TSTP Solution File: GRP037-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 Sep 16 22:25:36 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 82 ( 27 unt; 7 typ; 0 def)
% Number of atoms : 276 ( 57 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 364 ( 169 ~; 164 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 162 ( 150 !; 0 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(another_identity_type,type,
another_identity: $i ).
tff(a_type,type,
a: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(identity_type,type,
identity: $i ).
tff(subgroup_member_type,type,
subgroup_member: $i > $o ).
tff(another_inverse_type,type,
another_inverse: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
tff(5,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
product(identity,a,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( subgroup_member(a)
<=> subgroup_member(a) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).
tff(12,plain,
subgroup_member(a),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [A: $i] :
refl(
( ( ~ subgroup_member(A)
| product(another_identity,A,A) )
<=> ( ~ subgroup_member(A)
| product(another_identity,A,A) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) )
<=> ! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) )
<=> ! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_left_identity) ).
tff(17,plain,
! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) )
| ~ subgroup_member(a)
| product(another_identity,a,a) )
<=> ( ~ ! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) )
| ~ subgroup_member(a)
| product(another_identity,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) )
| ~ subgroup_member(a)
| product(another_identity,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [A: $i] :
( ~ subgroup_member(A)
| product(another_identity,A,A) )
| ~ subgroup_member(a)
| product(another_identity,a,a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
product(another_identity,a,a),
inference(unit_resolution,[status(thm)],[22,19,12]) ).
tff(24,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
<=> ( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
rewrite(
( ( ~ product(A,B,C)
| ~ product(D,B,C)
| ( D = A ) )
<=> ( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ~ product(D,B,C)
| ( D = A ) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ~ product(D,B,C)
| ( D = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
tff(30,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( identity = another_identity )
| ~ product(another_identity,a,a)
| ~ product(identity,a,a) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( identity = another_identity )
| ~ product(another_identity,a,a)
| ~ product(identity,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ product(another_identity,a,a)
| ( identity = another_identity )
| ~ product(identity,a,a) )
<=> ( ( identity = another_identity )
| ~ product(another_identity,a,a)
| ~ product(identity,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ~ product(another_identity,a,a)
| ( identity = another_identity )
| ~ product(identity,a,a) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( identity = another_identity )
| ~ product(another_identity,a,a)
| ~ product(identity,a,a) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ~ product(another_identity,a,a)
| ( identity = another_identity )
| ~ product(identity,a,a) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( identity = another_identity )
| ~ product(another_identity,a,a)
| ~ product(identity,a,a) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ~ product(another_identity,a,a)
| ( identity = another_identity )
| ~ product(identity,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( identity = another_identity )
| ~ product(another_identity,a,a)
| ~ product(identity,a,a) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
identity = another_identity,
inference(unit_resolution,[status(thm)],[39,33,23,9]) ).
tff(41,plain,
another_identity = identity,
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( product(inverse(a),a,another_identity)
<=> product(inverse(a),a,identity) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( product(inverse(a),a,identity)
<=> product(inverse(a),a,another_identity) ),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
^ [X: $i] :
refl(
( product(inverse(X),X,identity)
<=> product(inverse(X),X,identity) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X: $i] : product(inverse(X),X,identity)
<=> ! [X: $i] : product(inverse(X),X,identity) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
! [X: $i] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
tff(48,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $i] : product(inverse(X),X,identity),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [X: $i] : product(inverse(X),X,identity)
| product(inverse(a),a,identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
product(inverse(a),a,identity),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
product(inverse(a),a,another_identity),
inference(modus_ponens,[status(thm)],[52,43]) ).
tff(54,plain,
^ [A: $i] :
refl(
( ( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) )
<=> ( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) )
<=> ! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) )
<=> ! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_left_inverse) ).
tff(58,plain,
! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ( ~ ! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) )
| ~ subgroup_member(a)
| product(another_inverse(a),a,another_identity) )
<=> ( ~ ! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) )
| ~ subgroup_member(a)
| product(another_inverse(a),a,another_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) )
| ~ subgroup_member(a)
| product(another_inverse(a),a,another_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [A: $i] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) )
| ~ subgroup_member(a)
| product(another_inverse(a),a,another_identity) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
product(another_inverse(a),a,another_identity),
inference(unit_resolution,[status(thm)],[63,60,12]) ).
tff(65,plain,
( ( inverse(a) != another_inverse(a) )
<=> ( inverse(a) != another_inverse(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
inverse(a) != another_inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).
tff(67,plain,
inverse(a) != another_inverse(a),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( inverse(a) = another_inverse(a) )
| ~ product(another_inverse(a),a,another_identity)
| ~ product(inverse(a),a,another_identity) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( inverse(a) = another_inverse(a) )
| ~ product(another_inverse(a),a,another_identity)
| ~ product(inverse(a),a,another_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ product(another_inverse(a),a,another_identity)
| ( inverse(a) = another_inverse(a) )
| ~ product(inverse(a),a,another_identity) )
<=> ( ( inverse(a) = another_inverse(a) )
| ~ product(another_inverse(a),a,another_identity)
| ~ product(inverse(a),a,another_identity) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ~ product(another_inverse(a),a,another_identity)
| ( inverse(a) = another_inverse(a) )
| ~ product(inverse(a),a,another_identity) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( inverse(a) = another_inverse(a) )
| ~ product(another_inverse(a),a,another_identity)
| ~ product(inverse(a),a,another_identity) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ~ product(another_inverse(a),a,another_identity)
| ( inverse(a) = another_inverse(a) )
| ~ product(inverse(a),a,another_identity) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( inverse(a) = another_inverse(a) )
| ~ product(another_inverse(a),a,another_identity)
| ~ product(inverse(a),a,another_identity) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ~ product(another_inverse(a),a,another_identity)
| ( inverse(a) = another_inverse(a) )
| ~ product(inverse(a),a,another_identity) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ product(A,B,C)
| ( D = A )
| ~ product(D,B,C) )
| ( inverse(a) = another_inverse(a) )
| ~ product(another_inverse(a),a,another_identity)
| ~ product(inverse(a),a,another_identity) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
~ product(inverse(a),a,another_identity),
inference(unit_resolution,[status(thm)],[73,33,67,64]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 14:37:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------