TSTP Solution File: GRP205-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP205-1 : TPTP v8.1.2. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 11:13:29 EDT 2023
% Result : Unsatisfiable 4.32s 1.93s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 30 ( 21 unt; 9 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 102 ( 2 ~; 0 |; 0 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(z_type,type,
z: $i ).
thf(identity_type,type,
identity: $i ).
thf(left_division_type,type,
left_division: $i > $i > $i ).
thf(right_division_type,type,
right_division: $i > $i > $i ).
thf(right_inverse_type,type,
right_inverse: $i > $i ).
thf(left_inverse_type,type,
left_inverse: $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( right_division @ ( multiply @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_division_multiply) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( right_division @ ( multiply @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(14,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( left_division @ A @ ( multiply @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_division_multiply) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( left_division @ A @ ( multiply @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( multiply @ ( left_inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(28,plain,
! [A: $i] :
( ( multiply @ ( left_inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( right_division @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_right_division) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( multiply @ ( right_division @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ ( left_division @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_left_division) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( left_division @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(16,plain,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( multiply @ x @ ( multiply @ ( multiply @ y @ z ) @ x ) )
!= ( multiply @ ( multiply @ x @ y ) @ ( multiply @ z @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_moufang4) ).
thf(11,plain,
( ( multiply @ x @ ( multiply @ ( multiply @ y @ z ) @ x ) )
!= ( multiply @ ( multiply @ x @ y ) @ ( multiply @ z @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( multiply @ A @ ( right_inverse @ A ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(26,plain,
! [A: $i] :
( ( multiply @ A @ ( right_inverse @ A ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ ( multiply @ A @ B ) @ A ) @ C )
= ( multiply @ A @ ( multiply @ B @ ( multiply @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',moufang3) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ ( multiply @ A @ B ) @ A ) @ C )
= ( multiply @ A @ ( multiply @ B @ ( multiply @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(179,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,22,18,16,11,26,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP205-1 : TPTP v8.1.2. Released v2.3.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n026.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 : Fri May 19 02:15:06 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (107ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.65/1.18 % [INFO] eprover registered as external prover.
% 1.65/1.18 % [INFO] cvc4 registered as external prover.
% 1.65/1.18 % [INFO] Scanning for conjecture ...
% 1.81/1.23 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.81/1.25 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.81/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.81/1.27 % [INFO] Type checking passed.
% 1.81/1.27 % [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 ...
% 4.32/1.93 % External prover 'e' found a proof!
% 4.32/1.93 % [INFO] Killing All external provers ...
% 4.32/1.93 % Time passed: 1402ms (effective reasoning time: 949ms)
% 4.32/1.93 % 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)>
% 4.32/1.93 % Axioms used in derivation (9): left_division_multiply, left_identity, right_division_multiply, multiply_left_division, left_inverse, right_identity, right_inverse, multiply_right_division, moufang3
% 4.32/1.93 % No. of inferences in proof: 21
% 4.32/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1402 ms resp. 949 ms w/o parsing
% 4.32/1.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.32/1.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------