,
h: $i ).
thf(j_type,type,
j: $i ).
thf(k_type,type,
k: $i ).
thf(identity_type,type,
identity: $i ).
thf(ifeq2_type,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( product @ A @ A @ B ) @ true @ ( product @ A @ B @ identity ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity_1) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( product @ A @ A @ B ) @ true @ ( product @ A @ B @ identity ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( product @ A @ A @ B ) @ true @ ( product @ B @ A @ identity ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity_2) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( product @ A @ A @ B ) @ true @ ( product @ B @ A @ identity ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ D @ B @ E ) @ true @ ( ifeq @ ( product @ F @ D @ A ) @ true @ ( product @ F @ E @ C ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
thf(48,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ D @ B @ E ) @ true @ ( ifeq @ ( product @ F @ D @ A ) @ true @ ( product @ F @ E @ C ) @ true ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ D @ C @ E ) @ true @ ( ifeq @ ( product @ D @ A @ F ) @ true @ ( product @ F @ B @ E ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
thf(50,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( product @ A @ B @ C ) @ true @ ( ifeq @ ( product @ D @ C @ E ) @ true @ ( ifeq @ ( product @ D @ A @ F ) @ true @ ( product @ F @ B @ E ) @ true ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i] :
( ( product @ A @ ( inverse @ A ) @ identity )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(42,plain,
! [A: $i] :
( ( product @ A @ ( inverse @ A ) @ identity )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,negated_conjecture,
( ( product @ h @ b @ j )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
thf(24,plain,
( ( product @ h @ b @ j )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
( ( product @ a @ b @ c )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(20,plain,
( ( product @ a @ b @ c )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq2 @ ( product @ A @ B @ C ) @ true @ ( ifeq2 @ ( product @ A @ B @ D ) @ true @ D @ C ) @ C )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ifeq2 @ ( product @ A @ B @ C ) @ true @ ( ifeq2 @ ( product @ A @ B @ D ) @ true @ D @ C ) @ C )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i] :
( ( product @ A @ identity @ A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(38,plain,
! [A: $i] :
( ( product @ A @ identity @ A )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
( ( product @ k @ ( inverse @ b ) @ identity )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
thf(21,plain,
( ( product @ k @ ( inverse @ b ) @ identity )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,negated_conjecture,
( ( product @ c @ ( inverse @ a ) @ d )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
thf(22,plain,
( ( product @ c @ ( inverse @ a ) @ d )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( product @ A @ B @ ( multiply @ A @ B ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( product @ A @ B @ ( multiply @ A @ B ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( product @ ( inverse @ A ) @ A @ identity )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(40,plain,
! [A: $i] :
( ( product @ ( inverse @ A ) @ A @ identity )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
( ( product @ d @ ( inverse @ b ) @ h )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
thf(23,plain,
( ( product @ d @ ( inverse @ b ) @ h )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i] :
( ( product @ identity @ A @ A )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(36,plain,
! [A: $i] :
( ( product @ identity @ A @ A )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
( ( product @ j @ ( inverse @ h ) @ k )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
thf(19,plain,
( ( product @ j @ ( inverse @ h ) @ k )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(175,plain,
$false,
inference(e,[status(thm)],[52,54,48,50,42,24,20,46,38,21,32,34,22,44,40,23,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n017.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 01:15:47 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.06 % [INFO] Parsing done (136ms).
% 1.30/1.07 % [INFO] Running in sequential loop mode.
% 1.69/1.26 % [INFO] eprover registered as external prover.
% 1.69/1.27 % [INFO] cvc4 registered as external prover.
% 1.69/1.27 % [INFO] Scanning for conjecture ...
% 1.91/1.33 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.91/1.35 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.91/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 2.10/1.37 % [INFO] Type checking passed.
% 2.10/1.38 % [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 ...
% 4.99/2.14 % External prover 'e' found a proof!
% 4.99/2.14 % [INFO] Killing All external provers ...
% 4.99/2.14 % Time passed: 1607ms (effective reasoning time: 1068ms)
% 4.99/2.14 % 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)>
% 4.99/2.14 % Axioms used in derivation (12): ifeq_axiom_001, ifeq_axiom, left_identity, x_cubed_is_identity_1, left_inverse, right_identity, right_inverse, associativity1, total_function2, associativity2, x_cubed_is_identity_2, total_function1
% 4.99/2.14 % No. of inferences in proof: 37
% 4.99/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1607 ms resp. 1068 ms w/o parsing
% 4.99/2.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.99/2.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------