TSTP Solution File: GRP767-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP767-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:15:21 EDT 2023
% Result : Unsatisfiable 4.39s 2.04s
% Output : Refutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 54 ( 43 unt; 11 typ; 0 def)
% Number of atoms : 43 ( 42 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 308 ( 2 ~; 0 |; 0 &; 306 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 80 ( 0 ^; 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i ).
thf(j_type,type,
j: $i > $i ).
thf(x0_type,type,
x0: $i ).
thf(x1_type,type,
x1: $i ).
thf(i_type,type,
i: $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(l_type,type,
l: $i > $i > $i > $i ).
thf(eta_type,type,
eta: $i > $i ).
thf(t_type,type,
t: $i > $i > $i ).
thf(quotient_type,type,
quotient: $i > $i > $i ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( product @ ( i @ ( i @ A ) ) @ B )
= ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( product @ ( i @ ( i @ A ) ) @ B )
= ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( t @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( t @ ( eta @ A ) @ B ) @ ( t @ ( eta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos20) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( t @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( t @ ( eta @ A ) @ B ) @ ( t @ ( eta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
= ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
= ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( product @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
thf(49,plain,
! [A: $i] :
( ( product @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( t @ A @ B )
= ( quotient @ ( product @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( t @ A @ B )
= ( quotient @ ( product @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [A: $i] :
( ( eta @ A )
= ( product @ ( i @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
thf(63,plain,
! [A: $i] :
( ( eta @ A )
= ( product @ ( i @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( product @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( product @ ( eta @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( product @ ( eta @ A ) @ ( product @ B @ C ) )
= ( product @ ( product @ ( eta @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( l @ A @ A @ ( product @ B @ C ) )
= ( product @ ( l @ A @ A @ B ) @ ( l @ A @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( l @ A @ A @ ( product @ B @ C ) )
= ( product @ ( l @ A @ A @ B ) @ ( l @ A @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
= ( product @ ( j @ ( j @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
= ( product @ ( j @ ( j @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [A: $i] :
( ( j @ A )
= ( quotient @ one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
thf(51,plain,
! [A: $i] :
( ( j @ A )
= ( quotient @ one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) )
= ( quotient @ ( quotient @ ( product @ C @ ( product @ A @ B ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) )
= ( quotient @ ( quotient @ ( product @ C @ ( product @ A @ B ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [A: $i] :
( ( i @ A )
= ( difference @ A @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
thf(25,plain,
! [A: $i] :
( ( i @ A )
= ( difference @ A @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i] :
( ( product @ ( i @ A ) @ A )
= ( product @ A @ ( j @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
thf(57,plain,
! [A: $i] :
( ( product @ ( i @ A ) @ A )
= ( product @ A @ ( j @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [A: $i] :
( ( product @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
thf(29,plain,
! [A: $i] :
( ( product @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
!= ( j @ x1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(22,plain,
( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
!= ( j @ x1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ ( product @ ( product @ A @ B ) @ C ) )
= ( quotient @ ( product @ B @ ( product @ C @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ ( product @ ( product @ A @ B ) @ C ) )
= ( quotient @ ( product @ B @ ( product @ C @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( l @ A @ B @ C )
= ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( l @ A @ B @ C )
= ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(220,plain,
$false,
inference(e,[status(thm)],[61,33,53,41,45,49,39,35,63,31,43,55,51,47,37,25,57,29,22,59,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP767-1 : TPTP v8.1.2. Released v4.1.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 19 02:20:15 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/0.97 % [INFO] Parsing done (113ms).
% 1.29/0.98 % [INFO] Running in sequential loop mode.
% 1.61/1.17 % [INFO] eprover registered as external prover.
% 1.61/1.17 % [INFO] cvc4 registered as external prover.
% 1.61/1.17 % [INFO] Scanning for conjecture ...
% 1.71/1.22 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 1.91/1.26 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 1.91/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.28 % [INFO] Type checking passed.
% 1.91/1.29 % [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 ...
% 4.39/2.04 % External prover 'e' found a proof!
% 4.39/2.04 % [INFO] Killing All external provers ...
% 4.39/2.04 % Time passed: 1502ms (effective reasoning time: 1056ms)
% 4.39/2.04 % 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)>
% 4.39/2.04 % Axioms used in derivation (20): sos14, sos20, sos06, sos13, sos10, sos09, sos02, sos11, sos19, sos08, sos12, sos04, sos15, sos17, sos03, sos16, sos05, sos07, sos01, sos18
% 4.39/2.04 % No. of inferences in proof: 43
% 4.39/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1502 ms resp. 1056 ms w/o parsing
% 4.73/2.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.73/2.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------