TSTP Solution File: SYN166-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN166-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Thu Sep 29 23:54:01 EDT 2022
% Result : Unsatisfiable 0.83s 0.81s
% Output : Proof 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 82 ( 19 unt; 6 typ; 0 def)
% Number of atoms : 308 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 408 ( 185 ~; 176 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 126 ( 117 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( m0(a,X,a)
<=> m0(a,X,a) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : m0(a,X,a)
<=> ! [X: $i] : m0(a,X,a) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : m0(a,X,a)
<=> ! [X: $i] : m0(a,X,a) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : m0(a,X,a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_12) ).
tff(5,plain,
! [X: $i] : m0(a,X,a),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : m0(a,X,a),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : m0(a,X,a),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : m0(a,X,a)
| m0(a,b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
m0(a,b,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ p1(a,b,b)
<=> ~ p1(a,b,b) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
~ p1(a,b,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(12,plain,
~ p1(a,b,b),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
refl(
( ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(
monotonicity(
rewrite(
( ( p1(H,I,J)
| ~ m0(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J) ) )),
( ( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
rewrite(
( ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
( ( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [I: $i,A: $i,J: $i,H: $i] :
( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_082) ).
tff(19,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( m0(b,a,a)
<=> m0(b,a,a) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
m0(b,a,a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_38) ).
tff(25,plain,
m0(b,a,a),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ~ m0(b,a,a)
| p1(a,b,b)
| ~ p1(b,a,a) )
<=> ( p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,a,a)
| p1(a,b,b)
| ~ p1(b,a,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,a,a)
| p1(a,b,b)
| ~ p1(b,a,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,a,a)
| p1(a,b,b)
| ~ p1(b,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(a,b,b)
| ~ m0(b,a,a)
| ~ p1(b,a,a) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ p1(b,a,a),
inference(unit_resolution,[status(thm)],[31,25,22,12]) ).
tff(33,plain,
( p1(a,b,a)
<=> p1(a,b,a) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( p1(a,b,a)
| $false )
<=> p1(a,b,a) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( $false
| p1(a,a,a) )
<=> p1(a,a,a) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
l0(a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(38,plain,
( l0(a)
<=> $true ),
inference(iff_true,[status(thm)],[37]) ).
tff(39,plain,
( ~ l0(a)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ~ l0(a)
<=> $false ),
inference(transitivity,[status(thm)],[39,35]) ).
tff(41,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> ( $false
| p1(a,a,a) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> p1(a,a,a) ),
inference(transitivity,[status(thm)],[41,36]) ).
tff(43,plain,
( ( p1(a,a,a)
| ~ l0(a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_088) ).
tff(45,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
p1(a,a,a),
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
( p1(a,a,a)
<=> $true ),
inference(iff_true,[status(thm)],[46]) ).
tff(48,plain,
( ~ p1(a,a,a)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ~ p1(a,a,a)
<=> $false ),
inference(transitivity,[status(thm)],[48,35]) ).
tff(50,plain,
( ( p1(a,b,a)
| ~ p1(a,a,a) )
<=> ( p1(a,b,a)
| $false ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( p1(a,b,a)
| ~ p1(a,a,a) )
<=> p1(a,b,a) ),
inference(transitivity,[status(thm)],[50,34]) ).
tff(52,plain,
( ( $false
| p1(a,b,a)
| ~ p1(a,a,a) )
<=> ( p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
r0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(54,plain,
( r0(b)
<=> $true ),
inference(iff_true,[status(thm)],[53]) ).
tff(55,plain,
( ~ r0(b)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ r0(b)
<=> $false ),
inference(transitivity,[status(thm)],[55,35]) ).
tff(57,plain,
( ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) )
<=> ( $false
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) )
<=> ( p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(transitivity,[status(thm)],[57,52]) ).
tff(59,plain,
( ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) )
<=> ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) )
<=> ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( p1(a,b,a)
| ~ r0(b) )
<=> ( ~ r0(b)
| p1(a,b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( p1(a,b,a)
| ~ r0(b)
| ~ p1(a,a,a) )
<=> ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( p1(a,b,a)
| ~ r0(b)
| ~ p1(a,a,a) )
<=> ( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,axiom,
( p1(a,b,a)
| ~ r0(b)
| ~ p1(a,a,a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_087) ).
tff(65,plain,
( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ r0(b)
| p1(a,b,a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[65,59]) ).
tff(67,plain,
( p1(a,b,a)
| ~ p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[66,58]) ).
tff(68,plain,
p1(a,b,a),
inference(modus_ponens,[status(thm)],[67,51]) ).
tff(69,plain,
p1(a,b,a),
inference(modus_ponens,[status(thm)],[68,33]) ).
tff(70,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ m0(a,b,a)
| p1(b,a,a)
| ~ p1(a,b,a) )
<=> ( p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(a,b,a)
| p1(b,a,a)
| ~ p1(a,b,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(a,b,a)
| p1(b,a,a)
| ~ p1(a,b,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(a,b,a)
| p1(b,a,a)
| ~ p1(a,b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,a,a)
| ~ p1(a,b,a)
| ~ m0(a,b,a) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,22,69,32,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN166-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 02:09:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.83/0.81 % SZS status Unsatisfiable
% 0.83/0.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------