TSTP Solution File: GRP729-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP729-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:15:16 EDT 2023
% Result : Unsatisfiable 4.12s 2.01s
% Output : Refutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 36
% Syntax : Number of formulae : 60 ( 47 unt; 13 typ; 0 def)
% Number of atoms : 47 ( 46 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 350 ( 2 ~; 0 |; 0 &; 348 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 128 ( 0 ^; 128 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(asoc_type,type,
asoc: $i > $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(op_k_type,type,
op_k: $i > $i > $i ).
thf(c_type,type,
c: $i ).
thf(d_type,type,
d: $i ).
thf(unit_type,type,
unit: $i ).
thf(op_t_type,type,
op_t: $i > $i > $i ).
thf(op_r_type,type,
op_r: $i > $i > $i > $i ).
thf(op_l_type,type,
op_l: $i > $i > $i > $i ).
thf(mult_type,type,
mult: $i > $i > $i ).
thf(i_type,type,
i: $i > $i ).
thf(rd_type,type,
rd: $i > $i > $i ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( asoc @ A @ B @ ( asoc @ C @ D @ E ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c22) ).
thf(69,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( asoc @ A @ B @ ( asoc @ C @ D @ E ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ B )
= ( mult @ ( mult @ B @ A ) @ ( op_k @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( mult @ A @ B )
= ( mult @ ( mult @ B @ A ) @ ( op_k @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( op_r @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_r @ A @ D @ E ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c15) ).
thf(33,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( op_r @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_r @ A @ D @ E ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
thf(65,plain,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C )
= ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C )
= ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( i @ ( mult @ A @ B ) )
= ( mult @ ( i @ A ) @ ( i @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( i @ ( mult @ A @ B ) )
= ( mult @ ( i @ A ) @ ( i @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( op_l @ A @ B @ C )
= ( mult @ ( i @ ( mult @ C @ B ) ) @ ( mult @ C @ ( mult @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c12) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( op_l @ A @ B @ C )
= ( mult @ ( i @ ( mult @ C @ B ) ) @ ( mult @ C @ ( mult @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( op_t @ ( op_t @ A @ B ) @ C )
= ( op_t @ ( op_t @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c20) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( op_t @ ( op_t @ A @ B ) @ C )
= ( op_t @ ( op_t @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
thf(63,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( op_r @ A @ B @ C )
= ( rd @ ( mult @ ( mult @ A @ B ) @ C ) @ ( mult @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c13) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( op_r @ A @ B @ C )
= ( rd @ ( mult @ ( mult @ A @ B ) @ C ) @ ( mult @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
thf(55,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( op_t @ A @ B )
= ( mult @ ( i @ B ) @ ( mult @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c14) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( op_t @ A @ B )
= ( mult @ ( i @ B ) @ ( mult @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
( ( asoc @ a @ b @ ( op_k @ c @ d ) )
!= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(24,plain,
( ( asoc @ a @ b @ ( op_k @ c @ d ) )
!= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( op_l @ ( op_l @ A @ B @ C ) @ D @ E )
= ( op_l @ ( op_l @ A @ D @ E ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c17) ).
thf(37,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( op_l @ ( op_l @ A @ B @ C ) @ D @ E )
= ( op_l @ ( op_l @ A @ D @ E ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ ( asoc @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ ( asoc @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( op_t @ ( op_l @ A @ B @ C ) @ D )
= ( op_l @ ( op_t @ A @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c19) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( op_t @ ( op_l @ A @ B @ C ) @ D )
= ( op_l @ ( op_t @ A @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( asoc @ ( asoc @ A @ B @ C ) @ D @ E )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c21) ).
thf(59,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( asoc @ ( asoc @ A @ B @ C ) @ D @ E )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( op_t @ ( op_r @ A @ B @ C ) @ D )
= ( op_r @ ( op_t @ A @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c18) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( op_t @ ( op_r @ A @ B @ C ) @ D )
= ( op_r @ ( op_t @ A @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
thf(67,plain,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( op_l @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_l @ A @ D @ E ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c16) ).
thf(31,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( op_l @ ( op_r @ A @ B @ C ) @ D @ E )
= ( op_r @ ( op_l @ A @ D @ E ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(125,plain,
$false,
inference(e,[status(thm)],[69,61,33,65,53,41,45,49,39,35,63,43,55,51,47,24,37,57,29,59,27,67,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP729-1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n013.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 01:34:21 EDT 2023
% 0.16/0.36 % CPUTime :
% 1.01/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/1.01 % [INFO] Parsing done (136ms).
% 1.38/1.02 % [INFO] Running in sequential loop mode.
% 1.69/1.22 % [INFO] eprover registered as external prover.
% 1.69/1.22 % [INFO] cvc4 registered as external prover.
% 1.78/1.23 % [INFO] Scanning for conjecture ...
% 1.80/1.28 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 2.01/1.32 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.01/1.34 % [INFO] Problem is propositional (TPTP CNF).
% 2.01/1.34 % [INFO] Type checking passed.
% 2.01/1.35 % [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 ...
% 4.12/2.01 % External prover 'e' found a proof!
% 4.12/2.01 % [INFO] Killing All external provers ...
% 4.12/2.01 % Time passed: 1490ms (effective reasoning time: 983ms)
% 4.12/2.01 % 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)>
% 4.12/2.01 % Axioms used in derivation (22): c05, c11, c22, c01, c12, c16, c21, c03, c18, c06, c13, c20, c02, c14, c10, c08, c15, c09, c19, c04, c07, c17
% 4.12/2.01 % No. of inferences in proof: 47
% 4.12/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1490 ms resp. 983 ms w/o parsing
% 4.12/2.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.12/2.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------