TSTP Solution File: GRP766-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP766-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 6.07s 2.23s
% Output : Refutation 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 53 ( 41 unt; 12 typ; 0 def)
% Number of atoms : 41 ( 40 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 292 ( 2 ~; 0 |; 0 &; 290 @)
% ( 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 : 14 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i ).
thf(eta_type,type,
eta: $i > $i ).
thf(x0_type,type,
x0: $i ).
thf(x1_type,type,
x1: $i ).
thf(x2_type,type,
x2: $i ).
thf(j_type,type,
j: $i > $i ).
thf(quotient_type,type,
quotient: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(i_type,type,
i: $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(l_type,type,
l: $i > $i > $i > $i ).
thf(t_type,type,
t: $i > $i > $i ).
thf(18,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(56,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)],[18]) ).
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',sos19) ).
thf(52,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(13,axiom,
! [B: $i,A: $i] :
( ( t @ A @ B )
= ( quotient @ ( product @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( t @ A @ B )
= ( quotient @ ( product @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: $i] :
( ( eta @ A )
= ( product @ ( i @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
thf(60,plain,
! [A: $i] :
( ( eta @ A )
= ( product @ ( i @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i] :
( ( product @ ( i @ A ) @ A )
= ( product @ A @ ( j @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
thf(54,plain,
! [A: $i] :
( ( product @ ( i @ A ) @ A )
= ( product @ A @ ( j @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,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',sos13) ).
thf(48,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)],[14]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
= ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
thf(50,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)],[15]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: $i] :
( ( product @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
thf(42,plain,
! [A: $i] :
( ( product @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] :
( ( j @ A )
= ( quotient @ one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
thf(24,plain,
! [A: $i] :
( ( j @ A )
= ( quotient @ one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( product @ ( eta @ x0 ) @ ( product @ x1 @ x2 ) )
!= ( product @ ( product @ ( eta @ x0 ) @ x1 ) @ x2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(21,plain,
( ( product @ ( eta @ x0 ) @ ( product @ x1 @ x2 ) )
!= ( product @ ( product @ ( eta @ x0 ) @ x1 ) @ x2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [A: $i] :
( ( product @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
thf(28,plain,
! [A: $i] :
( ( product @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,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(32,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)],[6]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( product @ ( i @ ( i @ A ) ) @ B )
= ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( product @ ( i @ ( i @ A ) ) @ B )
= ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i] :
( ( i @ A )
= ( difference @ A @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
thf(26,plain,
! [A: $i] :
( ( i @ A )
= ( difference @ A @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
= ( product @ ( j @ ( j @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
= ( product @ ( j @ ( j @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,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',sos14) ).
thf(30,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)],[5]) ).
thf(376,plain,
$false,
inference(e,[status(thm)],[56,52,46,60,44,54,48,50,58,42,24,21,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP766-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 01:49:00 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (118ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.52/1.16 % [INFO] eprover registered as external prover.
% 1.52/1.17 % [INFO] cvc4 registered as external prover.
% 1.52/1.17 % [INFO] Scanning for conjecture ...
% 1.81/1.22 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 1.83/1.26 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 1.83/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.83/1.29 % [INFO] Type checking passed.
% 1.83/1.29 % [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 ...
% 6.07/2.22 % External prover 'e' found a proof!
% 6.07/2.22 % [INFO] Killing All external provers ...
% 6.07/2.22 % Time passed: 1704ms (effective reasoning time: 1256ms)
% 6.07/2.23 % 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)>
% 6.07/2.23 % Axioms used in derivation (19): sos14, sos06, sos13, sos10, sos09, sos02, sos11, sos19, sos08, sos12, sos04, sos15, sos17, sos03, sos16, sos05, sos07, sos01, sos18
% 6.07/2.23 % No. of inferences in proof: 41
% 6.07/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1704 ms resp. 1256 ms w/o parsing
% 6.07/2.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.07/2.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------